mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -1665,7 +1665,7 @@ theorem nontrivial_iff_exists_ne_one (S : Submonoid M) : Nontrivial S ↔ ∃ x
 /-- A submonoid is either the trivial submonoid or nontrivial. -/
 @[to_additive "An additive submonoid is either the trivial additive submonoid or nontrivial."]
 theorem bot_or_nontrivial (S : Submonoid M) : S = ⊥ ∨ Nontrivial S := by
-  simp only [eq_bot_iff_forall, nontrivial_iff_exists_ne_one, ← not_forall, Classical.em]
+  simp only [eq_bot_iff_forall, nontrivial_iff_exists_ne_one, ← Classical.not_forall, Classical.em]
 #align submonoid.bot_or_nontrivial Submonoid.bot_or_nontrivial
 #align add_submonoid.bot_or_nontrivial AddSubmonoid.bot_or_nontrivial
 -/

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

@@ -4,10 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
 Amelia Livingston, Yury Kudryashov
 -/
-import Mathbin.Algebra.Order.Monoid.Cancel.Basic
-import Mathbin.GroupTheory.GroupAction.Defs
-import Mathbin.GroupTheory.Submonoid.Basic
-import Mathbin.GroupTheory.Subsemigroup.Operations
+import Algebra.Order.Monoid.Cancel.Basic
+import GroupTheory.GroupAction.Defs
+import GroupTheory.Submonoid.Basic
+import GroupTheory.Subsemigroup.Operations
 
 #align_import group_theory.submonoid.operations from "leanprover-community/mathlib"@"cf8e77c636317b059a8ce20807a29cf3772a0640"
 

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

@@ -85,11 +85,11 @@ def Submonoid.toAddSubmonoid : Submonoid M ≃o AddSubmonoid (Additive M)
   toFun S :=
     { carrier := Additive.toMul ⁻¹' S
       zero_mem' := S.one_mem'
-      add_mem' := fun _ _ => S.mul_mem' }
+      add_mem' := fun _ _ => S.hMul_mem' }
   invFun S :=
     { carrier := Additive.ofMul ⁻¹' S
       one_mem' := S.zero_mem'
-      mul_mem' := fun _ _ => S.add_mem' }
+      hMul_mem' := fun _ _ => S.add_mem' }
   left_inv x := by cases x <;> rfl
   right_inv x := by cases x <;> rfl
   map_rel_iff' a b := Iff.rfl
@@ -137,11 +137,11 @@ def AddSubmonoid.toSubmonoid : AddSubmonoid A ≃o Submonoid (Multiplicative A)
   toFun S :=
     { carrier := Multiplicative.toAdd ⁻¹' S
       one_mem' := S.zero_mem'
-      mul_mem' := fun _ _ => S.add_mem' }
+      hMul_mem' := fun _ _ => S.add_mem' }
   invFun S :=
     { carrier := Multiplicative.ofAdd ⁻¹' S
       zero_mem' := S.one_mem'
-      add_mem' := fun _ _ => S.mul_mem' }
+      add_mem' := fun _ _ => S.hMul_mem' }
   left_inv x := by cases x <;> rfl
   right_inv x := by cases x <;> rfl
   map_rel_iff' a b := Iff.rfl
@@ -196,7 +196,7 @@ def comap (f : F) (S : Submonoid N) : Submonoid M
     where
   carrier := f ⁻¹' S
   one_mem' := show f 1 ∈ S by rw [map_one] <;> exact S.one_mem
-  mul_mem' a b ha hb := show f (a * b) ∈ S by rw [map_mul] <;> exact S.mul_mem ha hb
+  hMul_mem' a b ha hb := show f (a * b) ∈ S by rw [map_mul] <;> exact S.mul_mem ha hb
 #align submonoid.comap Submonoid.comap
 #align add_submonoid.comap AddSubmonoid.comap
 -/
@@ -242,7 +242,7 @@ def map (f : F) (S : Submonoid M) : Submonoid N
     where
   carrier := f '' S
   one_mem' := ⟨1, S.one_mem, map_one f⟩
-  mul_mem' := by rintro _ _ ⟨x, hx, rfl⟩ ⟨y, hy, rfl⟩;
+  hMul_mem' := by rintro _ _ ⟨x, hx, rfl⟩ ⟨y, hy, rfl⟩;
     exact ⟨x * y, S.mul_mem hx hy, by rw [map_mul] <;> rfl⟩
 #align submonoid.map Submonoid.map
 #align add_submonoid.map AddSubmonoid.map
@@ -804,7 +804,7 @@ namespace Submonoid
 /-- A submonoid of a monoid inherits a multiplication. -/
 @[to_additive "An `add_submonoid` of an `add_monoid` inherits an addition."]
 instance mul : Mul S :=
-  ⟨fun a b => ⟨a.1 * b.1, S.mul_mem a.2 b.2⟩⟩
+  ⟨fun a b => ⟨a.1 * b.1, S.hMul_mem a.2 b.2⟩⟩
 #align submonoid.has_mul Submonoid.mul
 #align add_submonoid.has_add AddSubmonoid.add
 -/
@@ -837,7 +837,7 @@ theorem coe_one : ((1 : S) : M) = 1 :=
 #print Submonoid.mk_mul_mk /-
 @[simp, to_additive]
 theorem mk_mul_mk (x y : M) (hx : x ∈ S) (hy : y ∈ S) :
-    (⟨x, hx⟩ : S) * ⟨y, hy⟩ = ⟨x * y, S.mul_mem hx hy⟩ :=
+    (⟨x, hx⟩ : S) * ⟨y, hy⟩ = ⟨x * y, S.hMul_mem hx hy⟩ :=
   rfl
 #align submonoid.mk_mul_mk Submonoid.mk_mul_mk
 #align add_submonoid.mk_add_mk AddSubmonoid.mk_add_mk
@@ -845,7 +845,7 @@ theorem mk_mul_mk (x y : M) (hx : x ∈ S) (hy : y ∈ S) :
 
 #print Submonoid.mul_def /-
 @[to_additive]
-theorem mul_def (x y : S) : x * y = ⟨x * y, S.mul_mem x.2 y.2⟩ :=
+theorem mul_def (x y : S) : x * y = ⟨x * y, S.hMul_mem x.2 y.2⟩ :=
   rfl
 #align submonoid.mul_def Submonoid.mul_def
 #align add_submonoid.add_def AddSubmonoid.add_def
@@ -993,7 +993,7 @@ use `mul_equiv.submonoid_map` for better definitional equalities. -/
 @[to_additive
       "An additive subgroup is isomorphic to its image under an injective function. If you\nhave an isomorphism, use `add_equiv.add_submonoid_map` for better definitional equalities."]
 noncomputable def equivMapOfInjective (f : M →* N) (hf : Function.Injective f) : S ≃* S.map f :=
-  { Equiv.Set.image f S hf with map_mul' := fun _ _ => Subtype.ext (f.map_mul _ _) }
+  { Equiv.Set.image f S hf with map_mul' := fun _ _ => Subtype.ext (f.map_hMul _ _) }
 #align submonoid.equiv_map_of_injective Submonoid.equivMapOfInjective
 #align add_submonoid.equiv_map_of_injective AddSubmonoid.equivMapOfInjective
 -/
@@ -1031,7 +1031,7 @@ def prod (s : Submonoid M) (t : Submonoid N) : Submonoid (M × N)
     where
   carrier := s ×ˢ t
   one_mem' := ⟨s.one_mem, t.one_mem⟩
-  mul_mem' p q hp hq := ⟨s.mul_mem hp.1 hq.1, t.mul_mem hp.2 hq.2⟩
+  hMul_mem' p q hp hq := ⟨s.hMul_mem hp.1 hq.1, t.hMul_mem hp.2 hq.2⟩
 #align submonoid.prod Submonoid.prod
 #align add_submonoid.prod AddSubmonoid.prod
 -/
@@ -1133,7 +1133,7 @@ theorem prod_bot_sup_bot_prod (s : Submonoid M) (t : Submonoid N) :
     s.Prod ⊥ ⊔ prod ⊥ t = s.Prod t :=
   le_antisymm (sup_le (prod_mono (le_refl s) bot_le) (prod_mono bot_le (le_refl t))) fun p hp =>
     Prod.fst_mul_snd p ▸
-      mul_mem ((le_sup_left : s.Prod ⊥ ≤ s.Prod ⊥ ⊔ prod ⊥ t) ⟨hp.1, Set.mem_singleton 1⟩)
+      hMul_mem ((le_sup_left : s.Prod ⊥ ≤ s.Prod ⊥ ⊔ prod ⊥ t) ⟨hp.1, Set.mem_singleton 1⟩)
         ((le_sup_right : prod ⊥ t ≤ s.Prod ⊥ ⊔ prod ⊥ t) ⟨Set.mem_singleton 1, hp.2⟩)
 #align submonoid.prod_bot_sup_bot_prod Submonoid.prod_bot_sup_bot_prod
 #align add_submonoid.prod_bot_sup_bot_prod AddSubmonoid.prod_bot_sup_bot_prod
@@ -1364,7 +1364,7 @@ def codRestrict {S} [SetLike S N] [SubmonoidClass S N] (f : M →* N) (s : S) (h
     M →* s where
   toFun n := ⟨f n, h n⟩
   map_one' := Subtype.eq f.map_one
-  map_mul' x y := Subtype.eq (f.map_mul x y)
+  map_mul' x y := Subtype.eq (f.map_hMul x y)
 #align monoid_hom.cod_restrict MonoidHom.codRestrict
 #align add_monoid_hom.cod_restrict AddMonoidHom.codRestrict
 -/
@@ -1512,7 +1512,7 @@ def submonoidComap (f : M →* N) (N' : Submonoid N) : N'.comap f →* N'
     where
   toFun x := ⟨f x, x.Prop⟩
   map_one' := Subtype.eq f.map_one
-  map_mul' x y := Subtype.eq (f.map_mul x y)
+  map_mul' x y := Subtype.eq (f.map_hMul x y)
 #align monoid_hom.submonoid_comap MonoidHom.submonoidComap
 #align add_monoid_hom.add_submonoid_comap AddMonoidHom.addSubmonoidComap
 -/
@@ -1527,7 +1527,7 @@ def submonoidMap (f : M →* N) (M' : Submonoid M) : M' →* M'.map f
     where
   toFun x := ⟨f x, ⟨x, x.Prop, rfl⟩⟩
   map_one' := Subtype.eq <| f.map_one
-  map_mul' x y := Subtype.eq <| f.map_mul x y
+  map_mul' x y := Subtype.eq <| f.map_hMul x y
 #align monoid_hom.submonoid_map MonoidHom.submonoidMap
 #align add_monoid_hom.add_submonoid_map AddMonoidHom.addSubmonoidMap
 -/

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

@@ -779,18 +779,18 @@ instance (priority := 75) toLinearOrderedCancelCommMonoid {M} [LinearOrderedCanc
 #align add_submonoid_class.to_linear_ordered_cancel_add_comm_monoid AddSubmonoidClass.toLinearOrderedCancelAddCommMonoid
 -/
 
-#print SubmonoidClass.Subtype /-
+#print SubmonoidClass.subtype /-
 /-- The natural monoid hom from a submonoid of monoid `M` to `M`. -/
 @[to_additive "The natural monoid hom from an `add_submonoid` of `add_monoid` `M` to `M`."]
-def Subtype : S' →* M :=
+def subtype : S' →* M :=
   ⟨coe, rfl, fun _ _ => rfl⟩
-#align submonoid_class.subtype SubmonoidClass.Subtype
-#align add_submonoid_class.subtype AddSubmonoidClass.Subtype
+#align submonoid_class.subtype SubmonoidClass.subtype
+#align add_submonoid_class.subtype AddSubmonoidClass.subtype
 -/
 
 #print SubmonoidClass.coe_subtype /-
 @[simp, to_additive]
-theorem coe_subtype : (SubmonoidClass.Subtype S' : S' → M) = coe :=
+theorem coe_subtype : (SubmonoidClass.subtype S' : S' → M) = coe :=
   rfl
 #align submonoid_class.coe_subtype SubmonoidClass.coe_subtype
 #align add_submonoid_class.coe_subtype AddSubmonoidClass.coe_subtype
@@ -1333,7 +1333,7 @@ theorem map_mclosure (f : F) (s : Set M) : (closure s).map f = closure (f '' s)
 @[to_additive "Restriction of an add_monoid hom to an `add_submonoid` of the domain."]
 def restrict {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M] (f : M →* N)
     (s : S) : s →* N :=
-  f.comp (SubmonoidClass.Subtype _)
+  f.comp (SubmonoidClass.subtype _)
 #align monoid_hom.restrict MonoidHom.restrict
 #align add_monoid_hom.restrict AddMonoidHom.restrict
 -/

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

@@ -3,17 +3,14 @@ Copyright (c) 2018 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
 Amelia Livingston, Yury Kudryashov
-
-! This file was ported from Lean 3 source module group_theory.submonoid.operations
-! leanprover-community/mathlib commit cf8e77c636317b059a8ce20807a29cf3772a0640
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Order.Monoid.Cancel.Basic
 import Mathbin.GroupTheory.GroupAction.Defs
 import Mathbin.GroupTheory.Submonoid.Basic
 import Mathbin.GroupTheory.Subsemigroup.Operations
 
+#align_import group_theory.submonoid.operations from "leanprover-community/mathlib"@"cf8e77c636317b059a8ce20807a29cf3772a0640"
+
 /-!
 # Operations on `submonoid`s
 

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

@@ -80,6 +80,7 @@ variable {M N P : Type _} [MulOneClass M] [MulOneClass N] [MulOneClass P] (S : S
 
 section
 
+#print Submonoid.toAddSubmonoid /-
 /-- Submonoids of monoid `M` are isomorphic to additive submonoids of `additive M`. -/
 @[simps]
 def Submonoid.toAddSubmonoid : Submonoid M ≃o AddSubmonoid (Additive M)
@@ -96,19 +97,25 @@ def Submonoid.toAddSubmonoid : Submonoid M ≃o AddSubmonoid (Additive M)
   right_inv x := by cases x <;> rfl
   map_rel_iff' a b := Iff.rfl
 #align submonoid.to_add_submonoid Submonoid.toAddSubmonoid
+-/
 
+#print AddSubmonoid.toSubmonoid' /-
 /-- Additive submonoids of an additive monoid `additive M` are isomorphic to submonoids of `M`. -/
 abbrev AddSubmonoid.toSubmonoid' : AddSubmonoid (Additive M) ≃o Submonoid M :=
   Submonoid.toAddSubmonoid.symm
 #align add_submonoid.to_submonoid' AddSubmonoid.toSubmonoid'
+-/
 
+#print Submonoid.toAddSubmonoid_closure /-
 theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
     (Submonoid.closure S).toAddSubmonoid = AddSubmonoid.closure (Additive.toMul ⁻¹' S) :=
   le_antisymm
     (Submonoid.toAddSubmonoid.le_symm_apply.1 <| Submonoid.closure_le.2 AddSubmonoid.subset_closure)
     (AddSubmonoid.closure_le.2 Submonoid.subset_closure)
 #align submonoid.to_add_submonoid_closure Submonoid.toAddSubmonoid_closure
+-/
 
+#print AddSubmonoid.toSubmonoid'_closure /-
 theorem AddSubmonoid.toSubmonoid'_closure (S : Set (Additive M)) :
     (AddSubmonoid.closure S).toSubmonoid' = Submonoid.closure (Multiplicative.ofAdd ⁻¹' S) :=
   le_antisymm
@@ -116,6 +123,7 @@ theorem AddSubmonoid.toSubmonoid'_closure (S : Set (Additive M)) :
       AddSubmonoid.closure_le.2 Submonoid.subset_closure)
     (Submonoid.closure_le.2 AddSubmonoid.subset_closure)
 #align add_submonoid.to_submonoid'_closure AddSubmonoid.toSubmonoid'_closure
+-/
 
 end
 
@@ -123,6 +131,7 @@ section
 
 variable {A : Type _} [AddZeroClass A]
 
+#print AddSubmonoid.toSubmonoid /-
 /-- Additive submonoids of an additive monoid `A` are isomorphic to
 multiplicative submonoids of `multiplicative A`. -/
 @[simps]
@@ -140,12 +149,16 @@ def AddSubmonoid.toSubmonoid : AddSubmonoid A ≃o Submonoid (Multiplicative A)
   right_inv x := by cases x <;> rfl
   map_rel_iff' a b := Iff.rfl
 #align add_submonoid.to_submonoid AddSubmonoid.toSubmonoid
+-/
 
+#print Submonoid.toAddSubmonoid' /-
 /-- Submonoids of a monoid `multiplicative A` are isomorphic to additive submonoids of `A`. -/
 abbrev Submonoid.toAddSubmonoid' : Submonoid (Multiplicative A) ≃o AddSubmonoid A :=
   AddSubmonoid.toSubmonoid.symm
 #align submonoid.to_add_submonoid' Submonoid.toAddSubmonoid'
+-/
 
+#print AddSubmonoid.toSubmonoid_closure /-
 theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
     (AddSubmonoid.closure S).toSubmonoid = Submonoid.closure (Multiplicative.toAdd ⁻¹' S) :=
   le_antisymm
@@ -153,7 +166,9 @@ theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
       AddSubmonoid.closure_le.2 Submonoid.subset_closure)
     (Submonoid.closure_le.2 AddSubmonoid.subset_closure)
 #align add_submonoid.to_submonoid_closure AddSubmonoid.toSubmonoid_closure
+-/
 
+#print Submonoid.toAddSubmonoid'_closure /-
 theorem Submonoid.toAddSubmonoid'_closure (S : Set (Multiplicative A)) :
     (Submonoid.closure S).toAddSubmonoid' = AddSubmonoid.closure (Additive.ofMul ⁻¹' S) :=
   le_antisymm
@@ -161,6 +176,7 @@ theorem Submonoid.toAddSubmonoid'_closure (S : Set (Multiplicative A)) :
       Submonoid.closure_le.2 AddSubmonoid.subset_closure)
     (AddSubmonoid.closure_le.2 Submonoid.subset_closure)
 #align submonoid.to_add_submonoid'_closure Submonoid.toAddSubmonoid'_closure
+-/
 
 end
 
@@ -175,8 +191,6 @@ open Set
 -/
 
 
-include mc
-
 #print Submonoid.comap /-
 /-- The preimage of a submonoid along a monoid homomorphism is a submonoid. -/
 @[to_additive
@@ -190,19 +204,21 @@ def comap (f : F) (S : Submonoid N) : Submonoid M
 #align add_submonoid.comap AddSubmonoid.comap
 -/
 
+#print Submonoid.coe_comap /-
 @[simp, to_additive]
 theorem coe_comap (S : Submonoid N) (f : F) : (S.comap f : Set M) = f ⁻¹' S :=
   rfl
 #align submonoid.coe_comap Submonoid.coe_comap
 #align add_submonoid.coe_comap AddSubmonoid.coe_comap
+-/
 
+#print Submonoid.mem_comap /-
 @[simp, to_additive]
 theorem mem_comap {S : Submonoid N} {f : F} {x : M} : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
 #align submonoid.mem_comap Submonoid.mem_comap
 #align add_submonoid.mem_comap AddSubmonoid.mem_comap
-
-omit mc
+-/
 
 #print Submonoid.comap_comap /-
 @[to_additive]
@@ -221,8 +237,6 @@ theorem comap_id (S : Submonoid P) : S.comap (MonoidHom.id P) = S :=
 #align add_submonoid.comap_id AddSubmonoid.comap_id
 -/
 
-include mc
-
 #print Submonoid.map /-
 /-- The image of a submonoid along a monoid homomorphism is a submonoid. -/
 @[to_additive
@@ -237,145 +251,183 @@ def map (f : F) (S : Submonoid M) : Submonoid N
 #align add_submonoid.map AddSubmonoid.map
 -/
 
+#print Submonoid.coe_map /-
 @[simp, to_additive]
 theorem coe_map (f : F) (S : Submonoid M) : (S.map f : Set N) = f '' S :=
   rfl
 #align submonoid.coe_map Submonoid.coe_map
 #align add_submonoid.coe_map AddSubmonoid.coe_map
+-/
 
+#print Submonoid.mem_map /-
 @[simp, to_additive]
 theorem mem_map {f : F} {S : Submonoid M} {y : N} : y ∈ S.map f ↔ ∃ x ∈ S, f x = y :=
   mem_image_iff_bex
 #align submonoid.mem_map Submonoid.mem_map
 #align add_submonoid.mem_map AddSubmonoid.mem_map
+-/
 
+#print Submonoid.mem_map_of_mem /-
 @[to_additive]
 theorem mem_map_of_mem (f : F) {S : Submonoid M} {x : M} (hx : x ∈ S) : f x ∈ S.map f :=
   mem_image_of_mem f hx
 #align submonoid.mem_map_of_mem Submonoid.mem_map_of_mem
 #align add_submonoid.mem_map_of_mem AddSubmonoid.mem_map_of_mem
+-/
 
+#print Submonoid.apply_coe_mem_map /-
 @[to_additive]
 theorem apply_coe_mem_map (f : F) (S : Submonoid M) (x : S) : f x ∈ S.map f :=
   mem_map_of_mem f x.Prop
 #align submonoid.apply_coe_mem_map Submonoid.apply_coe_mem_map
 #align add_submonoid.apply_coe_mem_map AddSubmonoid.apply_coe_mem_map
+-/
 
-omit mc
-
+#print Submonoid.map_map /-
 @[to_additive]
 theorem map_map (g : N →* P) (f : M →* N) : (S.map f).map g = S.map (g.comp f) :=
   SetLike.coe_injective <| image_image _ _ _
 #align submonoid.map_map Submonoid.map_map
 #align add_submonoid.map_map AddSubmonoid.map_map
+-/
 
-include mc
-
+#print Submonoid.mem_map_iff_mem /-
 @[to_additive]
 theorem mem_map_iff_mem {f : F} (hf : Function.Injective f) {S : Submonoid M} {x : M} :
     f x ∈ S.map f ↔ x ∈ S :=
   hf.mem_set_image
 #align submonoid.mem_map_iff_mem Submonoid.mem_map_iff_mem
 #align add_submonoid.mem_map_iff_mem AddSubmonoid.mem_map_iff_mem
+-/
 
+#print Submonoid.map_le_iff_le_comap /-
 @[to_additive]
 theorem map_le_iff_le_comap {f : F} {S : Submonoid M} {T : Submonoid N} :
     S.map f ≤ T ↔ S ≤ T.comap f :=
   image_subset_iff
 #align submonoid.map_le_iff_le_comap Submonoid.map_le_iff_le_comap
 #align add_submonoid.map_le_iff_le_comap AddSubmonoid.map_le_iff_le_comap
+-/
 
+#print Submonoid.gc_map_comap /-
 @[to_additive]
 theorem gc_map_comap (f : F) : GaloisConnection (map f) (comap f) := fun S T => map_le_iff_le_comap
 #align submonoid.gc_map_comap Submonoid.gc_map_comap
 #align add_submonoid.gc_map_comap AddSubmonoid.gc_map_comap
+-/
 
+#print Submonoid.map_le_of_le_comap /-
 @[to_additive]
 theorem map_le_of_le_comap {T : Submonoid N} {f : F} : S ≤ T.comap f → S.map f ≤ T :=
   (gc_map_comap f).l_le
 #align submonoid.map_le_of_le_comap Submonoid.map_le_of_le_comap
 #align add_submonoid.map_le_of_le_comap AddSubmonoid.map_le_of_le_comap
+-/
 
+#print Submonoid.le_comap_of_map_le /-
 @[to_additive]
 theorem le_comap_of_map_le {T : Submonoid N} {f : F} : S.map f ≤ T → S ≤ T.comap f :=
   (gc_map_comap f).le_u
 #align submonoid.le_comap_of_map_le Submonoid.le_comap_of_map_le
 #align add_submonoid.le_comap_of_map_le AddSubmonoid.le_comap_of_map_le
+-/
 
+#print Submonoid.le_comap_map /-
 @[to_additive]
 theorem le_comap_map {f : F} : S ≤ (S.map f).comap f :=
   (gc_map_comap f).le_u_l _
 #align submonoid.le_comap_map Submonoid.le_comap_map
 #align add_submonoid.le_comap_map AddSubmonoid.le_comap_map
+-/
 
+#print Submonoid.map_comap_le /-
 @[to_additive]
 theorem map_comap_le {S : Submonoid N} {f : F} : (S.comap f).map f ≤ S :=
   (gc_map_comap f).l_u_le _
 #align submonoid.map_comap_le Submonoid.map_comap_le
 #align add_submonoid.map_comap_le AddSubmonoid.map_comap_le
+-/
 
+#print Submonoid.monotone_map /-
 @[to_additive]
 theorem monotone_map {f : F} : Monotone (map f) :=
   (gc_map_comap f).monotone_l
 #align submonoid.monotone_map Submonoid.monotone_map
 #align add_submonoid.monotone_map AddSubmonoid.monotone_map
+-/
 
+#print Submonoid.monotone_comap /-
 @[to_additive]
 theorem monotone_comap {f : F} : Monotone (comap f) :=
   (gc_map_comap f).monotone_u
 #align submonoid.monotone_comap Submonoid.monotone_comap
 #align add_submonoid.monotone_comap AddSubmonoid.monotone_comap
+-/
 
+#print Submonoid.map_comap_map /-
 @[simp, to_additive]
 theorem map_comap_map {f : F} : ((S.map f).comap f).map f = S.map f :=
   (gc_map_comap f).l_u_l_eq_l _
 #align submonoid.map_comap_map Submonoid.map_comap_map
 #align add_submonoid.map_comap_map AddSubmonoid.map_comap_map
+-/
 
+#print Submonoid.comap_map_comap /-
 @[simp, to_additive]
 theorem comap_map_comap {S : Submonoid N} {f : F} : ((S.comap f).map f).comap f = S.comap f :=
   (gc_map_comap f).u_l_u_eq_u _
 #align submonoid.comap_map_comap Submonoid.comap_map_comap
 #align add_submonoid.comap_map_comap AddSubmonoid.comap_map_comap
+-/
 
+#print Submonoid.map_sup /-
 @[to_additive]
 theorem map_sup (S T : Submonoid M) (f : F) : (S ⊔ T).map f = S.map f ⊔ T.map f :=
   (gc_map_comap f : GaloisConnection (map f) (comap f)).l_sup
 #align submonoid.map_sup Submonoid.map_sup
 #align add_submonoid.map_sup AddSubmonoid.map_sup
+-/
 
+#print Submonoid.map_iSup /-
 @[to_additive]
 theorem map_iSup {ι : Sort _} (f : F) (s : ι → Submonoid M) : (iSup s).map f = ⨆ i, (s i).map f :=
   (gc_map_comap f : GaloisConnection (map f) (comap f)).l_iSup
 #align submonoid.map_supr Submonoid.map_iSup
 #align add_submonoid.map_supr AddSubmonoid.map_iSup
+-/
 
+#print Submonoid.comap_inf /-
 @[to_additive]
 theorem comap_inf (S T : Submonoid N) (f : F) : (S ⊓ T).comap f = S.comap f ⊓ T.comap f :=
   (gc_map_comap f : GaloisConnection (map f) (comap f)).u_inf
 #align submonoid.comap_inf Submonoid.comap_inf
 #align add_submonoid.comap_inf AddSubmonoid.comap_inf
+-/
 
+#print Submonoid.comap_iInf /-
 @[to_additive]
 theorem comap_iInf {ι : Sort _} (f : F) (s : ι → Submonoid N) :
     (iInf s).comap f = ⨅ i, (s i).comap f :=
   (gc_map_comap f : GaloisConnection (map f) (comap f)).u_iInf
 #align submonoid.comap_infi Submonoid.comap_iInf
 #align add_submonoid.comap_infi AddSubmonoid.comap_iInf
+-/
 
+#print Submonoid.map_bot /-
 @[simp, to_additive]
 theorem map_bot (f : F) : (⊥ : Submonoid M).map f = ⊥ :=
   (gc_map_comap f).l_bot
 #align submonoid.map_bot Submonoid.map_bot
 #align add_submonoid.map_bot AddSubmonoid.map_bot
+-/
 
+#print Submonoid.comap_top /-
 @[simp, to_additive]
 theorem comap_top (f : F) : (⊤ : Submonoid N).comap f = ⊤ :=
   (gc_map_comap f).u_top
 #align submonoid.comap_top Submonoid.comap_top
 #align add_submonoid.comap_top AddSubmonoid.comap_top
-
-omit mc
+-/
 
 #print Submonoid.map_id /-
 @[simp, to_additive]
@@ -389,68 +441,86 @@ section GaloisCoinsertion
 
 variable {ι : Type _} {f : F} (hf : Function.Injective f)
 
-include hf
-
+#print Submonoid.gciMapComap /-
 /-- `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. -/
 @[to_additive " `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. "]
 def gciMapComap : GaloisCoinsertion (map f) (comap f) :=
   (gc_map_comap f).toGaloisCoinsertion fun S x => by simp [mem_comap, mem_map, hf.eq_iff]
 #align submonoid.gci_map_comap Submonoid.gciMapComap
 #align add_submonoid.gci_map_comap AddSubmonoid.gciMapComap
+-/
 
+#print Submonoid.comap_map_eq_of_injective /-
 @[to_additive]
 theorem comap_map_eq_of_injective (S : Submonoid M) : (S.map f).comap f = S :=
   (gciMapComap hf).u_l_eq _
 #align submonoid.comap_map_eq_of_injective Submonoid.comap_map_eq_of_injective
 #align add_submonoid.comap_map_eq_of_injective AddSubmonoid.comap_map_eq_of_injective
+-/
 
+#print Submonoid.comap_surjective_of_injective /-
 @[to_additive]
 theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
   (gciMapComap hf).u_surjective
 #align submonoid.comap_surjective_of_injective Submonoid.comap_surjective_of_injective
 #align add_submonoid.comap_surjective_of_injective AddSubmonoid.comap_surjective_of_injective
+-/
 
+#print Submonoid.map_injective_of_injective /-
 @[to_additive]
 theorem map_injective_of_injective : Function.Injective (map f) :=
   (gciMapComap hf).l_injective
 #align submonoid.map_injective_of_injective Submonoid.map_injective_of_injective
 #align add_submonoid.map_injective_of_injective AddSubmonoid.map_injective_of_injective
+-/
 
+#print Submonoid.comap_inf_map_of_injective /-
 @[to_additive]
 theorem comap_inf_map_of_injective (S T : Submonoid M) : (S.map f ⊓ T.map f).comap f = S ⊓ T :=
   (gciMapComap hf).u_inf_l _ _
 #align submonoid.comap_inf_map_of_injective Submonoid.comap_inf_map_of_injective
 #align add_submonoid.comap_inf_map_of_injective AddSubmonoid.comap_inf_map_of_injective
+-/
 
+#print Submonoid.comap_iInf_map_of_injective /-
 @[to_additive]
 theorem comap_iInf_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).map f).comap f = iInf S :=
   (gciMapComap hf).u_iInf_l _
 #align submonoid.comap_infi_map_of_injective Submonoid.comap_iInf_map_of_injective
 #align add_submonoid.comap_infi_map_of_injective AddSubmonoid.comap_iInf_map_of_injective
+-/
 
+#print Submonoid.comap_sup_map_of_injective /-
 @[to_additive]
 theorem comap_sup_map_of_injective (S T : Submonoid M) : (S.map f ⊔ T.map f).comap f = S ⊔ T :=
   (gciMapComap hf).u_sup_l _ _
 #align submonoid.comap_sup_map_of_injective Submonoid.comap_sup_map_of_injective
 #align add_submonoid.comap_sup_map_of_injective AddSubmonoid.comap_sup_map_of_injective
+-/
 
+#print Submonoid.comap_iSup_map_of_injective /-
 @[to_additive]
 theorem comap_iSup_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).map f).comap f = iSup S :=
   (gciMapComap hf).u_iSup_l _
 #align submonoid.comap_supr_map_of_injective Submonoid.comap_iSup_map_of_injective
 #align add_submonoid.comap_supr_map_of_injective AddSubmonoid.comap_iSup_map_of_injective
+-/
 
+#print Submonoid.map_le_map_iff_of_injective /-
 @[to_additive]
 theorem map_le_map_iff_of_injective {S T : Submonoid M} : S.map f ≤ T.map f ↔ S ≤ T :=
   (gciMapComap hf).l_le_l_iff
 #align submonoid.map_le_map_iff_of_injective Submonoid.map_le_map_iff_of_injective
 #align add_submonoid.map_le_map_iff_of_injective AddSubmonoid.map_le_map_iff_of_injective
+-/
 
+#print Submonoid.map_strictMono_of_injective /-
 @[to_additive]
 theorem map_strictMono_of_injective : StrictMono (map f) :=
   (gciMapComap hf).strictMono_l
 #align submonoid.map_strict_mono_of_injective Submonoid.map_strictMono_of_injective
 #align add_submonoid.map_strict_mono_of_injective AddSubmonoid.map_strictMono_of_injective
+-/
 
 end GaloisCoinsertion
 
@@ -458,8 +528,7 @@ section GaloisInsertion
 
 variable {ι : Type _} {f : F} (hf : Function.Surjective f)
 
-include hf
-
+#print Submonoid.giMapComap /-
 /-- `map f` and `comap f` form a `galois_insertion` when `f` is surjective. -/
 @[to_additive " `map f` and `comap f` form a `galois_insertion` when `f` is surjective. "]
 def giMapComap : GaloisInsertion (map f) (comap f) :=
@@ -468,60 +537,79 @@ def giMapComap : GaloisInsertion (map f) (comap f) :=
     mem_map.2 ⟨y, by simp [hy, h]⟩
 #align submonoid.gi_map_comap Submonoid.giMapComap
 #align add_submonoid.gi_map_comap AddSubmonoid.giMapComap
+-/
 
+#print Submonoid.map_comap_eq_of_surjective /-
 @[to_additive]
 theorem map_comap_eq_of_surjective (S : Submonoid N) : (S.comap f).map f = S :=
   (giMapComap hf).l_u_eq _
 #align submonoid.map_comap_eq_of_surjective Submonoid.map_comap_eq_of_surjective
 #align add_submonoid.map_comap_eq_of_surjective AddSubmonoid.map_comap_eq_of_surjective
+-/
 
+#print Submonoid.map_surjective_of_surjective /-
 @[to_additive]
 theorem map_surjective_of_surjective : Function.Surjective (map f) :=
   (giMapComap hf).l_surjective
 #align submonoid.map_surjective_of_surjective Submonoid.map_surjective_of_surjective
 #align add_submonoid.map_surjective_of_surjective AddSubmonoid.map_surjective_of_surjective
+-/
 
+#print Submonoid.comap_injective_of_surjective /-
 @[to_additive]
 theorem comap_injective_of_surjective : Function.Injective (comap f) :=
   (giMapComap hf).u_injective
 #align submonoid.comap_injective_of_surjective Submonoid.comap_injective_of_surjective
 #align add_submonoid.comap_injective_of_surjective AddSubmonoid.comap_injective_of_surjective
+-/
 
+#print Submonoid.map_inf_comap_of_surjective /-
 @[to_additive]
 theorem map_inf_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊓ T.comap f).map f = S ⊓ T :=
   (giMapComap hf).l_inf_u _ _
 #align submonoid.map_inf_comap_of_surjective Submonoid.map_inf_comap_of_surjective
 #align add_submonoid.map_inf_comap_of_surjective AddSubmonoid.map_inf_comap_of_surjective
+-/
 
+#print Submonoid.map_iInf_comap_of_surjective /-
 @[to_additive]
 theorem map_iInf_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).comap f).map f = iInf S :=
   (giMapComap hf).l_iInf_u _
 #align submonoid.map_infi_comap_of_surjective Submonoid.map_iInf_comap_of_surjective
 #align add_submonoid.map_infi_comap_of_surjective AddSubmonoid.map_iInf_comap_of_surjective
+-/
 
+#print Submonoid.map_sup_comap_of_surjective /-
 @[to_additive]
 theorem map_sup_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊔ T.comap f).map f = S ⊔ T :=
   (giMapComap hf).l_sup_u _ _
 #align submonoid.map_sup_comap_of_surjective Submonoid.map_sup_comap_of_surjective
 #align add_submonoid.map_sup_comap_of_surjective AddSubmonoid.map_sup_comap_of_surjective
+-/
 
+#print Submonoid.map_iSup_comap_of_surjective /-
 @[to_additive]
 theorem map_iSup_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).comap f).map f = iSup S :=
   (giMapComap hf).l_iSup_u _
 #align submonoid.map_supr_comap_of_surjective Submonoid.map_iSup_comap_of_surjective
 #align add_submonoid.map_supr_comap_of_surjective AddSubmonoid.map_iSup_comap_of_surjective
+-/
 
+#print Submonoid.comap_le_comap_iff_of_surjective /-
 @[to_additive]
 theorem comap_le_comap_iff_of_surjective {S T : Submonoid N} : S.comap f ≤ T.comap f ↔ S ≤ T :=
   (giMapComap hf).u_le_u_iff
 #align submonoid.comap_le_comap_iff_of_surjective Submonoid.comap_le_comap_iff_of_surjective
 #align add_submonoid.comap_le_comap_iff_of_surjective AddSubmonoid.comap_le_comap_iff_of_surjective
+-/
 
+#print Submonoid.comap_strictMono_of_surjective /-
 @[to_additive]
 theorem comap_strictMono_of_surjective : StrictMono (comap f) :=
   (giMapComap hf).strictMono_u
 #align submonoid.comap_strict_mono_of_surjective Submonoid.comap_strictMono_of_surjective
 #align add_submonoid.comap_strict_mono_of_surjective AddSubmonoid.comap_strictMono_of_surjective
+-/
 
 end GaloisInsertion
 
@@ -531,8 +619,6 @@ namespace OneMemClass
 
 variable {A M₁ : Type _} [SetLike A M₁] [One M₁] [hA : OneMemClass A M₁] (S' : A)
 
-include hA
-
 #print OneMemClass.one /-
 /-- A submonoid of a monoid inherits a 1. -/
 @[to_additive "An `add_submonoid` of an `add_monoid` inherits a zero."]
@@ -593,19 +679,23 @@ instance nPow {M} [Monoid M] {A : Type _} [SetLike A M] [SubmonoidClass A M] (S
 
 attribute [to_additive] SubmonoidClass.nPow
 
+#print SubmonoidClass.coe_pow /-
 @[simp, norm_cast, to_additive]
 theorem coe_pow {M} [Monoid M] {A : Type _} [SetLike A M] [SubmonoidClass A M] {S : A} (x : S)
     (n : ℕ) : (↑(x ^ n) : M) = ↑x ^ n :=
   rfl
 #align submonoid_class.coe_pow SubmonoidClass.coe_pow
 #align add_submonoid_class.coe_nsmul AddSubmonoidClass.coe_nsmul
+-/
 
+#print SubmonoidClass.mk_pow /-
 @[simp, to_additive]
 theorem mk_pow {M} [Monoid M] {A : Type _} [SetLike A M] [SubmonoidClass A M] {S : A} (x : M)
     (hx : x ∈ S) (n : ℕ) : (⟨x, hx⟩ : S) ^ n = ⟨x ^ n, pow_mem hx n⟩ :=
   rfl
 #align submonoid_class.mk_pow SubmonoidClass.mk_pow
 #align add_submonoid_class.mk_nsmul AddSubmonoidClass.mk_nsmul
+-/
 
 #print SubmonoidClass.toMulOneClass /-
 -- Prefer subclasses of `monoid` over subclasses of `submonoid_class`.
@@ -692,8 +782,6 @@ instance (priority := 75) toLinearOrderedCancelCommMonoid {M} [LinearOrderedCanc
 #align add_submonoid_class.to_linear_ordered_cancel_add_comm_monoid AddSubmonoidClass.toLinearOrderedCancelAddCommMonoid
 -/
 
-include hA
-
 #print SubmonoidClass.Subtype /-
 /-- The natural monoid hom from a submonoid of monoid `M` to `M`. -/
 @[to_additive "The natural monoid hom from an `add_submonoid` of `add_monoid` `M` to `M`."]
@@ -703,61 +791,78 @@ def Subtype : S' →* M :=
 #align add_submonoid_class.subtype AddSubmonoidClass.Subtype
 -/
 
+#print SubmonoidClass.coe_subtype /-
 @[simp, to_additive]
 theorem coe_subtype : (SubmonoidClass.Subtype S' : S' → M) = coe :=
   rfl
 #align submonoid_class.coe_subtype SubmonoidClass.coe_subtype
 #align add_submonoid_class.coe_subtype AddSubmonoidClass.coe_subtype
+-/
 
 end SubmonoidClass
 
 namespace Submonoid
 
+#print Submonoid.mul /-
 /-- A submonoid of a monoid inherits a multiplication. -/
 @[to_additive "An `add_submonoid` of an `add_monoid` inherits an addition."]
 instance mul : Mul S :=
   ⟨fun a b => ⟨a.1 * b.1, S.mul_mem a.2 b.2⟩⟩
 #align submonoid.has_mul Submonoid.mul
 #align add_submonoid.has_add AddSubmonoid.add
+-/
 
+#print Submonoid.one /-
 /-- A submonoid of a monoid inherits a 1. -/
 @[to_additive "An `add_submonoid` of an `add_monoid` inherits a zero."]
 instance one : One S :=
   ⟨⟨_, S.one_mem⟩⟩
 #align submonoid.has_one Submonoid.one
 #align add_submonoid.has_zero AddSubmonoid.zero
+-/
 
+#print Submonoid.coe_mul /-
 @[simp, norm_cast, to_additive]
 theorem coe_mul (x y : S) : (↑(x * y) : M) = ↑x * ↑y :=
   rfl
 #align submonoid.coe_mul Submonoid.coe_mul
 #align add_submonoid.coe_add AddSubmonoid.coe_add
+-/
 
+#print Submonoid.coe_one /-
 @[simp, norm_cast, to_additive]
 theorem coe_one : ((1 : S) : M) = 1 :=
   rfl
 #align submonoid.coe_one Submonoid.coe_one
 #align add_submonoid.coe_zero AddSubmonoid.coe_zero
+-/
 
+#print Submonoid.mk_mul_mk /-
 @[simp, to_additive]
 theorem mk_mul_mk (x y : M) (hx : x ∈ S) (hy : y ∈ S) :
     (⟨x, hx⟩ : S) * ⟨y, hy⟩ = ⟨x * y, S.mul_mem hx hy⟩ :=
   rfl
 #align submonoid.mk_mul_mk Submonoid.mk_mul_mk
 #align add_submonoid.mk_add_mk AddSubmonoid.mk_add_mk
+-/
 
+#print Submonoid.mul_def /-
 @[to_additive]
 theorem mul_def (x y : S) : x * y = ⟨x * y, S.mul_mem x.2 y.2⟩ :=
   rfl
 #align submonoid.mul_def Submonoid.mul_def
 #align add_submonoid.add_def AddSubmonoid.add_def
+-/
 
+#print Submonoid.one_def /-
 @[to_additive]
 theorem one_def : (1 : S) = ⟨1, S.one_mem⟩ :=
   rfl
 #align submonoid.one_def Submonoid.one_def
 #align add_submonoid.zero_def AddSubmonoid.zero_def
+-/
 
+#print Submonoid.toMulOneClass /-
 /-- A submonoid of a unital magma inherits a unital magma structure. -/
 @[to_additive
       "An `add_submonoid` of an unital additive magma inherits an unital additive magma\nstructure."]
@@ -765,13 +870,16 @@ instance toMulOneClass {M : Type _} [MulOneClass M] (S : Submonoid M) : MulOneCl
   Subtype.coe_injective.MulOneClass coe rfl fun _ _ => rfl
 #align submonoid.to_mul_one_class Submonoid.toMulOneClass
 #align add_submonoid.to_add_zero_class AddSubmonoid.toAddZeroClass
+-/
 
+#print Submonoid.pow_mem /-
 @[to_additive]
 protected theorem pow_mem {M : Type _} [Monoid M] (S : Submonoid M) {x : M} (hx : x ∈ S) (n : ℕ) :
     x ^ n ∈ S :=
   pow_mem hx n
 #align submonoid.pow_mem Submonoid.pow_mem
 #align add_submonoid.nsmul_mem AddSubmonoid.nsmul_mem
+-/
 
 @[simp, norm_cast, to_additive]
 theorem coe_pow {M : Type _} [Monoid M] {S : Submonoid M} (x : S) (n : ℕ) :
@@ -780,20 +888,25 @@ theorem coe_pow {M : Type _} [Monoid M] {S : Submonoid M} (x : S) (n : ℕ) :
 #align submonoid.coe_pow Submonoid.coe_pow
 #align add_submonoid.coe_nsmul AddSubmonoid.coe_nsmul
 
+#print Submonoid.toMonoid /-
 /-- A submonoid of a monoid inherits a monoid structure. -/
 @[to_additive "An `add_submonoid` of an `add_monoid` inherits an `add_monoid`\nstructure."]
 instance toMonoid {M : Type _} [Monoid M] (S : Submonoid M) : Monoid S :=
   Subtype.coe_injective.Monoid coe rfl (fun _ _ => rfl) fun _ _ => rfl
 #align submonoid.to_monoid Submonoid.toMonoid
 #align add_submonoid.to_add_monoid AddSubmonoid.toAddMonoid
+-/
 
+#print Submonoid.toCommMonoid /-
 /-- A submonoid of a `comm_monoid` is a `comm_monoid`. -/
 @[to_additive "An `add_submonoid` of an `add_comm_monoid` is\nan `add_comm_monoid`."]
 instance toCommMonoid {M} [CommMonoid M] (S : Submonoid M) : CommMonoid S :=
   Subtype.coe_injective.CommMonoid coe rfl (fun _ _ => rfl) fun _ _ => rfl
 #align submonoid.to_comm_monoid Submonoid.toCommMonoid
 #align add_submonoid.to_add_comm_monoid AddSubmonoid.toAddCommMonoid
+-/
 
+#print Submonoid.toOrderedCommMonoid /-
 /-- A submonoid of an `ordered_comm_monoid` is an `ordered_comm_monoid`. -/
 @[to_additive
       "An `add_submonoid` of an `ordered_add_comm_monoid` is\nan `ordered_add_comm_monoid`."]
@@ -801,7 +914,9 @@ instance toOrderedCommMonoid {M} [OrderedCommMonoid M] (S : Submonoid M) : Order
   Subtype.coe_injective.OrderedCommMonoid coe rfl (fun _ _ => rfl) fun _ _ => rfl
 #align submonoid.to_ordered_comm_monoid Submonoid.toOrderedCommMonoid
 #align add_submonoid.to_ordered_add_comm_monoid AddSubmonoid.toOrderedAddCommMonoid
+-/
 
+#print Submonoid.toLinearOrderedCommMonoid /-
 /-- A submonoid of a `linear_ordered_comm_monoid` is a `linear_ordered_comm_monoid`. -/
 @[to_additive
       "An `add_submonoid` of a `linear_ordered_add_comm_monoid` is\na `linear_ordered_add_comm_monoid`."]
@@ -811,7 +926,9 @@ instance toLinearOrderedCommMonoid {M} [LinearOrderedCommMonoid M] (S : Submonoi
     (fun _ _ => rfl) fun _ _ => rfl
 #align submonoid.to_linear_ordered_comm_monoid Submonoid.toLinearOrderedCommMonoid
 #align add_submonoid.to_linear_ordered_add_comm_monoid AddSubmonoid.toLinearOrderedAddCommMonoid
+-/
 
+#print Submonoid.toOrderedCancelCommMonoid /-
 /-- A submonoid of an `ordered_cancel_comm_monoid` is an `ordered_cancel_comm_monoid`. -/
 @[to_additive
       "An `add_submonoid` of an `ordered_cancel_add_comm_monoid` is\nan `ordered_cancel_add_comm_monoid`."]
@@ -820,7 +937,9 @@ instance toOrderedCancelCommMonoid {M} [OrderedCancelCommMonoid M] (S : Submonoi
   Subtype.coe_injective.OrderedCancelCommMonoid coe rfl (fun _ _ => rfl) fun _ _ => rfl
 #align submonoid.to_ordered_cancel_comm_monoid Submonoid.toOrderedCancelCommMonoid
 #align add_submonoid.to_ordered_cancel_add_comm_monoid AddSubmonoid.toOrderedCancelAddCommMonoid
+-/
 
+#print Submonoid.toLinearOrderedCancelCommMonoid /-
 /-- A submonoid of a `linear_ordered_cancel_comm_monoid` is a `linear_ordered_cancel_comm_monoid`.
 -/
 @[to_additive
@@ -831,20 +950,26 @@ instance toLinearOrderedCancelCommMonoid {M} [LinearOrderedCancelCommMonoid M] (
     (fun _ _ => rfl) fun _ _ => rfl
 #align submonoid.to_linear_ordered_cancel_comm_monoid Submonoid.toLinearOrderedCancelCommMonoid
 #align add_submonoid.to_linear_ordered_cancel_add_comm_monoid AddSubmonoid.toLinearOrderedCancelAddCommMonoid
+-/
 
+#print Submonoid.subtype /-
 /-- The natural monoid hom from a submonoid of monoid `M` to `M`. -/
 @[to_additive "The natural monoid hom from an `add_submonoid` of `add_monoid` `M` to `M`."]
 def subtype : S →* M :=
   ⟨coe, rfl, fun _ _ => rfl⟩
 #align submonoid.subtype Submonoid.subtype
 #align add_submonoid.subtype AddSubmonoid.subtype
+-/
 
+#print Submonoid.coe_subtype /-
 @[simp, to_additive]
 theorem coe_subtype : ⇑S.Subtype = coe :=
   rfl
 #align submonoid.coe_subtype Submonoid.coe_subtype
 #align add_submonoid.coe_subtype AddSubmonoid.coe_subtype
+-/
 
+#print Submonoid.topEquiv /-
 /-- The top submonoid is isomorphic to the monoid. -/
 @[to_additive "The top additive submonoid is isomorphic to the additive monoid.", simps]
 def topEquiv : (⊤ : Submonoid M) ≃* M where
@@ -855,13 +980,17 @@ def topEquiv : (⊤ : Submonoid M) ≃* M where
   map_mul' _ _ := rfl
 #align submonoid.top_equiv Submonoid.topEquiv
 #align add_submonoid.top_equiv AddSubmonoid.topEquiv
+-/
 
+#print Submonoid.topEquiv_toMonoidHom /-
 @[simp, to_additive]
 theorem topEquiv_toMonoidHom : (topEquiv : _ ≃* M).toMonoidHom = (⊤ : Submonoid M).Subtype :=
   rfl
 #align submonoid.top_equiv_to_monoid_hom Submonoid.topEquiv_toMonoidHom
 #align add_submonoid.top_equiv_to_add_monoid_hom AddSubmonoid.topEquiv_toAddMonoidHom
+-/
 
+#print Submonoid.equivMapOfInjective /-
 /-- A subgroup is isomorphic to its image under an injective function. If you have an isomorphism,
 use `mul_equiv.submonoid_map` for better definitional equalities. -/
 @[to_additive
@@ -870,14 +999,18 @@ noncomputable def equivMapOfInjective (f : M →* N) (hf : Function.Injective f)
   { Equiv.Set.image f S hf with map_mul' := fun _ _ => Subtype.ext (f.map_mul _ _) }
 #align submonoid.equiv_map_of_injective Submonoid.equivMapOfInjective
 #align add_submonoid.equiv_map_of_injective AddSubmonoid.equivMapOfInjective
+-/
 
+#print Submonoid.coe_equivMapOfInjective_apply /-
 @[simp, to_additive]
 theorem coe_equivMapOfInjective_apply (f : M →* N) (hf : Function.Injective f) (x : S) :
     (equivMapOfInjective S f hf x : N) = f x :=
   rfl
 #align submonoid.coe_equiv_map_of_injective_apply Submonoid.coe_equivMapOfInjective_apply
 #align add_submonoid.coe_equiv_map_of_injective_apply AddSubmonoid.coe_equivMapOfInjective_apply
+-/
 
+#print Submonoid.closure_closure_coe_preimage /-
 @[simp, to_additive]
 theorem closure_closure_coe_preimage {s : Set M} : closure ((coe : closure s → M) ⁻¹' s) = ⊤ :=
   eq_top_iff.2 fun x =>
@@ -889,8 +1022,10 @@ theorem closure_closure_coe_preimage {s : Set M} : closure ((coe : closure s →
       · exact Submonoid.mul_mem _
 #align submonoid.closure_closure_coe_preimage Submonoid.closure_closure_coe_preimage
 #align add_submonoid.closure_closure_coe_preimage AddSubmonoid.closure_closure_coe_preimage
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Submonoid.prod /-
 /-- Given `submonoid`s `s`, `t` of monoids `M`, `N` respectively, `s × t` as a submonoid
 of `M × N`. -/
 @[to_additive Prod
@@ -902,52 +1037,68 @@ def prod (s : Submonoid M) (t : Submonoid N) : Submonoid (M × N)
   mul_mem' p q hp hq := ⟨s.mul_mem hp.1 hq.1, t.mul_mem hp.2 hq.2⟩
 #align submonoid.prod Submonoid.prod
 #align add_submonoid.prod AddSubmonoid.prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Submonoid.coe_prod /-
 @[to_additive coe_prod]
 theorem coe_prod (s : Submonoid M) (t : Submonoid N) : (s.Prod t : Set (M × N)) = s ×ˢ t :=
   rfl
 #align submonoid.coe_prod Submonoid.coe_prod
 #align add_submonoid.coe_prod AddSubmonoid.coe_prod
+-/
 
+#print Submonoid.mem_prod /-
 @[to_additive mem_prod]
 theorem mem_prod {s : Submonoid M} {t : Submonoid N} {p : M × N} :
     p ∈ s.Prod t ↔ p.1 ∈ s ∧ p.2 ∈ t :=
   Iff.rfl
 #align submonoid.mem_prod Submonoid.mem_prod
 #align add_submonoid.mem_prod AddSubmonoid.mem_prod
+-/
 
+#print Submonoid.prod_mono /-
 @[to_additive prod_mono]
 theorem prod_mono {s₁ s₂ : Submonoid M} {t₁ t₂ : Submonoid N} (hs : s₁ ≤ s₂) (ht : t₁ ≤ t₂) :
     s₁.Prod t₁ ≤ s₂.Prod t₂ :=
   Set.prod_mono hs ht
 #align submonoid.prod_mono Submonoid.prod_mono
 #align add_submonoid.prod_mono AddSubmonoid.prod_mono
+-/
 
+#print Submonoid.prod_top /-
 @[to_additive prod_top]
 theorem prod_top (s : Submonoid M) : s.Prod (⊤ : Submonoid N) = s.comap (MonoidHom.fst M N) :=
   ext fun x => by simp [mem_prod, MonoidHom.coe_fst]
 #align submonoid.prod_top Submonoid.prod_top
 #align add_submonoid.prod_top AddSubmonoid.prod_top
+-/
 
+#print Submonoid.top_prod /-
 @[to_additive top_prod]
 theorem top_prod (s : Submonoid N) : (⊤ : Submonoid M).Prod s = s.comap (MonoidHom.snd M N) :=
   ext fun x => by simp [mem_prod, MonoidHom.coe_snd]
 #align submonoid.top_prod Submonoid.top_prod
 #align add_submonoid.top_prod AddSubmonoid.top_prod
+-/
 
+#print Submonoid.top_prod_top /-
 @[simp, to_additive top_prod_top]
 theorem top_prod_top : (⊤ : Submonoid M).Prod (⊤ : Submonoid N) = ⊤ :=
   (top_prod _).trans <| comap_top _
 #align submonoid.top_prod_top Submonoid.top_prod_top
 #align add_submonoid.top_prod_top AddSubmonoid.top_prod_top
+-/
 
+#print Submonoid.bot_prod_bot /-
 @[to_additive]
 theorem bot_prod_bot : (⊥ : Submonoid M).Prod (⊥ : Submonoid N) = ⊥ :=
   SetLike.coe_injective <| by simp [coe_prod, Prod.one_eq_mk]
 #align submonoid.bot_prod_bot Submonoid.bot_prod_bot
 #align add_submonoid.bot_sum_bot AddSubmonoid.bot_prod_bot
+-/
 
+#print Submonoid.prodEquiv /-
 /-- The product of submonoids is isomorphic to their product as monoids. -/
 @[to_additive prod_equiv
       "The product of additive submonoids is isomorphic to their product\nas additive monoids"]
@@ -955,9 +1106,11 @@ def prodEquiv (s : Submonoid M) (t : Submonoid N) : s.Prod t ≃* s × t :=
   { Equiv.Set.prod ↑s ↑t with map_mul' := fun x y => rfl }
 #align submonoid.prod_equiv Submonoid.prodEquiv
 #align add_submonoid.prod_equiv AddSubmonoid.prodEquiv
+-/
 
 open MonoidHom
 
+#print Submonoid.map_inl /-
 @[to_additive]
 theorem map_inl (s : Submonoid M) : s.map (inl M N) = s.Prod ⊥ :=
   ext fun p =>
@@ -965,7 +1118,9 @@ theorem map_inl (s : Submonoid M) : s.map (inl M N) = s.Prod ⊥ :=
       ⟨p.1, hps, Prod.ext rfl <| (Set.eq_of_mem_singleton hp1).symm⟩⟩
 #align submonoid.map_inl Submonoid.map_inl
 #align add_submonoid.map_inl AddSubmonoid.map_inl
+-/
 
+#print Submonoid.map_inr /-
 @[to_additive]
 theorem map_inr (s : Submonoid N) : s.map (inr M N) = prod ⊥ s :=
   ext fun p =>
@@ -973,7 +1128,9 @@ theorem map_inr (s : Submonoid N) : s.map (inr M N) = prod ⊥ s :=
       ⟨p.2, hps, Prod.ext (Set.eq_of_mem_singleton hp1).symm rfl⟩⟩
 #align submonoid.map_inr Submonoid.map_inr
 #align add_submonoid.map_inr AddSubmonoid.map_inr
+-/
 
+#print Submonoid.prod_bot_sup_bot_prod /-
 @[simp, to_additive prod_bot_sup_bot_prod]
 theorem prod_bot_sup_bot_prod (s : Submonoid M) (t : Submonoid N) :
     s.Prod ⊥ ⊔ prod ⊥ t = s.Prod t :=
@@ -983,34 +1140,44 @@ theorem prod_bot_sup_bot_prod (s : Submonoid M) (t : Submonoid N) :
         ((le_sup_right : prod ⊥ t ≤ s.Prod ⊥ ⊔ prod ⊥ t) ⟨Set.mem_singleton 1, hp.2⟩)
 #align submonoid.prod_bot_sup_bot_prod Submonoid.prod_bot_sup_bot_prod
 #align add_submonoid.prod_bot_sup_bot_prod AddSubmonoid.prod_bot_sup_bot_prod
+-/
 
+#print Submonoid.mem_map_equiv /-
 @[to_additive]
 theorem mem_map_equiv {f : M ≃* N} {K : Submonoid M} {x : N} :
     x ∈ K.map f.toMonoidHom ↔ f.symm x ∈ K :=
   @Set.mem_image_equiv _ _ (↑K) f.toEquiv x
 #align submonoid.mem_map_equiv Submonoid.mem_map_equiv
 #align add_submonoid.mem_map_equiv AddSubmonoid.mem_map_equiv
+-/
 
+#print Submonoid.map_equiv_eq_comap_symm /-
 @[to_additive]
 theorem map_equiv_eq_comap_symm (f : M ≃* N) (K : Submonoid M) :
     K.map f.toMonoidHom = K.comap f.symm.toMonoidHom :=
   SetLike.coe_injective (f.toEquiv.image_eq_preimage K)
 #align submonoid.map_equiv_eq_comap_symm Submonoid.map_equiv_eq_comap_symm
 #align add_submonoid.map_equiv_eq_comap_symm AddSubmonoid.map_equiv_eq_comap_symm
+-/
 
+#print Submonoid.comap_equiv_eq_map_symm /-
 @[to_additive]
 theorem comap_equiv_eq_map_symm (f : N ≃* M) (K : Submonoid M) :
     K.comap f.toMonoidHom = K.map f.symm.toMonoidHom :=
   (map_equiv_eq_comap_symm f.symm K).symm
 #align submonoid.comap_equiv_eq_map_symm Submonoid.comap_equiv_eq_map_symm
 #align add_submonoid.comap_equiv_eq_map_symm AddSubmonoid.comap_equiv_eq_map_symm
+-/
 
+#print Submonoid.map_equiv_top /-
 @[simp, to_additive]
 theorem map_equiv_top (f : M ≃* N) : (⊤ : Submonoid M).map f.toMonoidHom = ⊤ :=
   SetLike.coe_injective <| Set.image_univ.trans f.Surjective.range_eq
 #align submonoid.map_equiv_top Submonoid.map_equiv_top
 #align add_submonoid.map_equiv_top AddSubmonoid.map_equiv_top
+-/
 
+#print Submonoid.le_prod_iff /-
 @[to_additive le_prod_iff]
 theorem le_prod_iff {s : Submonoid M} {t : Submonoid N} {u : Submonoid (M × N)} :
     u ≤ s.Prod t ↔ u.map (fst M N) ≤ s ∧ u.map (snd M N) ≤ t :=
@@ -1023,7 +1190,9 @@ theorem le_prod_iff {s : Submonoid M} {t : Submonoid N} {u : Submonoid (M × N)}
   · rintro ⟨hH, hK⟩ ⟨x1, x2⟩ h; exact ⟨hH ⟨_, h, rfl⟩, hK ⟨_, h, rfl⟩⟩
 #align submonoid.le_prod_iff Submonoid.le_prod_iff
 #align add_submonoid.le_prod_iff AddSubmonoid.le_prod_iff
+-/
 
+#print Submonoid.prod_le_iff /-
 @[to_additive prod_le_iff]
 theorem prod_le_iff {s : Submonoid M} {t : Submonoid N} {u : Submonoid (M × N)} :
     s.Prod t ≤ u ↔ s.map (inl M N) ≤ u ∧ t.map (inr M N) ≤ u :=
@@ -1039,6 +1208,7 @@ theorem prod_le_iff {s : Submonoid M} {t : Submonoid N} {u : Submonoid (M × N)}
     simpa using Submonoid.mul_mem _ h1' h2'
 #align submonoid.prod_le_iff Submonoid.prod_le_iff
 #align add_submonoid.prod_le_iff AddSubmonoid.prod_le_iff
+-/
 
 end Submonoid
 
@@ -1080,8 +1250,6 @@ def mrange (f : M →* N) : submonoid N :=
 -/
 
 
-include mc
-
 #print MonoidHom.mrange /-
 /-- The range of a monoid homomorphism is a submonoid. See Note [range copy pattern]. -/
 @[to_additive "The range of an `add_monoid_hom` is an `add_submonoid`."]
@@ -1091,40 +1259,47 @@ def mrange (f : F) : Submonoid N :=
 #align add_monoid_hom.mrange AddMonoidHom.mrange
 -/
 
+#print MonoidHom.coe_mrange /-
 @[simp, to_additive]
 theorem coe_mrange (f : F) : (mrange f : Set N) = Set.range f :=
   rfl
 #align monoid_hom.coe_mrange MonoidHom.coe_mrange
 #align add_monoid_hom.coe_mrange AddMonoidHom.coe_mrange
+-/
 
+#print MonoidHom.mem_mrange /-
 @[simp, to_additive]
 theorem mem_mrange {f : F} {y : N} : y ∈ mrange f ↔ ∃ x, f x = y :=
   Iff.rfl
 #align monoid_hom.mem_mrange MonoidHom.mem_mrange
 #align add_monoid_hom.mem_mrange AddMonoidHom.mem_mrange
+-/
 
+#print MonoidHom.mrange_eq_map /-
 @[to_additive]
 theorem mrange_eq_map (f : F) : mrange f = (⊤ : Submonoid M).map f :=
   Submonoid.copy_eq _
 #align monoid_hom.mrange_eq_map MonoidHom.mrange_eq_map
 #align add_monoid_hom.mrange_eq_map AddMonoidHom.mrange_eq_map
+-/
 
-omit mc
-
+#print MonoidHom.map_mrange /-
 @[to_additive]
 theorem map_mrange (g : N →* P) (f : M →* N) : f.mrange.map g = (g.comp f).mrange := by
   simpa only [mrange_eq_map] using (⊤ : Submonoid M).map_map g f
 #align monoid_hom.map_mrange MonoidHom.map_mrange
 #align add_monoid_hom.map_mrange AddMonoidHom.map_mrange
+-/
 
-include mc
-
+#print MonoidHom.mrange_top_iff_surjective /-
 @[to_additive]
 theorem mrange_top_iff_surjective {f : F} : mrange f = (⊤ : Submonoid N) ↔ Function.Surjective f :=
   SetLike.ext'_iff.trans <| Iff.trans (by rw [coe_mrange, coe_top]) Set.range_iff_surjective
 #align monoid_hom.mrange_top_iff_surjective MonoidHom.mrange_top_iff_surjective
 #align add_monoid_hom.mrange_top_iff_surjective AddMonoidHom.mrange_top_iff_surjective
+-/
 
+#print MonoidHom.mrange_top_of_surjective /-
 /-- The range of a surjective monoid hom is the whole of the codomain. -/
 @[to_additive "The range of a surjective `add_monoid` hom is the whole of the codomain."]
 theorem mrange_top_of_surjective (f : F) (hf : Function.Surjective f) :
@@ -1132,13 +1307,17 @@ theorem mrange_top_of_surjective (f : F) (hf : Function.Surjective f) :
   mrange_top_iff_surjective.2 hf
 #align monoid_hom.mrange_top_of_surjective MonoidHom.mrange_top_of_surjective
 #align add_monoid_hom.mrange_top_of_surjective AddMonoidHom.mrange_top_of_surjective
+-/
 
+#print MonoidHom.mclosure_preimage_le /-
 @[to_additive]
 theorem mclosure_preimage_le (f : F) (s : Set N) : closure (f ⁻¹' s) ≤ (closure s).comap f :=
   closure_le.2 fun x hx => SetLike.mem_coe.2 <| mem_comap.2 <| subset_closure hx
 #align monoid_hom.mclosure_preimage_le MonoidHom.mclosure_preimage_le
 #align add_monoid_hom.mclosure_preimage_le AddMonoidHom.mclosure_preimage_le
+-/
 
+#print MonoidHom.map_mclosure /-
 /-- The image under a monoid hom of the submonoid generated by a set equals the submonoid generated
     by the image of the set. -/
 @[to_additive
@@ -1150,8 +1329,7 @@ theorem map_mclosure (f : F) (s : Set M) : (closure s).map f = closure (f '' s)
     (closure_le.2 <| Set.image_subset _ subset_closure)
 #align monoid_hom.map_mclosure MonoidHom.map_mclosure
 #align add_monoid_hom.map_mclosure AddMonoidHom.map_mclosure
-
-omit mc
+-/
 
 #print MonoidHom.restrict /-
 /-- Restriction of a monoid hom to a submonoid of the domain. -/
@@ -1163,20 +1341,25 @@ def restrict {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M] (
 #align add_monoid_hom.restrict AddMonoidHom.restrict
 -/
 
+#print MonoidHom.restrict_apply /-
 @[simp, to_additive]
 theorem restrict_apply {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M]
     (f : M →* N) (s : S) (x : s) : f.restrict s x = f x :=
   rfl
 #align monoid_hom.restrict_apply MonoidHom.restrict_apply
 #align add_monoid_hom.restrict_apply AddMonoidHom.restrict_apply
+-/
 
+#print MonoidHom.restrict_mrange /-
 @[simp, to_additive]
 theorem restrict_mrange (f : M →* N) : (f.restrict S).mrange = S.map f := by
   simp_rw [SetLike.ext_iff, mem_mrange, mem_map, restrict_apply, SetLike.exists, Subtype.coe_mk,
     iff_self_iff, forall_const]
 #align monoid_hom.restrict_mrange MonoidHom.restrict_mrange
 #align add_monoid_hom.restrict_mrange AddMonoidHom.restrict_mrange
+-/
 
+#print MonoidHom.codRestrict /-
 /-- Restriction of a monoid hom to a submonoid of the codomain. -/
 @[to_additive "Restriction of an `add_monoid` hom to an `add_submonoid` of the codomain.",
   simps apply]
@@ -1187,28 +1370,33 @@ def codRestrict {S} [SetLike S N] [SubmonoidClass S N] (f : M →* N) (s : S) (h
   map_mul' x y := Subtype.eq (f.map_mul x y)
 #align monoid_hom.cod_restrict MonoidHom.codRestrict
 #align add_monoid_hom.cod_restrict AddMonoidHom.codRestrict
+-/
 
+#print MonoidHom.mrangeRestrict /-
 /-- Restriction of a monoid hom to its range interpreted as a submonoid. -/
 @[to_additive "Restriction of an `add_monoid` hom to its range interpreted as a submonoid."]
 def mrangeRestrict {N} [MulOneClass N] (f : M →* N) : M →* f.mrange :=
   f.codRestrict f.mrange fun x => ⟨x, rfl⟩
 #align monoid_hom.mrange_restrict MonoidHom.mrangeRestrict
 #align add_monoid_hom.mrange_restrict AddMonoidHom.mrangeRestrict
+-/
 
+#print MonoidHom.coe_mrangeRestrict /-
 @[simp, to_additive]
 theorem coe_mrangeRestrict {N} [MulOneClass N] (f : M →* N) (x : M) :
     (f.mrangeRestrict x : N) = f x :=
   rfl
 #align monoid_hom.coe_mrange_restrict MonoidHom.coe_mrangeRestrict
 #align add_monoid_hom.coe_mrange_restrict AddMonoidHom.coe_mrangeRestrict
+-/
 
+#print MonoidHom.mrangeRestrict_surjective /-
 @[to_additive]
 theorem mrangeRestrict_surjective (f : M →* N) : Function.Surjective f.mrangeRestrict :=
   fun ⟨_, ⟨x, rfl⟩⟩ => ⟨x, rfl⟩
 #align monoid_hom.mrange_restrict_surjective MonoidHom.mrangeRestrict_surjective
 #align add_monoid_hom.mrange_restrict_surjective AddMonoidHom.mrangeRestrict_surjective
-
-include mc
+-/
 
 #print MonoidHom.mker /-
 /-- The multiplicative kernel of a monoid homomorphism is the submonoid of elements `x : G` such
@@ -1221,48 +1409,55 @@ def mker (f : F) : Submonoid M :=
 #align add_monoid_hom.mker AddMonoidHom.mker
 -/
 
+#print MonoidHom.mem_mker /-
 @[to_additive]
 theorem mem_mker (f : F) {x : M} : x ∈ mker f ↔ f x = 1 :=
   Iff.rfl
 #align monoid_hom.mem_mker MonoidHom.mem_mker
 #align add_monoid_hom.mem_mker AddMonoidHom.mem_mker
+-/
 
+#print MonoidHom.coe_mker /-
 @[to_additive]
 theorem coe_mker (f : F) : (mker f : Set M) = (f : M → N) ⁻¹' {1} :=
   rfl
 #align monoid_hom.coe_mker MonoidHom.coe_mker
 #align add_monoid_hom.coe_mker AddMonoidHom.coe_mker
+-/
 
+#print MonoidHom.decidableMemMker /-
 @[to_additive]
 instance decidableMemMker [DecidableEq N] (f : F) : DecidablePred (· ∈ mker f) := fun x =>
   decidable_of_iff (f x = 1) (mem_mker f)
 #align monoid_hom.decidable_mem_mker MonoidHom.decidableMemMker
 #align add_monoid_hom.decidable_mem_mker AddMonoidHom.decidableMemMker
+-/
 
-omit mc
-
+#print MonoidHom.comap_mker /-
 @[to_additive]
 theorem comap_mker (g : N →* P) (f : M →* N) : g.mker.comap f = (g.comp f).mker :=
   rfl
 #align monoid_hom.comap_mker MonoidHom.comap_mker
 #align add_monoid_hom.comap_mker AddMonoidHom.comap_mker
+-/
 
-include mc
-
+#print MonoidHom.comap_bot' /-
 @[simp, to_additive]
 theorem comap_bot' (f : F) : (⊥ : Submonoid N).comap f = mker f :=
   rfl
 #align monoid_hom.comap_bot' MonoidHom.comap_bot'
 #align add_monoid_hom.comap_bot' AddMonoidHom.comap_bot'
+-/
 
-omit mc
-
+#print MonoidHom.restrict_mker /-
 @[simp, to_additive]
 theorem restrict_mker (f : M →* N) : (f.restrict S).mker = f.mker.comap S.Subtype :=
   rfl
 #align monoid_hom.restrict_mker MonoidHom.restrict_mker
 #align add_monoid_hom.restrict_mker AddMonoidHom.restrict_mker
+-/
 
+#print MonoidHom.mrangeRestrict_mker /-
 @[to_additive]
 theorem mrangeRestrict_mker (f : M →* N) : mker (mrangeRestrict f) = mker f :=
   by
@@ -1271,12 +1466,16 @@ theorem mrangeRestrict_mker (f : M →* N) : mker (mrangeRestrict f) = mker f :=
   simp only
 #align monoid_hom.range_restrict_mker MonoidHom.mrangeRestrict_mker
 #align add_monoid_hom.range_restrict_mker AddMonoidHom.mrangeRestrict_mker
+-/
 
+#print MonoidHom.mker_one /-
 @[simp, to_additive]
 theorem mker_one : (1 : M →* N).mker = ⊤ := by ext; simp [mem_mker]
 #align monoid_hom.mker_one MonoidHom.mker_one
 #align add_monoid_hom.mker_zero AddMonoidHom.mker_zero
+-/
 
+#print MonoidHom.prod_map_comap_prod' /-
 @[to_additive]
 theorem prod_map_comap_prod' {M' : Type _} {N' : Type _} [MulOneClass M'] [MulOneClass N']
     (f : M →* N) (g : M' →* N') (S : Submonoid N) (S' : Submonoid N') :
@@ -1284,24 +1483,32 @@ theorem prod_map_comap_prod' {M' : Type _} {N' : Type _} [MulOneClass M'] [MulOn
   SetLike.coe_injective <| Set.preimage_prod_map_prod f g _ _
 #align monoid_hom.prod_map_comap_prod' MonoidHom.prod_map_comap_prod'
 #align add_monoid_hom.sum_map_comap_sum' AddMonoidHom.prod_map_comap_prod'
+-/
 
+#print MonoidHom.mker_prod_map /-
 @[to_additive]
 theorem mker_prod_map {M' : Type _} {N' : Type _} [MulOneClass M'] [MulOneClass N'] (f : M →* N)
     (g : M' →* N') : (prodMap f g).mker = f.mker.Prod g.mker := by
   rw [← comap_bot', ← comap_bot', ← comap_bot', ← prod_map_comap_prod', bot_prod_bot]
 #align monoid_hom.mker_prod_map MonoidHom.mker_prod_map
 #align add_monoid_hom.mker_sum_map AddMonoidHom.mker_prod_map
+-/
 
+#print MonoidHom.mker_inl /-
 @[simp, to_additive]
 theorem mker_inl : (inl M N).mker = ⊥ := by ext x; simp [mem_mker]
 #align monoid_hom.mker_inl MonoidHom.mker_inl
 #align add_monoid_hom.mker_inl AddMonoidHom.mker_inl
+-/
 
+#print MonoidHom.mker_inr /-
 @[simp, to_additive]
 theorem mker_inr : (inr M N).mker = ⊥ := by ext x; simp [mem_mker]
 #align monoid_hom.mker_inr MonoidHom.mker_inr
 #align add_monoid_hom.mker_inr AddMonoidHom.mker_inr
+-/
 
+#print MonoidHom.submonoidComap /-
 /-- The `monoid_hom` from the preimage of a submonoid to itself. -/
 @[to_additive "the `add_monoid_hom` from the preimage of an additive submonoid to itself.", simps]
 def submonoidComap (f : M →* N) (N' : Submonoid N) : N'.comap f →* N'
@@ -1311,7 +1518,9 @@ def submonoidComap (f : M →* N) (N' : Submonoid N) : N'.comap f →* N'
   map_mul' x y := Subtype.eq (f.map_mul x y)
 #align monoid_hom.submonoid_comap MonoidHom.submonoidComap
 #align add_monoid_hom.add_submonoid_comap AddMonoidHom.addSubmonoidComap
+-/
 
+#print MonoidHom.submonoidMap /-
 /-- The `monoid_hom` from a submonoid to its image.
 See `mul_equiv.submonoid_map` for a variant for `mul_equiv`s. -/
 @[to_additive
@@ -1324,12 +1533,15 @@ def submonoidMap (f : M →* N) (M' : Submonoid M) : M' →* M'.map f
   map_mul' x y := Subtype.eq <| f.map_mul x y
 #align monoid_hom.submonoid_map MonoidHom.submonoidMap
 #align add_monoid_hom.add_submonoid_map AddMonoidHom.addSubmonoidMap
+-/
 
+#print MonoidHom.submonoidMap_surjective /-
 @[to_additive]
 theorem submonoidMap_surjective (f : M →* N) (M' : Submonoid M) :
     Function.Surjective (f.submonoidMap M') := by rintro ⟨_, x, hx, rfl⟩; exact ⟨⟨x, hx⟩, rfl⟩
 #align monoid_hom.submonoid_map_surjective MonoidHom.submonoidMap_surjective
 #align add_monoid_hom.add_submonoid_map_surjective AddMonoidHom.addSubmonoidMap_surjective
+-/
 
 end MonoidHom
 
@@ -1337,84 +1549,111 @@ namespace Submonoid
 
 open MonoidHom
 
+#print Submonoid.mrange_inl /-
 @[to_additive]
 theorem mrange_inl : (inl M N).mrange = prod ⊤ ⊥ := by simpa only [mrange_eq_map] using map_inl ⊤
 #align submonoid.mrange_inl Submonoid.mrange_inl
 #align add_submonoid.mrange_inl AddSubmonoid.mrange_inl
+-/
 
+#print Submonoid.mrange_inr /-
 @[to_additive]
 theorem mrange_inr : (inr M N).mrange = prod ⊥ ⊤ := by simpa only [mrange_eq_map] using map_inr ⊤
 #align submonoid.mrange_inr Submonoid.mrange_inr
 #align add_submonoid.mrange_inr AddSubmonoid.mrange_inr
+-/
 
+#print Submonoid.mrange_inl' /-
 @[to_additive]
 theorem mrange_inl' : (inl M N).mrange = comap (snd M N) ⊥ :=
   mrange_inl.trans (top_prod _)
 #align submonoid.mrange_inl' Submonoid.mrange_inl'
 #align add_submonoid.mrange_inl' AddSubmonoid.mrange_inl'
+-/
 
+#print Submonoid.mrange_inr' /-
 @[to_additive]
 theorem mrange_inr' : (inr M N).mrange = comap (fst M N) ⊥ :=
   mrange_inr.trans (prod_top _)
 #align submonoid.mrange_inr' Submonoid.mrange_inr'
 #align add_submonoid.mrange_inr' AddSubmonoid.mrange_inr'
+-/
 
+#print Submonoid.mrange_fst /-
 @[simp, to_additive]
 theorem mrange_fst : (fst M N).mrange = ⊤ :=
   mrange_top_of_surjective (fst M N) <| @Prod.fst_surjective _ _ ⟨1⟩
 #align submonoid.mrange_fst Submonoid.mrange_fst
 #align add_submonoid.mrange_fst AddSubmonoid.mrange_fst
+-/
 
+#print Submonoid.mrange_snd /-
 @[simp, to_additive]
 theorem mrange_snd : (snd M N).mrange = ⊤ :=
   mrange_top_of_surjective (snd M N) <| @Prod.snd_surjective _ _ ⟨1⟩
 #align submonoid.mrange_snd Submonoid.mrange_snd
 #align add_submonoid.mrange_snd AddSubmonoid.mrange_snd
+-/
 
+#print Submonoid.prod_eq_bot_iff /-
 @[to_additive]
 theorem prod_eq_bot_iff {s : Submonoid M} {t : Submonoid N} : s.Prod t = ⊥ ↔ s = ⊥ ∧ t = ⊥ := by
   simp only [eq_bot_iff, prod_le_iff, (gc_map_comap _).le_iff_le, comap_bot', mker_inl, mker_inr]
 #align submonoid.prod_eq_bot_iff Submonoid.prod_eq_bot_iff
 #align add_submonoid.sum_eq_bot_iff AddSubmonoid.prod_eq_bot_iff
+-/
 
+#print Submonoid.prod_eq_top_iff /-
 @[to_additive]
 theorem prod_eq_top_iff {s : Submonoid M} {t : Submonoid N} : s.Prod t = ⊤ ↔ s = ⊤ ∧ t = ⊤ := by
   simp only [eq_top_iff, le_prod_iff, ← (gc_map_comap _).le_iff_le, ← mrange_eq_map, mrange_fst,
     mrange_snd]
 #align submonoid.prod_eq_top_iff Submonoid.prod_eq_top_iff
 #align add_submonoid.sum_eq_top_iff AddSubmonoid.prod_eq_top_iff
+-/
 
+#print Submonoid.mrange_inl_sup_mrange_inr /-
 @[simp, to_additive]
 theorem mrange_inl_sup_mrange_inr : (inl M N).mrange ⊔ (inr M N).mrange = ⊤ := by
   simp only [mrange_inl, mrange_inr, prod_bot_sup_bot_prod, top_prod_top]
 #align submonoid.mrange_inl_sup_mrange_inr Submonoid.mrange_inl_sup_mrange_inr
 #align add_submonoid.mrange_inl_sup_mrange_inr AddSubmonoid.mrange_inl_sup_mrange_inr
+-/
 
+#print Submonoid.inclusion /-
 /-- The monoid hom associated to an inclusion of submonoids. -/
 @[to_additive "The `add_monoid` hom associated to an inclusion of submonoids."]
 def inclusion {S T : Submonoid M} (h : S ≤ T) : S →* T :=
   S.Subtype.codRestrict _ fun x => h x.2
 #align submonoid.inclusion Submonoid.inclusion
 #align add_submonoid.inclusion AddSubmonoid.inclusion
+-/
 
+#print Submonoid.range_subtype /-
 @[simp, to_additive]
 theorem range_subtype (s : Submonoid M) : s.Subtype.mrange = s :=
   SetLike.coe_injective <| (coe_mrange _).trans <| Subtype.range_coe
 #align submonoid.range_subtype Submonoid.range_subtype
 #align add_submonoid.range_subtype AddSubmonoid.range_subtype
+-/
 
+#print Submonoid.eq_top_iff' /-
 @[to_additive]
 theorem eq_top_iff' : S = ⊤ ↔ ∀ x : M, x ∈ S :=
   eq_top_iff.trans ⟨fun h m => h <| mem_top m, fun h m _ => h m⟩
 #align submonoid.eq_top_iff' Submonoid.eq_top_iff'
 #align add_submonoid.eq_top_iff' AddSubmonoid.eq_top_iff'
+-/
 
+#print Submonoid.eq_bot_iff_forall /-
 @[to_additive]
 theorem eq_bot_iff_forall : S = ⊥ ↔ ∀ x ∈ S, x = (1 : M) :=
   SetLike.ext_iff.trans <| by simp (config := { contextual := true }) [iff_def, S.one_mem]
 #align submonoid.eq_bot_iff_forall Submonoid.eq_bot_iff_forall
 #align add_submonoid.eq_bot_iff_forall AddSubmonoid.eq_bot_iff_forall
+-/
 
+#print Submonoid.nontrivial_iff_exists_ne_one /-
 @[to_additive]
 theorem nontrivial_iff_exists_ne_one (S : Submonoid M) : Nontrivial S ↔ ∃ x ∈ S, x ≠ (1 : M) :=
   calc
@@ -1423,14 +1662,18 @@ theorem nontrivial_iff_exists_ne_one (S : Submonoid M) : Nontrivial S ↔ ∃ x
     _ ↔ ∃ x ∈ S, x ≠ (1 : M) := by simp only [Ne.def]
 #align submonoid.nontrivial_iff_exists_ne_one Submonoid.nontrivial_iff_exists_ne_one
 #align add_submonoid.nontrivial_iff_exists_ne_zero AddSubmonoid.nontrivial_iff_exists_ne_zero
+-/
 
+#print Submonoid.bot_or_nontrivial /-
 /-- A submonoid is either the trivial submonoid or nontrivial. -/
 @[to_additive "An additive submonoid is either the trivial additive submonoid or nontrivial."]
 theorem bot_or_nontrivial (S : Submonoid M) : S = ⊥ ∨ Nontrivial S := by
   simp only [eq_bot_iff_forall, nontrivial_iff_exists_ne_one, ← not_forall, Classical.em]
 #align submonoid.bot_or_nontrivial Submonoid.bot_or_nontrivial
 #align add_submonoid.bot_or_nontrivial AddSubmonoid.bot_or_nontrivial
+-/
 
+#print Submonoid.bot_or_exists_ne_one /-
 /-- A submonoid is either the trivial submonoid or contains a nonzero element. -/
 @[to_additive
       "An additive submonoid is either the trivial additive submonoid or contains a nonzero\nelement."]
@@ -1438,6 +1681,7 @@ theorem bot_or_exists_ne_one (S : Submonoid M) : S = ⊥ ∨ ∃ x ∈ S, x ≠
   S.bot_or_nontrivial.imp_right S.nontrivial_iff_exists_ne_one.mp
 #align submonoid.bot_or_exists_ne_one Submonoid.bot_or_exists_ne_one
 #align add_submonoid.bot_or_exists_ne_zero AddSubmonoid.bot_or_exists_ne_zero
+-/
 
 end Submonoid
 
@@ -1445,6 +1689,7 @@ namespace MulEquiv
 
 variable {S} {T : Submonoid M}
 
+#print MulEquiv.submonoidCongr /-
 /-- Makes the identity isomorphism from a proof that two submonoids of a multiplicative
     monoid are equal. -/
 @[to_additive
@@ -1453,7 +1698,9 @@ def submonoidCongr (h : S = T) : S ≃* T :=
   { Equiv.setCongr <| congr_arg _ h with map_mul' := fun _ _ => rfl }
 #align mul_equiv.submonoid_congr MulEquiv.submonoidCongr
 #align add_equiv.add_submonoid_congr AddEquiv.addSubmonoidCongr
+-/
 
+#print MulEquiv.ofLeftInverse' /-
 -- this name is primed so that the version to `f.range` instead of `f.mrange` can be unprimed.
 /-- A monoid homomorphism `f : M →* N` with a left-inverse `g : N → M` defines a multiplicative
 equivalence between `M` and `f.mrange`.
@@ -1473,7 +1720,9 @@ def ofLeftInverse' (f : M →* N) {g : N → M} (h : Function.LeftInverse g f) :
         show f (g x) = x by rw [← hx', h x'] }
 #align mul_equiv.of_left_inverse' MulEquiv.ofLeftInverse'
 #align add_equiv.of_left_inverse' AddEquiv.ofLeftInverse'
+-/
 
+#print MulEquiv.submonoidMap /-
 /-- A `mul_equiv` `φ` between two monoids `M` and `N` induces a `mul_equiv` between
 a submonoid `S ≤ M` and the submonoid `φ(S) ≤ N`.
 See `monoid_hom.submonoid_map` for a variant for `monoid_hom`s. -/
@@ -1483,28 +1732,35 @@ def submonoidMap (e : M ≃* N) (S : Submonoid M) : S ≃* S.map e.toMonoidHom :
   { (e : M ≃ N).image S with map_mul' := fun _ _ => Subtype.ext (map_mul e _ _) }
 #align mul_equiv.submonoid_map MulEquiv.submonoidMap
 #align add_equiv.add_submonoid_map AddEquiv.addSubmonoidMap
+-/
 
+#print MulEquiv.coe_submonoidMap_apply /-
 @[simp, to_additive]
 theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
     ((submonoidMap e S g : S.map (e : M →* N)) : N) = e g :=
   rfl
 #align mul_equiv.coe_submonoid_map_apply MulEquiv.coe_submonoidMap_apply
 #align add_equiv.coe_add_submonoid_map_apply AddEquiv.coe_addSubmonoidMap_apply
+-/
 
+#print MulEquiv.submonoidMap_symm_apply /-
 @[simp, to_additive AddEquiv.add_submonoid_map_symm_apply]
 theorem submonoidMap_symm_apply (e : M ≃* N) (S : Submonoid M) (g : S.map (e : M →* N)) :
     (e.submonoidMap S).symm g = ⟨e.symm g, SetLike.mem_coe.1 <| Set.mem_image_equiv.1 g.2⟩ :=
   rfl
 #align mul_equiv.submonoid_map_symm_apply MulEquiv.submonoidMap_symm_apply
 #align add_equiv.add_submonoid_map_symm_apply AddEquiv.add_submonoid_map_symm_apply
+-/
 
 end MulEquiv
 
+#print Submonoid.equivMapOfInjective_coe_mulEquiv /-
 @[simp, to_additive]
 theorem Submonoid.equivMapOfInjective_coe_mulEquiv (e : M ≃* N) :
     S.equivMapOfInjective (e : M →* N) (EquivLike.injective e) = e.submonoidMap S := by ext; rfl
 #align submonoid.equiv_map_of_injective_coe_mul_equiv Submonoid.equivMapOfInjective_coe_mulEquiv
 #align add_submonoid.equiv_map_of_injective_coe_add_equiv AddSubmonoid.equivMapOfInjective_coe_addEquiv
+-/
 
 section Actions
 
@@ -1530,30 +1786,36 @@ variable [MulOneClass M']
 instance [SMul M' α] (S : Submonoid M') : SMul S α :=
   SMul.comp _ S.Subtype
 
+#print Submonoid.smulCommClass_left /-
 @[to_additive]
 instance smulCommClass_left [SMul M' β] [SMul α β] [SMulCommClass M' α β] (S : Submonoid M') :
     SMulCommClass S α β :=
   ⟨fun a => (smul_comm (a : M') : _)⟩
 #align submonoid.smul_comm_class_left Submonoid.smulCommClass_left
 #align add_submonoid.vadd_comm_class_left AddSubmonoid.vaddCommClass_left
+-/
 
+#print Submonoid.smulCommClass_right /-
 @[to_additive]
 instance smulCommClass_right [SMul α β] [SMul M' β] [SMulCommClass α M' β] (S : Submonoid M') :
     SMulCommClass α S β :=
   ⟨fun a s => (smul_comm a (s : M') : _)⟩
 #align submonoid.smul_comm_class_right Submonoid.smulCommClass_right
 #align add_submonoid.vadd_comm_class_right AddSubmonoid.vaddCommClass_right
+-/
 
 /-- Note that this provides `is_scalar_tower S M' M'` which is needed by `smul_mul_assoc`. -/
 instance [SMul α β] [SMul M' α] [SMul M' β] [IsScalarTower M' α β] (S : Submonoid M') :
     IsScalarTower S α β :=
   ⟨fun a => (smul_assoc (a : M') : _)⟩
 
+#print Submonoid.smul_def /-
 @[to_additive]
 theorem smul_def [SMul M' α] {S : Submonoid M'} (g : S) (m : α) : g • m = (g : M') • m :=
   rfl
 #align submonoid.smul_def Submonoid.smul_def
 #align add_submonoid.vadd_def AddSubmonoid.vadd_def
+-/
 
 instance [SMul M' α] [FaithfulSMul M' α] (S : Submonoid M') : FaithfulSMul S α :=
   ⟨fun x y h => Subtype.ext <| eq_of_smul_eq_smul h⟩

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

@@ -1421,7 +1421,6 @@ theorem nontrivial_iff_exists_ne_one (S : Submonoid M) : Nontrivial S ↔ ∃ x
     Nontrivial S ↔ ∃ x : S, x ≠ 1 := nontrivial_iff_exists_ne 1
     _ ↔ ∃ (x : _) (hx : x ∈ S), (⟨x, hx⟩ : S) ≠ ⟨1, S.one_mem⟩ := Subtype.exists
     _ ↔ ∃ x ∈ S, x ≠ (1 : M) := by simp only [Ne.def]
-    
 #align submonoid.nontrivial_iff_exists_ne_one Submonoid.nontrivial_iff_exists_ne_one
 #align add_submonoid.nontrivial_iff_exists_ne_zero AddSubmonoid.nontrivial_iff_exists_ne_zero
 

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

@@ -1419,7 +1419,7 @@ theorem eq_bot_iff_forall : S = ⊥ ↔ ∀ x ∈ S, x = (1 : M) :=
 theorem nontrivial_iff_exists_ne_one (S : Submonoid M) : Nontrivial S ↔ ∃ x ∈ S, x ≠ (1 : M) :=
   calc
     Nontrivial S ↔ ∃ x : S, x ≠ 1 := nontrivial_iff_exists_ne 1
-    _ ↔ ∃ (x : _)(hx : x ∈ S), (⟨x, hx⟩ : S) ≠ ⟨1, S.one_mem⟩ := Subtype.exists
+    _ ↔ ∃ (x : _) (hx : x ∈ S), (⟨x, hx⟩ : S) ≠ ⟨1, S.one_mem⟩ := Subtype.exists
     _ ↔ ∃ x ∈ S, x ≠ (1 : M) := by simp only [Ne.def]
     
 #align submonoid.nontrivial_iff_exists_ne_one Submonoid.nontrivial_iff_exists_ne_one

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

@@ -773,13 +773,12 @@ protected theorem pow_mem {M : Type _} [Monoid M] (S : Submonoid M) {x : M} (hx
 #align submonoid.pow_mem Submonoid.pow_mem
 #align add_submonoid.nsmul_mem AddSubmonoid.nsmul_mem
 
-/- warning: submonoid.coe_pow clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align submonoid.coe_pow [anonymous]ₓ'. -/
 @[simp, norm_cast, to_additive]
-theorem [anonymous] {M : Type _} [Monoid M] {S : Submonoid M} (x : S) (n : ℕ) :
+theorem coe_pow {M : Type _} [Monoid M] {S : Submonoid M} (x : S) (n : ℕ) :
     ↑(x ^ n) = (x ^ n : M) :=
   rfl
-#align submonoid.coe_pow [anonymous]
+#align submonoid.coe_pow Submonoid.coe_pow
+#align add_submonoid.coe_nsmul AddSubmonoid.coe_nsmul
 
 /-- A submonoid of a monoid inherits a monoid structure. -/
 @[to_additive "An `add_submonoid` of an `add_monoid` inherits an `add_monoid`\nstructure."]

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

@@ -80,12 +80,6 @@ variable {M N P : Type _} [MulOneClass M] [MulOneClass N] [MulOneClass P] (S : S
 
 section
 
-/- warning: submonoid.to_add_submonoid -> Submonoid.toAddSubmonoid is a dubious translation:
-lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M], OrderIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))
-but is expected to have type
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 /-- Submonoids of monoid `M` are isomorphic to additive submonoids of `additive M`. -/
 @[simps]
 def Submonoid.toAddSubmonoid : Submonoid M ≃o AddSubmonoid (Additive M)
@@ -103,20 +97,11 @@ def Submonoid.toAddSubmonoid : Submonoid M ≃o AddSubmonoid (Additive M)
   map_rel_iff' a b := Iff.rfl
 #align submonoid.to_add_submonoid Submonoid.toAddSubmonoid
 
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 /-- Additive submonoids of an additive monoid `additive M` are isomorphic to submonoids of `M`. -/
 abbrev AddSubmonoid.toSubmonoid' : AddSubmonoid (Additive M) ≃o Submonoid M :=
   Submonoid.toAddSubmonoid.symm
 #align add_submonoid.to_submonoid' AddSubmonoid.toSubmonoid'
 
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-<too large>
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 theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
     (Submonoid.closure S).toAddSubmonoid = AddSubmonoid.closure (Additive.toMul ⁻¹' S) :=
   le_antisymm
@@ -124,9 +109,6 @@ theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
     (AddSubmonoid.closure_le.2 Submonoid.subset_closure)
 #align submonoid.to_add_submonoid_closure Submonoid.toAddSubmonoid_closure
 
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 theorem AddSubmonoid.toSubmonoid'_closure (S : Set (Additive M)) :
     (AddSubmonoid.closure S).toSubmonoid' = Submonoid.closure (Multiplicative.ofAdd ⁻¹' S) :=
   le_antisymm
@@ -141,12 +123,6 @@ section
 
 variable {A : Type _} [AddZeroClass A]
 
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 /-- Additive submonoids of an additive monoid `A` are isomorphic to
 multiplicative submonoids of `multiplicative A`. -/
 @[simps]
@@ -165,20 +141,11 @@ def AddSubmonoid.toSubmonoid : AddSubmonoid A ≃o Submonoid (Multiplicative A)
   map_rel_iff' a b := Iff.rfl
 #align add_submonoid.to_submonoid AddSubmonoid.toSubmonoid
 
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 /-- Submonoids of a monoid `multiplicative A` are isomorphic to additive submonoids of `A`. -/
 abbrev Submonoid.toAddSubmonoid' : Submonoid (Multiplicative A) ≃o AddSubmonoid A :=
   AddSubmonoid.toSubmonoid.symm
 #align submonoid.to_add_submonoid' Submonoid.toAddSubmonoid'
 
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 theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
     (AddSubmonoid.closure S).toSubmonoid = Submonoid.closure (Multiplicative.toAdd ⁻¹' S) :=
   le_antisymm
@@ -187,9 +154,6 @@ theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
     (Submonoid.closure_le.2 AddSubmonoid.subset_closure)
 #align add_submonoid.to_submonoid_closure AddSubmonoid.toSubmonoid_closure
 
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 theorem Submonoid.toAddSubmonoid'_closure (S : Set (Multiplicative A)) :
     (Submonoid.closure S).toAddSubmonoid' = AddSubmonoid.closure (Additive.ofMul ⁻¹' S) :=
   le_antisymm
@@ -226,24 +190,12 @@ def comap (f : F) (S : Submonoid N) : Submonoid M
 #align add_submonoid.comap AddSubmonoid.comap
 -/
 
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 @[simp, to_additive]
 theorem coe_comap (S : Submonoid N) (f : F) : (S.comap f : Set M) = f ⁻¹' S :=
   rfl
 #align submonoid.coe_comap Submonoid.coe_comap
 #align add_submonoid.coe_comap AddSubmonoid.coe_comap
 
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 @[simp, to_additive]
 theorem mem_comap {S : Submonoid N} {f : F} {x : M} : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
@@ -285,48 +237,24 @@ def map (f : F) (S : Submonoid M) : Submonoid N
 #align add_submonoid.map AddSubmonoid.map
 -/
 
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 @[simp, to_additive]
 theorem coe_map (f : F) (S : Submonoid M) : (S.map f : Set N) = f '' S :=
   rfl
 #align submonoid.coe_map Submonoid.coe_map
 #align add_submonoid.coe_map AddSubmonoid.coe_map
 
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 @[simp, to_additive]
 theorem mem_map {f : F} {S : Submonoid M} {y : N} : y ∈ S.map f ↔ ∃ x ∈ S, f x = y :=
   mem_image_iff_bex
 #align submonoid.mem_map Submonoid.mem_map
 #align add_submonoid.mem_map AddSubmonoid.mem_map
 
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 @[to_additive]
 theorem mem_map_of_mem (f : F) {S : Submonoid M} {x : M} (hx : x ∈ S) : f x ∈ S.map f :=
   mem_image_of_mem f hx
 #align submonoid.mem_map_of_mem Submonoid.mem_map_of_mem
 #align add_submonoid.mem_map_of_mem AddSubmonoid.mem_map_of_mem
 
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 @[to_additive]
 theorem apply_coe_mem_map (f : F) (S : Submonoid M) (x : S) : f x ∈ S.map f :=
   mem_map_of_mem f x.Prop
@@ -335,12 +263,6 @@ theorem apply_coe_mem_map (f : F) (S : Submonoid M) (x : S) : f x ∈ S.map f :=
 
 omit mc
 
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 @[to_additive]
 theorem map_map (g : N →* P) (f : M →* N) : (S.map f).map g = S.map (g.comp f) :=
   SetLike.coe_injective <| image_image _ _ _
@@ -349,12 +271,6 @@ theorem map_map (g : N →* P) (f : M →* N) : (S.map f).map g = S.map (g.comp
 
 include mc
 
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 @[to_additive]
 theorem mem_map_iff_mem {f : F} (hf : Function.Injective f) {S : Submonoid M} {x : M} :
     f x ∈ S.map f ↔ x ∈ S :=
@@ -362,12 +278,6 @@ theorem mem_map_iff_mem {f : F} (hf : Function.Injective f) {S : Submonoid M} {x
 #align submonoid.mem_map_iff_mem Submonoid.mem_map_iff_mem
 #align add_submonoid.mem_map_iff_mem AddSubmonoid.mem_map_iff_mem
 
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 @[to_additive]
 theorem map_le_iff_le_comap {f : F} {S : Submonoid M} {T : Submonoid N} :
     S.map f ≤ T ↔ S ≤ T.comap f :=
@@ -375,155 +285,77 @@ theorem map_le_iff_le_comap {f : F} {S : Submonoid M} {T : Submonoid N} :
 #align submonoid.map_le_iff_le_comap Submonoid.map_le_iff_le_comap
 #align add_submonoid.map_le_iff_le_comap AddSubmonoid.map_le_iff_le_comap
 
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 @[to_additive]
 theorem gc_map_comap (f : F) : GaloisConnection (map f) (comap f) := fun S T => map_le_iff_le_comap
 #align submonoid.gc_map_comap Submonoid.gc_map_comap
 #align add_submonoid.gc_map_comap AddSubmonoid.gc_map_comap
 
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 @[to_additive]
 theorem map_le_of_le_comap {T : Submonoid N} {f : F} : S ≤ T.comap f → S.map f ≤ T :=
   (gc_map_comap f).l_le
 #align submonoid.map_le_of_le_comap Submonoid.map_le_of_le_comap
 #align add_submonoid.map_le_of_le_comap AddSubmonoid.map_le_of_le_comap
 
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 @[to_additive]
 theorem le_comap_of_map_le {T : Submonoid N} {f : F} : S.map f ≤ T → S ≤ T.comap f :=
   (gc_map_comap f).le_u
 #align submonoid.le_comap_of_map_le Submonoid.le_comap_of_map_le
 #align add_submonoid.le_comap_of_map_le AddSubmonoid.le_comap_of_map_le
 
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 @[to_additive]
 theorem le_comap_map {f : F} : S ≤ (S.map f).comap f :=
   (gc_map_comap f).le_u_l _
 #align submonoid.le_comap_map Submonoid.le_comap_map
 #align add_submonoid.le_comap_map AddSubmonoid.le_comap_map
 
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 @[to_additive]
 theorem map_comap_le {S : Submonoid N} {f : F} : (S.comap f).map f ≤ S :=
   (gc_map_comap f).l_u_le _
 #align submonoid.map_comap_le Submonoid.map_comap_le
 #align add_submonoid.map_comap_le AddSubmonoid.map_comap_le
 
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 @[to_additive]
 theorem monotone_map {f : F} : Monotone (map f) :=
   (gc_map_comap f).monotone_l
 #align submonoid.monotone_map Submonoid.monotone_map
 #align add_submonoid.monotone_map AddSubmonoid.monotone_map
 
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 @[to_additive]
 theorem monotone_comap {f : F} : Monotone (comap f) :=
   (gc_map_comap f).monotone_u
 #align submonoid.monotone_comap Submonoid.monotone_comap
 #align add_submonoid.monotone_comap AddSubmonoid.monotone_comap
 
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 @[simp, to_additive]
 theorem map_comap_map {f : F} : ((S.map f).comap f).map f = S.map f :=
   (gc_map_comap f).l_u_l_eq_l _
 #align submonoid.map_comap_map Submonoid.map_comap_map
 #align add_submonoid.map_comap_map AddSubmonoid.map_comap_map
 
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 @[simp, to_additive]
 theorem comap_map_comap {S : Submonoid N} {f : F} : ((S.comap f).map f).comap f = S.comap f :=
   (gc_map_comap f).u_l_u_eq_u _
 #align submonoid.comap_map_comap Submonoid.comap_map_comap
 #align add_submonoid.comap_map_comap AddSubmonoid.comap_map_comap
 
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 @[to_additive]
 theorem map_sup (S T : Submonoid M) (f : F) : (S ⊔ T).map f = S.map f ⊔ T.map f :=
   (gc_map_comap f : GaloisConnection (map f) (comap f)).l_sup
 #align submonoid.map_sup Submonoid.map_sup
 #align add_submonoid.map_sup AddSubmonoid.map_sup
 
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 @[to_additive]
 theorem map_iSup {ι : Sort _} (f : F) (s : ι → Submonoid M) : (iSup s).map f = ⨆ i, (s i).map f :=
   (gc_map_comap f : GaloisConnection (map f) (comap f)).l_iSup
 #align submonoid.map_supr Submonoid.map_iSup
 #align add_submonoid.map_supr AddSubmonoid.map_iSup
 
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 @[to_additive]
 theorem comap_inf (S T : Submonoid N) (f : F) : (S ⊓ T).comap f = S.comap f ⊓ T.comap f :=
   (gc_map_comap f : GaloisConnection (map f) (comap f)).u_inf
 #align submonoid.comap_inf Submonoid.comap_inf
 #align add_submonoid.comap_inf AddSubmonoid.comap_inf
 
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 @[to_additive]
 theorem comap_iInf {ι : Sort _} (f : F) (s : ι → Submonoid N) :
     (iInf s).comap f = ⨅ i, (s i).comap f :=
@@ -531,24 +363,12 @@ theorem comap_iInf {ι : Sort _} (f : F) (s : ι → Submonoid N) :
 #align submonoid.comap_infi Submonoid.comap_iInf
 #align add_submonoid.comap_infi AddSubmonoid.comap_iInf
 
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 @[simp, to_additive]
 theorem map_bot (f : F) : (⊥ : Submonoid M).map f = ⊥ :=
   (gc_map_comap f).l_bot
 #align submonoid.map_bot Submonoid.map_bot
 #align add_submonoid.map_bot AddSubmonoid.map_bot
 
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 @[simp, to_additive]
 theorem comap_top (f : F) : (⊤ : Submonoid N).comap f = ⊤ :=
   (gc_map_comap f).u_top
@@ -571,12 +391,6 @@ variable {ι : Type _} {f : F} (hf : Function.Injective f)
 
 include hf
 
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 /-- `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. -/
 @[to_additive " `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. "]
 def gciMapComap : GaloisCoinsertion (map f) (comap f) :=
@@ -584,108 +398,54 @@ def gciMapComap : GaloisCoinsertion (map f) (comap f) :=
 #align submonoid.gci_map_comap Submonoid.gciMapComap
 #align add_submonoid.gci_map_comap AddSubmonoid.gciMapComap
 
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 @[to_additive]
 theorem comap_map_eq_of_injective (S : Submonoid M) : (S.map f).comap f = S :=
   (gciMapComap hf).u_l_eq _
 #align submonoid.comap_map_eq_of_injective Submonoid.comap_map_eq_of_injective
 #align add_submonoid.comap_map_eq_of_injective AddSubmonoid.comap_map_eq_of_injective
 
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 @[to_additive]
 theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
   (gciMapComap hf).u_surjective
 #align submonoid.comap_surjective_of_injective Submonoid.comap_surjective_of_injective
 #align add_submonoid.comap_surjective_of_injective AddSubmonoid.comap_surjective_of_injective
 
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 @[to_additive]
 theorem map_injective_of_injective : Function.Injective (map f) :=
   (gciMapComap hf).l_injective
 #align submonoid.map_injective_of_injective Submonoid.map_injective_of_injective
 #align add_submonoid.map_injective_of_injective AddSubmonoid.map_injective_of_injective
 
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 @[to_additive]
 theorem comap_inf_map_of_injective (S T : Submonoid M) : (S.map f ⊓ T.map f).comap f = S ⊓ T :=
   (gciMapComap hf).u_inf_l _ _
 #align submonoid.comap_inf_map_of_injective Submonoid.comap_inf_map_of_injective
 #align add_submonoid.comap_inf_map_of_injective AddSubmonoid.comap_inf_map_of_injective
 
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 @[to_additive]
 theorem comap_iInf_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).map f).comap f = iInf S :=
   (gciMapComap hf).u_iInf_l _
 #align submonoid.comap_infi_map_of_injective Submonoid.comap_iInf_map_of_injective
 #align add_submonoid.comap_infi_map_of_injective AddSubmonoid.comap_iInf_map_of_injective
 
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 @[to_additive]
 theorem comap_sup_map_of_injective (S T : Submonoid M) : (S.map f ⊔ T.map f).comap f = S ⊔ T :=
   (gciMapComap hf).u_sup_l _ _
 #align submonoid.comap_sup_map_of_injective Submonoid.comap_sup_map_of_injective
 #align add_submonoid.comap_sup_map_of_injective AddSubmonoid.comap_sup_map_of_injective
 
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 @[to_additive]
 theorem comap_iSup_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).map f).comap f = iSup S :=
   (gciMapComap hf).u_iSup_l _
 #align submonoid.comap_supr_map_of_injective Submonoid.comap_iSup_map_of_injective
 #align add_submonoid.comap_supr_map_of_injective AddSubmonoid.comap_iSup_map_of_injective
 
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 @[to_additive]
 theorem map_le_map_iff_of_injective {S T : Submonoid M} : S.map f ≤ T.map f ↔ S ≤ T :=
   (gciMapComap hf).l_le_l_iff
 #align submonoid.map_le_map_iff_of_injective Submonoid.map_le_map_iff_of_injective
 #align add_submonoid.map_le_map_iff_of_injective AddSubmonoid.map_le_map_iff_of_injective
 
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 @[to_additive]
 theorem map_strictMono_of_injective : StrictMono (map f) :=
   (gciMapComap hf).strictMono_l
@@ -700,12 +460,6 @@ variable {ι : Type _} {f : F} (hf : Function.Surjective f)
 
 include hf
 
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 /-- `map f` and `comap f` form a `galois_insertion` when `f` is surjective. -/
 @[to_additive " `map f` and `comap f` form a `galois_insertion` when `f` is surjective. "]
 def giMapComap : GaloisInsertion (map f) (comap f) :=
@@ -715,108 +469,54 @@ def giMapComap : GaloisInsertion (map f) (comap f) :=
 #align submonoid.gi_map_comap Submonoid.giMapComap
 #align add_submonoid.gi_map_comap AddSubmonoid.giMapComap
 
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 @[to_additive]
 theorem map_comap_eq_of_surjective (S : Submonoid N) : (S.comap f).map f = S :=
   (giMapComap hf).l_u_eq _
 #align submonoid.map_comap_eq_of_surjective Submonoid.map_comap_eq_of_surjective
 #align add_submonoid.map_comap_eq_of_surjective AddSubmonoid.map_comap_eq_of_surjective
 
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 @[to_additive]
 theorem map_surjective_of_surjective : Function.Surjective (map f) :=
   (giMapComap hf).l_surjective
 #align submonoid.map_surjective_of_surjective Submonoid.map_surjective_of_surjective
 #align add_submonoid.map_surjective_of_surjective AddSubmonoid.map_surjective_of_surjective
 
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 @[to_additive]
 theorem comap_injective_of_surjective : Function.Injective (comap f) :=
   (giMapComap hf).u_injective
 #align submonoid.comap_injective_of_surjective Submonoid.comap_injective_of_surjective
 #align add_submonoid.comap_injective_of_surjective AddSubmonoid.comap_injective_of_surjective
 
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 @[to_additive]
 theorem map_inf_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊓ T.comap f).map f = S ⊓ T :=
   (giMapComap hf).l_inf_u _ _
 #align submonoid.map_inf_comap_of_surjective Submonoid.map_inf_comap_of_surjective
 #align add_submonoid.map_inf_comap_of_surjective AddSubmonoid.map_inf_comap_of_surjective
 
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 @[to_additive]
 theorem map_iInf_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).comap f).map f = iInf S :=
   (giMapComap hf).l_iInf_u _
 #align submonoid.map_infi_comap_of_surjective Submonoid.map_iInf_comap_of_surjective
 #align add_submonoid.map_infi_comap_of_surjective AddSubmonoid.map_iInf_comap_of_surjective
 
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 @[to_additive]
 theorem map_sup_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊔ T.comap f).map f = S ⊔ T :=
   (giMapComap hf).l_sup_u _ _
 #align submonoid.map_sup_comap_of_surjective Submonoid.map_sup_comap_of_surjective
 #align add_submonoid.map_sup_comap_of_surjective AddSubmonoid.map_sup_comap_of_surjective
 
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 @[to_additive]
 theorem map_iSup_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).comap f).map f = iSup S :=
   (giMapComap hf).l_iSup_u _
 #align submonoid.map_supr_comap_of_surjective Submonoid.map_iSup_comap_of_surjective
 #align add_submonoid.map_supr_comap_of_surjective AddSubmonoid.map_iSup_comap_of_surjective
 
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 @[to_additive]
 theorem comap_le_comap_iff_of_surjective {S T : Submonoid N} : S.comap f ≤ T.comap f ↔ S ≤ T :=
   (giMapComap hf).u_le_u_iff
 #align submonoid.comap_le_comap_iff_of_surjective Submonoid.comap_le_comap_iff_of_surjective
 #align add_submonoid.comap_le_comap_iff_of_surjective AddSubmonoid.comap_le_comap_iff_of_surjective
 
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 @[to_additive]
 theorem comap_strictMono_of_surjective : StrictMono (comap f) :=
   (giMapComap hf).strictMono_u
@@ -893,12 +593,6 @@ instance nPow {M} [Monoid M] {A : Type _} [SetLike A M] [SubmonoidClass A M] (S
 
 attribute [to_additive] SubmonoidClass.nPow
 
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 @[simp, norm_cast, to_additive]
 theorem coe_pow {M} [Monoid M] {A : Type _} [SetLike A M] [SubmonoidClass A M] {S : A} (x : S)
     (n : ℕ) : (↑(x ^ n) : M) = ↑x ^ n :=
@@ -906,12 +600,6 @@ theorem coe_pow {M} [Monoid M] {A : Type _} [SetLike A M] [SubmonoidClass A M] {
 #align submonoid_class.coe_pow SubmonoidClass.coe_pow
 #align add_submonoid_class.coe_nsmul AddSubmonoidClass.coe_nsmul
 
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 @[simp, to_additive]
 theorem mk_pow {M} [Monoid M] {A : Type _} [SetLike A M] [SubmonoidClass A M] {S : A} (x : M)
     (hx : x ∈ S) (n : ℕ) : (⟨x, hx⟩ : S) ^ n = ⟨x ^ n, pow_mem hx n⟩ :=
@@ -1015,12 +703,6 @@ def Subtype : S' →* M :=
 #align add_submonoid_class.subtype AddSubmonoidClass.Subtype
 -/
 
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 @[simp, to_additive]
 theorem coe_subtype : (SubmonoidClass.Subtype S' : S' → M) = coe :=
   rfl
@@ -1031,12 +713,6 @@ end SubmonoidClass
 
 namespace Submonoid
 
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 /-- A submonoid of a monoid inherits a multiplication. -/
 @[to_additive "An `add_submonoid` of an `add_monoid` inherits an addition."]
 instance mul : Mul S :=
@@ -1044,12 +720,6 @@ instance mul : Mul S :=
 #align submonoid.has_mul Submonoid.mul
 #align add_submonoid.has_add AddSubmonoid.add
 
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 /-- A submonoid of a monoid inherits a 1. -/
 @[to_additive "An `add_submonoid` of an `add_monoid` inherits a zero."]
 instance one : One S :=
@@ -1057,36 +727,18 @@ instance one : One S :=
 #align submonoid.has_one Submonoid.one
 #align add_submonoid.has_zero AddSubmonoid.zero
 
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 @[simp, norm_cast, to_additive]
 theorem coe_mul (x y : S) : (↑(x * y) : M) = ↑x * ↑y :=
   rfl
 #align submonoid.coe_mul Submonoid.coe_mul
 #align add_submonoid.coe_add AddSubmonoid.coe_add
 
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 @[simp, norm_cast, to_additive]
 theorem coe_one : ((1 : S) : M) = 1 :=
   rfl
 #align submonoid.coe_one Submonoid.coe_one
 #align add_submonoid.coe_zero AddSubmonoid.coe_zero
 
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 @[simp, to_additive]
 theorem mk_mul_mk (x y : M) (hx : x ∈ S) (hy : y ∈ S) :
     (⟨x, hx⟩ : S) * ⟨y, hy⟩ = ⟨x * y, S.mul_mem hx hy⟩ :=
@@ -1094,36 +746,18 @@ theorem mk_mul_mk (x y : M) (hx : x ∈ S) (hy : y ∈ S) :
 #align submonoid.mk_mul_mk Submonoid.mk_mul_mk
 #align add_submonoid.mk_add_mk AddSubmonoid.mk_add_mk
 
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 @[to_additive]
 theorem mul_def (x y : S) : x * y = ⟨x * y, S.mul_mem x.2 y.2⟩ :=
   rfl
 #align submonoid.mul_def Submonoid.mul_def
 #align add_submonoid.add_def AddSubmonoid.add_def
 
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 @[to_additive]
 theorem one_def : (1 : S) = ⟨1, S.one_mem⟩ :=
   rfl
 #align submonoid.one_def Submonoid.one_def
 #align add_submonoid.zero_def AddSubmonoid.zero_def
 
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 /-- A submonoid of a unital magma inherits a unital magma structure. -/
 @[to_additive
       "An `add_submonoid` of an unital additive magma inherits an unital additive magma\nstructure."]
@@ -1132,12 +766,6 @@ instance toMulOneClass {M : Type _} [MulOneClass M] (S : Submonoid M) : MulOneCl
 #align submonoid.to_mul_one_class Submonoid.toMulOneClass
 #align add_submonoid.to_add_zero_class AddSubmonoid.toAddZeroClass
 
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 @[to_additive]
 protected theorem pow_mem {M : Type _} [Monoid M] (S : Submonoid M) {x : M} (hx : x ∈ S) (n : ℕ) :
     x ^ n ∈ S :=
@@ -1146,11 +774,6 @@ protected theorem pow_mem {M : Type _} [Monoid M] (S : Submonoid M) {x : M} (hx
 #align add_submonoid.nsmul_mem AddSubmonoid.nsmul_mem
 
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 @[simp, norm_cast, to_additive]
 theorem [anonymous] {M : Type _} [Monoid M] {S : Submonoid M} (x : S) (n : ℕ) :
@@ -1158,12 +781,6 @@ theorem [anonymous] {M : Type _} [Monoid M] {S : Submonoid M} (x : S) (n : ℕ)
   rfl
 #align submonoid.coe_pow [anonymous]
 
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 /-- A submonoid of a monoid inherits a monoid structure. -/
 @[to_additive "An `add_submonoid` of an `add_monoid` inherits an `add_monoid`\nstructure."]
 instance toMonoid {M : Type _} [Monoid M] (S : Submonoid M) : Monoid S :=
@@ -1171,12 +788,6 @@ instance toMonoid {M : Type _} [Monoid M] (S : Submonoid M) : Monoid S :=
 #align submonoid.to_monoid Submonoid.toMonoid
 #align add_submonoid.to_add_monoid AddSubmonoid.toAddMonoid
 
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 /-- A submonoid of a `comm_monoid` is a `comm_monoid`. -/
 @[to_additive "An `add_submonoid` of an `add_comm_monoid` is\nan `add_comm_monoid`."]
 instance toCommMonoid {M} [CommMonoid M] (S : Submonoid M) : CommMonoid S :=
@@ -1184,12 +795,6 @@ instance toCommMonoid {M} [CommMonoid M] (S : Submonoid M) : CommMonoid S :=
 #align submonoid.to_comm_monoid Submonoid.toCommMonoid
 #align add_submonoid.to_add_comm_monoid AddSubmonoid.toAddCommMonoid
 
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 /-- A submonoid of an `ordered_comm_monoid` is an `ordered_comm_monoid`. -/
 @[to_additive
       "An `add_submonoid` of an `ordered_add_comm_monoid` is\nan `ordered_add_comm_monoid`."]
@@ -1198,12 +803,6 @@ instance toOrderedCommMonoid {M} [OrderedCommMonoid M] (S : Submonoid M) : Order
 #align submonoid.to_ordered_comm_monoid Submonoid.toOrderedCommMonoid
 #align add_submonoid.to_ordered_add_comm_monoid AddSubmonoid.toOrderedAddCommMonoid
 
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 /-- A submonoid of a `linear_ordered_comm_monoid` is a `linear_ordered_comm_monoid`. -/
 @[to_additive
       "An `add_submonoid` of a `linear_ordered_add_comm_monoid` is\na `linear_ordered_add_comm_monoid`."]
@@ -1214,12 +813,6 @@ instance toLinearOrderedCommMonoid {M} [LinearOrderedCommMonoid M] (S : Submonoi
 #align submonoid.to_linear_ordered_comm_monoid Submonoid.toLinearOrderedCommMonoid
 #align add_submonoid.to_linear_ordered_add_comm_monoid AddSubmonoid.toLinearOrderedAddCommMonoid
 
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 /-- A submonoid of an `ordered_cancel_comm_monoid` is an `ordered_cancel_comm_monoid`. -/
 @[to_additive
       "An `add_submonoid` of an `ordered_cancel_add_comm_monoid` is\nan `ordered_cancel_add_comm_monoid`."]
@@ -1229,12 +822,6 @@ instance toOrderedCancelCommMonoid {M} [OrderedCancelCommMonoid M] (S : Submonoi
 #align submonoid.to_ordered_cancel_comm_monoid Submonoid.toOrderedCancelCommMonoid
 #align add_submonoid.to_ordered_cancel_add_comm_monoid AddSubmonoid.toOrderedCancelAddCommMonoid
 
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 /-- A submonoid of a `linear_ordered_cancel_comm_monoid` is a `linear_ordered_cancel_comm_monoid`.
 -/
 @[to_additive
@@ -1246,12 +833,6 @@ instance toLinearOrderedCancelCommMonoid {M} [LinearOrderedCancelCommMonoid M] (
 #align submonoid.to_linear_ordered_cancel_comm_monoid Submonoid.toLinearOrderedCancelCommMonoid
 #align add_submonoid.to_linear_ordered_cancel_add_comm_monoid AddSubmonoid.toLinearOrderedCancelAddCommMonoid
 
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 /-- The natural monoid hom from a submonoid of monoid `M` to `M`. -/
 @[to_additive "The natural monoid hom from an `add_submonoid` of `add_monoid` `M` to `M`."]
 def subtype : S →* M :=
@@ -1259,24 +840,12 @@ def subtype : S →* M :=
 #align submonoid.subtype Submonoid.subtype
 #align add_submonoid.subtype AddSubmonoid.subtype
 
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 @[simp, to_additive]
 theorem coe_subtype : ⇑S.Subtype = coe :=
   rfl
 #align submonoid.coe_subtype Submonoid.coe_subtype
 #align add_submonoid.coe_subtype AddSubmonoid.coe_subtype
 
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 /-- The top submonoid is isomorphic to the monoid. -/
 @[to_additive "The top additive submonoid is isomorphic to the additive monoid.", simps]
 def topEquiv : (⊤ : Submonoid M) ≃* M where
@@ -1288,24 +857,12 @@ def topEquiv : (⊤ : Submonoid M) ≃* M where
 #align submonoid.top_equiv Submonoid.topEquiv
 #align add_submonoid.top_equiv AddSubmonoid.topEquiv
 
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 @[simp, to_additive]
 theorem topEquiv_toMonoidHom : (topEquiv : _ ≃* M).toMonoidHom = (⊤ : Submonoid M).Subtype :=
   rfl
 #align submonoid.top_equiv_to_monoid_hom Submonoid.topEquiv_toMonoidHom
 #align add_submonoid.top_equiv_to_add_monoid_hom AddSubmonoid.topEquiv_toAddMonoidHom
 
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 /-- A subgroup is isomorphic to its image under an injective function. If you have an isomorphism,
 use `mul_equiv.submonoid_map` for better definitional equalities. -/
 @[to_additive
@@ -1315,9 +872,6 @@ noncomputable def equivMapOfInjective (f : M →* N) (hf : Function.Injective f)
 #align submonoid.equiv_map_of_injective Submonoid.equivMapOfInjective
 #align add_submonoid.equiv_map_of_injective AddSubmonoid.equivMapOfInjective
 
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 @[simp, to_additive]
 theorem coe_equivMapOfInjective_apply (f : M →* N) (hf : Function.Injective f) (x : S) :
     (equivMapOfInjective S f hf x : N) = f x :=
@@ -1325,12 +879,6 @@ theorem coe_equivMapOfInjective_apply (f : M →* N) (hf : Function.Injective f)
 #align submonoid.coe_equiv_map_of_injective_apply Submonoid.coe_equivMapOfInjective_apply
 #align add_submonoid.coe_equiv_map_of_injective_apply AddSubmonoid.coe_equivMapOfInjective_apply
 
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 @[simp, to_additive]
 theorem closure_closure_coe_preimage {s : Set M} : closure ((coe : closure s → M) ⁻¹' s) = ⊤ :=
   eq_top_iff.2 fun x =>
@@ -1343,12 +891,6 @@ theorem closure_closure_coe_preimage {s : Set M} : closure ((coe : closure s →
 #align submonoid.closure_closure_coe_preimage Submonoid.closure_closure_coe_preimage
 #align add_submonoid.closure_closure_coe_preimage AddSubmonoid.closure_closure_coe_preimage
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- Given `submonoid`s `s`, `t` of monoids `M`, `N` respectively, `s × t` as a submonoid
 of `M × N`. -/
@@ -1362,12 +904,6 @@ def prod (s : Submonoid M) (t : Submonoid N) : Submonoid (M × N)
 #align submonoid.prod Submonoid.prod
 #align add_submonoid.prod AddSubmonoid.prod
 
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 @[to_additive coe_prod]
 theorem coe_prod (s : Submonoid M) (t : Submonoid N) : (s.Prod t : Set (M × N)) = s ×ˢ t :=
@@ -1375,12 +911,6 @@ theorem coe_prod (s : Submonoid M) (t : Submonoid N) : (s.Prod t : Set (M × N))
 #align submonoid.coe_prod Submonoid.coe_prod
 #align add_submonoid.coe_prod AddSubmonoid.coe_prod
 
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 @[to_additive mem_prod]
 theorem mem_prod {s : Submonoid M} {t : Submonoid N} {p : M × N} :
     p ∈ s.Prod t ↔ p.1 ∈ s ∧ p.2 ∈ t :=
@@ -1388,12 +918,6 @@ theorem mem_prod {s : Submonoid M} {t : Submonoid N} {p : M × N} :
 #align submonoid.mem_prod Submonoid.mem_prod
 #align add_submonoid.mem_prod AddSubmonoid.mem_prod
 
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 @[to_additive prod_mono]
 theorem prod_mono {s₁ s₂ : Submonoid M} {t₁ t₂ : Submonoid N} (hs : s₁ ≤ s₂) (ht : t₁ ≤ t₂) :
     s₁.Prod t₁ ≤ s₂.Prod t₂ :=
@@ -1401,60 +925,30 @@ theorem prod_mono {s₁ s₂ : Submonoid M} {t₁ t₂ : Submonoid N} (hs : s₁
 #align submonoid.prod_mono Submonoid.prod_mono
 #align add_submonoid.prod_mono AddSubmonoid.prod_mono
 
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 @[to_additive prod_top]
 theorem prod_top (s : Submonoid M) : s.Prod (⊤ : Submonoid N) = s.comap (MonoidHom.fst M N) :=
   ext fun x => by simp [mem_prod, MonoidHom.coe_fst]
 #align submonoid.prod_top Submonoid.prod_top
 #align add_submonoid.prod_top AddSubmonoid.prod_top
 
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 @[to_additive top_prod]
 theorem top_prod (s : Submonoid N) : (⊤ : Submonoid M).Prod s = s.comap (MonoidHom.snd M N) :=
   ext fun x => by simp [mem_prod, MonoidHom.coe_snd]
 #align submonoid.top_prod Submonoid.top_prod
 #align add_submonoid.top_prod AddSubmonoid.top_prod
 
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 @[simp, to_additive top_prod_top]
 theorem top_prod_top : (⊤ : Submonoid M).Prod (⊤ : Submonoid N) = ⊤ :=
   (top_prod _).trans <| comap_top _
 #align submonoid.top_prod_top Submonoid.top_prod_top
 #align add_submonoid.top_prod_top AddSubmonoid.top_prod_top
 
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 @[to_additive]
 theorem bot_prod_bot : (⊥ : Submonoid M).Prod (⊥ : Submonoid N) = ⊥ :=
   SetLike.coe_injective <| by simp [coe_prod, Prod.one_eq_mk]
 #align submonoid.bot_prod_bot Submonoid.bot_prod_bot
 #align add_submonoid.bot_sum_bot AddSubmonoid.bot_prod_bot
 
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 /-- The product of submonoids is isomorphic to their product as monoids. -/
 @[to_additive prod_equiv
       "The product of additive submonoids is isomorphic to their product\nas additive monoids"]
@@ -1465,12 +959,6 @@ def prodEquiv (s : Submonoid M) (t : Submonoid N) : s.Prod t ≃* s × t :=
 
 open MonoidHom
 
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 @[to_additive]
 theorem map_inl (s : Submonoid M) : s.map (inl M N) = s.Prod ⊥ :=
   ext fun p =>
@@ -1479,12 +967,6 @@ theorem map_inl (s : Submonoid M) : s.map (inl M N) = s.Prod ⊥ :=
 #align submonoid.map_inl Submonoid.map_inl
 #align add_submonoid.map_inl AddSubmonoid.map_inl
 
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 @[to_additive]
 theorem map_inr (s : Submonoid N) : s.map (inr M N) = prod ⊥ s :=
   ext fun p =>
@@ -1493,12 +975,6 @@ theorem map_inr (s : Submonoid N) : s.map (inr M N) = prod ⊥ s :=
 #align submonoid.map_inr Submonoid.map_inr
 #align add_submonoid.map_inr AddSubmonoid.map_inr
 
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 @[simp, to_additive prod_bot_sup_bot_prod]
 theorem prod_bot_sup_bot_prod (s : Submonoid M) (t : Submonoid N) :
     s.Prod ⊥ ⊔ prod ⊥ t = s.Prod t :=
@@ -1509,12 +985,6 @@ theorem prod_bot_sup_bot_prod (s : Submonoid M) (t : Submonoid N) :
 #align submonoid.prod_bot_sup_bot_prod Submonoid.prod_bot_sup_bot_prod
 #align add_submonoid.prod_bot_sup_bot_prod AddSubmonoid.prod_bot_sup_bot_prod
 
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 @[to_additive]
 theorem mem_map_equiv {f : M ≃* N} {K : Submonoid M} {x : N} :
     x ∈ K.map f.toMonoidHom ↔ f.symm x ∈ K :=
@@ -1522,12 +992,6 @@ theorem mem_map_equiv {f : M ≃* N} {K : Submonoid M} {x : N} :
 #align submonoid.mem_map_equiv Submonoid.mem_map_equiv
 #align add_submonoid.mem_map_equiv AddSubmonoid.mem_map_equiv
 
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 @[to_additive]
 theorem map_equiv_eq_comap_symm (f : M ≃* N) (K : Submonoid M) :
     K.map f.toMonoidHom = K.comap f.symm.toMonoidHom :=
@@ -1535,12 +999,6 @@ theorem map_equiv_eq_comap_symm (f : M ≃* N) (K : Submonoid M) :
 #align submonoid.map_equiv_eq_comap_symm Submonoid.map_equiv_eq_comap_symm
 #align add_submonoid.map_equiv_eq_comap_symm AddSubmonoid.map_equiv_eq_comap_symm
 
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 @[to_additive]
 theorem comap_equiv_eq_map_symm (f : N ≃* M) (K : Submonoid M) :
     K.comap f.toMonoidHom = K.map f.symm.toMonoidHom :=
@@ -1548,24 +1006,12 @@ theorem comap_equiv_eq_map_symm (f : N ≃* M) (K : Submonoid M) :
 #align submonoid.comap_equiv_eq_map_symm Submonoid.comap_equiv_eq_map_symm
 #align add_submonoid.comap_equiv_eq_map_symm AddSubmonoid.comap_equiv_eq_map_symm
 
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 @[simp, to_additive]
 theorem map_equiv_top (f : M ≃* N) : (⊤ : Submonoid M).map f.toMonoidHom = ⊤ :=
   SetLike.coe_injective <| Set.image_univ.trans f.Surjective.range_eq
 #align submonoid.map_equiv_top Submonoid.map_equiv_top
 #align add_submonoid.map_equiv_top AddSubmonoid.map_equiv_top
 
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 @[to_additive le_prod_iff]
 theorem le_prod_iff {s : Submonoid M} {t : Submonoid N} {u : Submonoid (M × N)} :
     u ≤ s.Prod t ↔ u.map (fst M N) ≤ s ∧ u.map (snd M N) ≤ t :=
@@ -1579,12 +1025,6 @@ theorem le_prod_iff {s : Submonoid M} {t : Submonoid N} {u : Submonoid (M × N)}
 #align submonoid.le_prod_iff Submonoid.le_prod_iff
 #align add_submonoid.le_prod_iff AddSubmonoid.le_prod_iff
 
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 @[to_additive prod_le_iff]
 theorem prod_le_iff {s : Submonoid M} {t : Submonoid N} {u : Submonoid (M × N)} :
     s.Prod t ≤ u ↔ s.map (inl M N) ≤ u ∧ t.map (inr M N) ≤ u :=
@@ -1652,36 +1092,18 @@ def mrange (f : F) : Submonoid N :=
 #align add_monoid_hom.mrange AddMonoidHom.mrange
 -/
 
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 @[simp, to_additive]
 theorem coe_mrange (f : F) : (mrange f : Set N) = Set.range f :=
   rfl
 #align monoid_hom.coe_mrange MonoidHom.coe_mrange
 #align add_monoid_hom.coe_mrange AddMonoidHom.coe_mrange
 
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 @[simp, to_additive]
 theorem mem_mrange {f : F} {y : N} : y ∈ mrange f ↔ ∃ x, f x = y :=
   Iff.rfl
 #align monoid_hom.mem_mrange MonoidHom.mem_mrange
 #align add_monoid_hom.mem_mrange AddMonoidHom.mem_mrange
 
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 @[to_additive]
 theorem mrange_eq_map (f : F) : mrange f = (⊤ : Submonoid M).map f :=
   Submonoid.copy_eq _
@@ -1690,12 +1112,6 @@ theorem mrange_eq_map (f : F) : mrange f = (⊤ : Submonoid M).map f :=
 
 omit mc
 
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 @[to_additive]
 theorem map_mrange (g : N →* P) (f : M →* N) : f.mrange.map g = (g.comp f).mrange := by
   simpa only [mrange_eq_map] using (⊤ : Submonoid M).map_map g f
@@ -1704,24 +1120,12 @@ theorem map_mrange (g : N →* P) (f : M →* N) : f.mrange.map g = (g.comp f).m
 
 include mc
 
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 @[to_additive]
 theorem mrange_top_iff_surjective {f : F} : mrange f = (⊤ : Submonoid N) ↔ Function.Surjective f :=
   SetLike.ext'_iff.trans <| Iff.trans (by rw [coe_mrange, coe_top]) Set.range_iff_surjective
 #align monoid_hom.mrange_top_iff_surjective MonoidHom.mrange_top_iff_surjective
 #align add_monoid_hom.mrange_top_iff_surjective AddMonoidHom.mrange_top_iff_surjective
 
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 /-- The range of a surjective monoid hom is the whole of the codomain. -/
 @[to_additive "The range of a surjective `add_monoid` hom is the whole of the codomain."]
 theorem mrange_top_of_surjective (f : F) (hf : Function.Surjective f) :
@@ -1730,24 +1134,12 @@ theorem mrange_top_of_surjective (f : F) (hf : Function.Surjective f) :
 #align monoid_hom.mrange_top_of_surjective MonoidHom.mrange_top_of_surjective
 #align add_monoid_hom.mrange_top_of_surjective AddMonoidHom.mrange_top_of_surjective
 
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 @[to_additive]
 theorem mclosure_preimage_le (f : F) (s : Set N) : closure (f ⁻¹' s) ≤ (closure s).comap f :=
   closure_le.2 fun x hx => SetLike.mem_coe.2 <| mem_comap.2 <| subset_closure hx
 #align monoid_hom.mclosure_preimage_le MonoidHom.mclosure_preimage_le
 #align add_monoid_hom.mclosure_preimage_le AddMonoidHom.mclosure_preimage_le
 
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 /-- The image under a monoid hom of the submonoid generated by a set equals the submonoid generated
     by the image of the set. -/
 @[to_additive
@@ -1772,9 +1164,6 @@ def restrict {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M] (
 #align add_monoid_hom.restrict AddMonoidHom.restrict
 -/
 
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 @[simp, to_additive]
 theorem restrict_apply {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M]
     (f : M →* N) (s : S) (x : s) : f.restrict s x = f x :=
@@ -1782,12 +1171,6 @@ theorem restrict_apply {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidCl
 #align monoid_hom.restrict_apply MonoidHom.restrict_apply
 #align add_monoid_hom.restrict_apply AddMonoidHom.restrict_apply
 
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 @[simp, to_additive]
 theorem restrict_mrange (f : M →* N) : (f.restrict S).mrange = S.map f := by
   simp_rw [SetLike.ext_iff, mem_mrange, mem_map, restrict_apply, SetLike.exists, Subtype.coe_mk,
@@ -1795,12 +1178,6 @@ theorem restrict_mrange (f : M →* N) : (f.restrict S).mrange = S.map f := by
 #align monoid_hom.restrict_mrange MonoidHom.restrict_mrange
 #align add_monoid_hom.restrict_mrange AddMonoidHom.restrict_mrange
 
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 /-- Restriction of a monoid hom to a submonoid of the codomain. -/
 @[to_additive "Restriction of an `add_monoid` hom to an `add_submonoid` of the codomain.",
   simps apply]
@@ -1812,12 +1189,6 @@ def codRestrict {S} [SetLike S N] [SubmonoidClass S N] (f : M →* N) (s : S) (h
 #align monoid_hom.cod_restrict MonoidHom.codRestrict
 #align add_monoid_hom.cod_restrict AddMonoidHom.codRestrict
 
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 /-- Restriction of a monoid hom to its range interpreted as a submonoid. -/
 @[to_additive "Restriction of an `add_monoid` hom to its range interpreted as a submonoid."]
 def mrangeRestrict {N} [MulOneClass N] (f : M →* N) : M →* f.mrange :=
@@ -1825,9 +1196,6 @@ def mrangeRestrict {N} [MulOneClass N] (f : M →* N) : M →* f.mrange :=
 #align monoid_hom.mrange_restrict MonoidHom.mrangeRestrict
 #align add_monoid_hom.mrange_restrict AddMonoidHom.mrangeRestrict
 
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 @[simp, to_additive]
 theorem coe_mrangeRestrict {N} [MulOneClass N] (f : M →* N) (x : M) :
     (f.mrangeRestrict x : N) = f x :=
@@ -1835,12 +1203,6 @@ theorem coe_mrangeRestrict {N} [MulOneClass N] (f : M →* N) (x : M) :
 #align monoid_hom.coe_mrange_restrict MonoidHom.coe_mrangeRestrict
 #align add_monoid_hom.coe_mrange_restrict AddMonoidHom.coe_mrangeRestrict
 
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 @[to_additive]
 theorem mrangeRestrict_surjective (f : M →* N) : Function.Surjective f.mrangeRestrict :=
   fun ⟨_, ⟨x, rfl⟩⟩ => ⟨x, rfl⟩
@@ -1860,36 +1222,18 @@ def mker (f : F) : Submonoid M :=
 #align add_monoid_hom.mker AddMonoidHom.mker
 -/
 
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 @[to_additive]
 theorem mem_mker (f : F) {x : M} : x ∈ mker f ↔ f x = 1 :=
   Iff.rfl
 #align monoid_hom.mem_mker MonoidHom.mem_mker
 #align add_monoid_hom.mem_mker AddMonoidHom.mem_mker
 
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 @[to_additive]
 theorem coe_mker (f : F) : (mker f : Set M) = (f : M → N) ⁻¹' {1} :=
   rfl
 #align monoid_hom.coe_mker MonoidHom.coe_mker
 #align add_monoid_hom.coe_mker AddMonoidHom.coe_mker
 
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 @[to_additive]
 instance decidableMemMker [DecidableEq N] (f : F) : DecidablePred (· ∈ mker f) := fun x =>
   decidable_of_iff (f x = 1) (mem_mker f)
@@ -1898,12 +1242,6 @@ instance decidableMemMker [DecidableEq N] (f : F) : DecidablePred (· ∈ mker f
 
 omit mc
 
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 @[to_additive]
 theorem comap_mker (g : N →* P) (f : M →* N) : g.mker.comap f = (g.comp f).mker :=
   rfl
@@ -1912,12 +1250,6 @@ theorem comap_mker (g : N →* P) (f : M →* N) : g.mker.comap f = (g.comp f).m
 
 include mc
 
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 @[simp, to_additive]
 theorem comap_bot' (f : F) : (⊥ : Submonoid N).comap f = mker f :=
   rfl
@@ -1926,24 +1258,12 @@ theorem comap_bot' (f : F) : (⊥ : Submonoid N).comap f = mker f :=
 
 omit mc
 
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 @[simp, to_additive]
 theorem restrict_mker (f : M →* N) : (f.restrict S).mker = f.mker.comap S.Subtype :=
   rfl
 #align monoid_hom.restrict_mker MonoidHom.restrict_mker
 #align add_monoid_hom.restrict_mker AddMonoidHom.restrict_mker
 
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 @[to_additive]
 theorem mrangeRestrict_mker (f : M →* N) : mker (mrangeRestrict f) = mker f :=
   by
@@ -1953,23 +1273,11 @@ theorem mrangeRestrict_mker (f : M →* N) : mker (mrangeRestrict f) = mker f :=
 #align monoid_hom.range_restrict_mker MonoidHom.mrangeRestrict_mker
 #align add_monoid_hom.range_restrict_mker AddMonoidHom.mrangeRestrict_mker
 
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 @[simp, to_additive]
 theorem mker_one : (1 : M →* N).mker = ⊤ := by ext; simp [mem_mker]
 #align monoid_hom.mker_one MonoidHom.mker_one
 #align add_monoid_hom.mker_zero AddMonoidHom.mker_zero
 
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 @[to_additive]
 theorem prod_map_comap_prod' {M' : Type _} {N' : Type _} [MulOneClass M'] [MulOneClass N']
     (f : M →* N) (g : M' →* N') (S : Submonoid N) (S' : Submonoid N') :
@@ -1978,12 +1286,6 @@ theorem prod_map_comap_prod' {M' : Type _} {N' : Type _} [MulOneClass M'] [MulOn
 #align monoid_hom.prod_map_comap_prod' MonoidHom.prod_map_comap_prod'
 #align add_monoid_hom.sum_map_comap_sum' AddMonoidHom.prod_map_comap_prod'
 
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 @[to_additive]
 theorem mker_prod_map {M' : Type _} {N' : Type _} [MulOneClass M'] [MulOneClass N'] (f : M →* N)
     (g : M' →* N') : (prodMap f g).mker = f.mker.Prod g.mker := by
@@ -1991,34 +1293,16 @@ theorem mker_prod_map {M' : Type _} {N' : Type _} [MulOneClass M'] [MulOneClass
 #align monoid_hom.mker_prod_map MonoidHom.mker_prod_map
 #align add_monoid_hom.mker_sum_map AddMonoidHom.mker_prod_map
 
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 @[simp, to_additive]
 theorem mker_inl : (inl M N).mker = ⊥ := by ext x; simp [mem_mker]
 #align monoid_hom.mker_inl MonoidHom.mker_inl
 #align add_monoid_hom.mker_inl AddMonoidHom.mker_inl
 
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 @[simp, to_additive]
 theorem mker_inr : (inr M N).mker = ⊥ := by ext x; simp [mem_mker]
 #align monoid_hom.mker_inr MonoidHom.mker_inr
 #align add_monoid_hom.mker_inr AddMonoidHom.mker_inr
 
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 /-- The `monoid_hom` from the preimage of a submonoid to itself. -/
 @[to_additive "the `add_monoid_hom` from the preimage of an additive submonoid to itself.", simps]
 def submonoidComap (f : M →* N) (N' : Submonoid N) : N'.comap f →* N'
@@ -2029,12 +1313,6 @@ def submonoidComap (f : M →* N) (N' : Submonoid N) : N'.comap f →* N'
 #align monoid_hom.submonoid_comap MonoidHom.submonoidComap
 #align add_monoid_hom.add_submonoid_comap AddMonoidHom.addSubmonoidComap
 
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 /-- The `monoid_hom` from a submonoid to its image.
 See `mul_equiv.submonoid_map` for a variant for `mul_equiv`s. -/
 @[to_additive
@@ -2048,9 +1326,6 @@ def submonoidMap (f : M →* N) (M' : Submonoid M) : M' →* M'.map f
 #align monoid_hom.submonoid_map MonoidHom.submonoidMap
 #align add_monoid_hom.add_submonoid_map AddMonoidHom.addSubmonoidMap
 
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 @[to_additive]
 theorem submonoidMap_surjective (f : M →* N) (M' : Submonoid M) :
     Function.Surjective (f.submonoidMap M') := by rintro ⟨_, x, hx, rfl⟩; exact ⟨⟨x, hx⟩, rfl⟩
@@ -2063,94 +1338,46 @@ namespace Submonoid
 
 open MonoidHom
 
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 @[to_additive]
 theorem mrange_inl : (inl M N).mrange = prod ⊤ ⊥ := by simpa only [mrange_eq_map] using map_inl ⊤
 #align submonoid.mrange_inl Submonoid.mrange_inl
 #align add_submonoid.mrange_inl AddSubmonoid.mrange_inl
 
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 @[to_additive]
 theorem mrange_inr : (inr M N).mrange = prod ⊥ ⊤ := by simpa only [mrange_eq_map] using map_inr ⊤
 #align submonoid.mrange_inr Submonoid.mrange_inr
 #align add_submonoid.mrange_inr AddSubmonoid.mrange_inr
 
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 @[to_additive]
 theorem mrange_inl' : (inl M N).mrange = comap (snd M N) ⊥ :=
   mrange_inl.trans (top_prod _)
 #align submonoid.mrange_inl' Submonoid.mrange_inl'
 #align add_submonoid.mrange_inl' AddSubmonoid.mrange_inl'
 
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 @[to_additive]
 theorem mrange_inr' : (inr M N).mrange = comap (fst M N) ⊥ :=
   mrange_inr.trans (prod_top _)
 #align submonoid.mrange_inr' Submonoid.mrange_inr'
 #align add_submonoid.mrange_inr' AddSubmonoid.mrange_inr'
 
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 @[simp, to_additive]
 theorem mrange_fst : (fst M N).mrange = ⊤ :=
   mrange_top_of_surjective (fst M N) <| @Prod.fst_surjective _ _ ⟨1⟩
 #align submonoid.mrange_fst Submonoid.mrange_fst
 #align add_submonoid.mrange_fst AddSubmonoid.mrange_fst
 
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 @[simp, to_additive]
 theorem mrange_snd : (snd M N).mrange = ⊤ :=
   mrange_top_of_surjective (snd M N) <| @Prod.snd_surjective _ _ ⟨1⟩
 #align submonoid.mrange_snd Submonoid.mrange_snd
 #align add_submonoid.mrange_snd AddSubmonoid.mrange_snd
 
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 @[to_additive]
 theorem prod_eq_bot_iff {s : Submonoid M} {t : Submonoid N} : s.Prod t = ⊥ ↔ s = ⊥ ∧ t = ⊥ := by
   simp only [eq_bot_iff, prod_le_iff, (gc_map_comap _).le_iff_le, comap_bot', mker_inl, mker_inr]
 #align submonoid.prod_eq_bot_iff Submonoid.prod_eq_bot_iff
 #align add_submonoid.sum_eq_bot_iff AddSubmonoid.prod_eq_bot_iff
 
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 @[to_additive]
 theorem prod_eq_top_iff {s : Submonoid M} {t : Submonoid N} : s.Prod t = ⊤ ↔ s = ⊤ ∧ t = ⊤ := by
   simp only [eq_top_iff, le_prod_iff, ← (gc_map_comap _).le_iff_le, ← mrange_eq_map, mrange_fst,
@@ -2158,24 +1385,12 @@ theorem prod_eq_top_iff {s : Submonoid M} {t : Submonoid N} : s.Prod t = ⊤ ↔
 #align submonoid.prod_eq_top_iff Submonoid.prod_eq_top_iff
 #align add_submonoid.sum_eq_top_iff AddSubmonoid.prod_eq_top_iff
 
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 @[simp, to_additive]
 theorem mrange_inl_sup_mrange_inr : (inl M N).mrange ⊔ (inr M N).mrange = ⊤ := by
   simp only [mrange_inl, mrange_inr, prod_bot_sup_bot_prod, top_prod_top]
 #align submonoid.mrange_inl_sup_mrange_inr Submonoid.mrange_inl_sup_mrange_inr
 #align add_submonoid.mrange_inl_sup_mrange_inr AddSubmonoid.mrange_inl_sup_mrange_inr
 
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 /-- The monoid hom associated to an inclusion of submonoids. -/
 @[to_additive "The `add_monoid` hom associated to an inclusion of submonoids."]
 def inclusion {S T : Submonoid M} (h : S ≤ T) : S →* T :=
@@ -2183,48 +1398,24 @@ def inclusion {S T : Submonoid M} (h : S ≤ T) : S →* T :=
 #align submonoid.inclusion Submonoid.inclusion
 #align add_submonoid.inclusion AddSubmonoid.inclusion
 
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 @[simp, to_additive]
 theorem range_subtype (s : Submonoid M) : s.Subtype.mrange = s :=
   SetLike.coe_injective <| (coe_mrange _).trans <| Subtype.range_coe
 #align submonoid.range_subtype Submonoid.range_subtype
 #align add_submonoid.range_subtype AddSubmonoid.range_subtype
 
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 @[to_additive]
 theorem eq_top_iff' : S = ⊤ ↔ ∀ x : M, x ∈ S :=
   eq_top_iff.trans ⟨fun h m => h <| mem_top m, fun h m _ => h m⟩
 #align submonoid.eq_top_iff' Submonoid.eq_top_iff'
 #align add_submonoid.eq_top_iff' AddSubmonoid.eq_top_iff'
 
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 @[to_additive]
 theorem eq_bot_iff_forall : S = ⊥ ↔ ∀ x ∈ S, x = (1 : M) :=
   SetLike.ext_iff.trans <| by simp (config := { contextual := true }) [iff_def, S.one_mem]
 #align submonoid.eq_bot_iff_forall Submonoid.eq_bot_iff_forall
 #align add_submonoid.eq_bot_iff_forall AddSubmonoid.eq_bot_iff_forall
 
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 @[to_additive]
 theorem nontrivial_iff_exists_ne_one (S : Submonoid M) : Nontrivial S ↔ ∃ x ∈ S, x ≠ (1 : M) :=
   calc
@@ -2235,12 +1426,6 @@ theorem nontrivial_iff_exists_ne_one (S : Submonoid M) : Nontrivial S ↔ ∃ x
 #align submonoid.nontrivial_iff_exists_ne_one Submonoid.nontrivial_iff_exists_ne_one
 #align add_submonoid.nontrivial_iff_exists_ne_zero AddSubmonoid.nontrivial_iff_exists_ne_zero
 
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 /-- A submonoid is either the trivial submonoid or nontrivial. -/
 @[to_additive "An additive submonoid is either the trivial additive submonoid or nontrivial."]
 theorem bot_or_nontrivial (S : Submonoid M) : S = ⊥ ∨ Nontrivial S := by
@@ -2248,12 +1433,6 @@ theorem bot_or_nontrivial (S : Submonoid M) : S = ⊥ ∨ Nontrivial S := by
 #align submonoid.bot_or_nontrivial Submonoid.bot_or_nontrivial
 #align add_submonoid.bot_or_nontrivial AddSubmonoid.bot_or_nontrivial
 
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 /-- A submonoid is either the trivial submonoid or contains a nonzero element. -/
 @[to_additive
       "An additive submonoid is either the trivial additive submonoid or contains a nonzero\nelement."]
@@ -2268,12 +1447,6 @@ namespace MulEquiv
 
 variable {S} {T : Submonoid M}
 
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 /-- Makes the identity isomorphism from a proof that two submonoids of a multiplicative
     monoid are equal. -/
 @[to_additive
@@ -2283,12 +1456,6 @@ def submonoidCongr (h : S = T) : S ≃* T :=
 #align mul_equiv.submonoid_congr MulEquiv.submonoidCongr
 #align add_equiv.add_submonoid_congr AddEquiv.addSubmonoidCongr
 
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 -- this name is primed so that the version to `f.range` instead of `f.mrange` can be unprimed.
 /-- A monoid homomorphism `f : M →* N` with a left-inverse `g : N → M` defines a multiplicative
 equivalence between `M` and `f.mrange`.
@@ -2309,12 +1476,6 @@ def ofLeftInverse' (f : M →* N) {g : N → M} (h : Function.LeftInverse g f) :
 #align mul_equiv.of_left_inverse' MulEquiv.ofLeftInverse'
 #align add_equiv.of_left_inverse' AddEquiv.ofLeftInverse'
 
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 /-- A `mul_equiv` `φ` between two monoids `M` and `N` induces a `mul_equiv` between
 a submonoid `S ≤ M` and the submonoid `φ(S) ≤ N`.
 See `monoid_hom.submonoid_map` for a variant for `monoid_hom`s. -/
@@ -2325,9 +1486,6 @@ def submonoidMap (e : M ≃* N) (S : Submonoid M) : S ≃* S.map e.toMonoidHom :
 #align mul_equiv.submonoid_map MulEquiv.submonoidMap
 #align add_equiv.add_submonoid_map AddEquiv.addSubmonoidMap
 
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 @[simp, to_additive]
 theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
     ((submonoidMap e S g : S.map (e : M →* N)) : N) = e g :=
@@ -2335,9 +1493,6 @@ theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
 #align mul_equiv.coe_submonoid_map_apply MulEquiv.coe_submonoidMap_apply
 #align add_equiv.coe_add_submonoid_map_apply AddEquiv.coe_addSubmonoidMap_apply
 
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 @[simp, to_additive AddEquiv.add_submonoid_map_symm_apply]
 theorem submonoidMap_symm_apply (e : M ≃* N) (S : Submonoid M) (g : S.map (e : M →* N)) :
     (e.submonoidMap S).symm g = ⟨e.symm g, SetLike.mem_coe.1 <| Set.mem_image_equiv.1 g.2⟩ :=
@@ -2347,12 +1502,6 @@ theorem submonoidMap_symm_apply (e : M ≃* N) (S : Submonoid M) (g : S.map (e :
 
 end MulEquiv
 
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 @[simp, to_additive]
 theorem Submonoid.equivMapOfInjective_coe_mulEquiv (e : M ≃* N) :
     S.equivMapOfInjective (e : M →* N) (EquivLike.injective e) = e.submonoidMap S := by ext; rfl
@@ -2383,12 +1532,6 @@ variable [MulOneClass M']
 instance [SMul M' α] (S : Submonoid M') : SMul S α :=
   SMul.comp _ S.Subtype
 
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 @[to_additive]
 instance smulCommClass_left [SMul M' β] [SMul α β] [SMulCommClass M' α β] (S : Submonoid M') :
     SMulCommClass S α β :=
@@ -2396,12 +1539,6 @@ instance smulCommClass_left [SMul M' β] [SMul α β] [SMulCommClass M' α β] (
 #align submonoid.smul_comm_class_left Submonoid.smulCommClass_left
 #align add_submonoid.vadd_comm_class_left AddSubmonoid.vaddCommClass_left
 
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 @[to_additive]
 instance smulCommClass_right [SMul α β] [SMul M' β] [SMulCommClass α M' β] (S : Submonoid M') :
     SMulCommClass α S β :=
@@ -2414,12 +1551,6 @@ instance [SMul α β] [SMul M' α] [SMul M' β] [IsScalarTower M' α β] (S : Su
     IsScalarTower S α β :=
   ⟨fun a => (smul_assoc (a : M') : _)⟩
 
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 @[to_additive]
 theorem smul_def [SMul M' α] {S : Submonoid M'} (g : S) (m : α) : g • m = (g : M') • m :=
   rfl

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

@@ -1573,12 +1573,9 @@ theorem le_prod_iff {s : Submonoid M} {t : Submonoid N} {u : Submonoid (M × N)}
   constructor
   · intro h
     constructor
-    · rintro x ⟨⟨y1, y2⟩, ⟨hy1, rfl⟩⟩
-      exact (h hy1).1
-    · rintro x ⟨⟨y1, y2⟩, ⟨hy1, rfl⟩⟩
-      exact (h hy1).2
-  · rintro ⟨hH, hK⟩ ⟨x1, x2⟩ h
-    exact ⟨hH ⟨_, h, rfl⟩, hK ⟨_, h, rfl⟩⟩
+    · rintro x ⟨⟨y1, y2⟩, ⟨hy1, rfl⟩⟩; exact (h hy1).1
+    · rintro x ⟨⟨y1, y2⟩, ⟨hy1, rfl⟩⟩; exact (h hy1).2
+  · rintro ⟨hH, hK⟩ ⟨x1, x2⟩ h; exact ⟨hH ⟨_, h, rfl⟩, hK ⟨_, h, rfl⟩⟩
 #align submonoid.le_prod_iff Submonoid.le_prod_iff
 #align add_submonoid.le_prod_iff AddSubmonoid.le_prod_iff
 
@@ -1595,19 +1592,11 @@ theorem prod_le_iff {s : Submonoid M} {t : Submonoid N} {u : Submonoid (M × N)}
   constructor
   · intro h
     constructor
-    · rintro _ ⟨x, hx, rfl⟩
-      apply h
-      exact ⟨hx, Submonoid.one_mem _⟩
-    · rintro _ ⟨x, hx, rfl⟩
-      apply h
-      exact ⟨Submonoid.one_mem _, hx⟩
+    · rintro _ ⟨x, hx, rfl⟩; apply h; exact ⟨hx, Submonoid.one_mem _⟩
+    · rintro _ ⟨x, hx, rfl⟩; apply h; exact ⟨Submonoid.one_mem _, hx⟩
   · rintro ⟨hH, hK⟩ ⟨x1, x2⟩ ⟨h1, h2⟩
-    have h1' : inl M N x1 ∈ u := by
-      apply hH
-      simpa using h1
-    have h2' : inr M N x2 ∈ u := by
-      apply hK
-      simpa using h2
+    have h1' : inl M N x1 ∈ u := by apply hH; simpa using h1
+    have h2' : inr M N x2 ∈ u := by apply hK; simpa using h2
     simpa using Submonoid.mul_mem _ h1' h2'
 #align submonoid.prod_le_iff Submonoid.prod_le_iff
 #align add_submonoid.prod_le_iff AddSubmonoid.prod_le_iff
@@ -1971,9 +1960,7 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align monoid_hom.mker_one MonoidHom.mker_oneₓ'. -/
 @[simp, to_additive]
-theorem mker_one : (1 : M →* N).mker = ⊤ := by
-  ext
-  simp [mem_mker]
+theorem mker_one : (1 : M →* N).mker = ⊤ := by ext; simp [mem_mker]
 #align monoid_hom.mker_one MonoidHom.mker_one
 #align add_monoid_hom.mker_zero AddMonoidHom.mker_zero
 
@@ -2011,9 +1998,7 @@ but is expected to have type
   forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N], Eq.{succ u2} (Submonoid.{u2} M _inst_1) (MonoidHom.mker.{u2, max u2 u1, max u2 u1} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.{u2, max u1 u2} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u2, max u2 u1} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.inl.{u2, u1} M N _inst_1 _inst_2)) (Bot.bot.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instBotSubmonoid.{u2} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mker_inl MonoidHom.mker_inlₓ'. -/
 @[simp, to_additive]
-theorem mker_inl : (inl M N).mker = ⊥ := by
-  ext x
-  simp [mem_mker]
+theorem mker_inl : (inl M N).mker = ⊥ := by ext x; simp [mem_mker]
 #align monoid_hom.mker_inl MonoidHom.mker_inl
 #align add_monoid_hom.mker_inl AddMonoidHom.mker_inl
 
@@ -2024,9 +2009,7 @@ but is expected to have type
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N], Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mker.{u2, max u1 u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.instMulOneClassProd.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.{u2, max u2 u1} N (Prod.{u1, u2} M N) _inst_2 (Prod.instMulOneClassProd.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.instMulOneClassProd.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.inr.{u1, u2} M N _inst_1 _inst_2)) (Bot.bot.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instBotSubmonoid.{u2} N _inst_2))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mker_inr MonoidHom.mker_inrₓ'. -/
 @[simp, to_additive]
-theorem mker_inr : (inr M N).mker = ⊥ := by
-  ext x
-  simp [mem_mker]
+theorem mker_inr : (inr M N).mker = ⊥ := by ext x; simp [mem_mker]
 #align monoid_hom.mker_inr MonoidHom.mker_inr
 #align add_monoid_hom.mker_inr AddMonoidHom.mker_inr
 
@@ -2070,10 +2053,7 @@ def submonoidMap (f : M →* N) (M' : Submonoid M) : M' →* M'.map f
 Case conversion may be inaccurate. Consider using '#align monoid_hom.submonoid_map_surjective MonoidHom.submonoidMap_surjectiveₓ'. -/
 @[to_additive]
 theorem submonoidMap_surjective (f : M →* N) (M' : Submonoid M) :
-    Function.Surjective (f.submonoidMap M') :=
-  by
-  rintro ⟨_, x, hx, rfl⟩
-  exact ⟨⟨x, hx⟩, rfl⟩
+    Function.Surjective (f.submonoidMap M') := by rintro ⟨_, x, hx, rfl⟩; exact ⟨⟨x, hx⟩, rfl⟩
 #align monoid_hom.submonoid_map_surjective MonoidHom.submonoidMap_surjective
 #align add_monoid_hom.add_submonoid_map_surjective AddMonoidHom.addSubmonoidMap_surjective
 
@@ -2375,10 +2355,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align submonoid.equiv_map_of_injective_coe_mul_equiv Submonoid.equivMapOfInjective_coe_mulEquivₓ'. -/
 @[simp, to_additive]
 theorem Submonoid.equivMapOfInjective_coe_mulEquiv (e : M ≃* N) :
-    S.equivMapOfInjective (e : M →* N) (EquivLike.injective e) = e.submonoidMap S :=
-  by
-  ext
-  rfl
+    S.equivMapOfInjective (e : M →* N) (EquivLike.injective e) = e.submonoidMap S := by ext; rfl
 #align submonoid.equiv_map_of_injective_coe_mul_equiv Submonoid.equivMapOfInjective_coe_mulEquiv
 #align add_submonoid.equiv_map_of_injective_coe_add_equiv AddSubmonoid.equivMapOfInjective_coe_addEquiv
 

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

@@ -115,10 +115,7 @@ abbrev AddSubmonoid.toSubmonoid' : AddSubmonoid (Additive M) ≃o Submonoid M :=
 #align add_submonoid.to_submonoid' AddSubmonoid.toSubmonoid'
 
 /- warning: submonoid.to_add_submonoid_closure -> Submonoid.toAddSubmonoid_closure is a dubious translation:
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(Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Submonoid.toAddSubmonoid.{u1} M _inst_1) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.{u1} M) (fun (_x : Additive.{u1} M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Additive.{u1} M) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid_closure Submonoid.toAddSubmonoid_closureₓ'. -/
 theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
     (Submonoid.closure S).toAddSubmonoid = AddSubmonoid.closure (Additive.toMul ⁻¹' S) :=
@@ -128,10 +125,7 @@ theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
 #align submonoid.to_add_submonoid_closure Submonoid.toAddSubmonoid_closure
 
 /- warning: add_submonoid.to_submonoid'_closure -> AddSubmonoid.toSubmonoid'_closure is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid'_closure AddSubmonoid.toSubmonoid'_closureₓ'. -/
 theorem AddSubmonoid.toSubmonoid'_closure (S : Set (Additive M)) :
     (AddSubmonoid.closure S).toSubmonoid' = Submonoid.closure (Multiplicative.ofAdd ⁻¹' S) :=
@@ -183,10 +177,7 @@ abbrev Submonoid.toAddSubmonoid' : Submonoid (Multiplicative A) ≃o AddSubmonoi
 #align submonoid.to_add_submonoid' Submonoid.toAddSubmonoid'
 
 /- warning: add_submonoid.to_submonoid_closure -> AddSubmonoid.toSubmonoid_closure is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid_closure AddSubmonoid.toSubmonoid_closureₓ'. -/
 theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
     (AddSubmonoid.closure S).toSubmonoid = Submonoid.closure (Multiplicative.toAdd ⁻¹' S) :=
@@ -197,10 +188,7 @@ theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
 #align add_submonoid.to_submonoid_closure AddSubmonoid.toSubmonoid_closure
 
 /- warning: submonoid.to_add_submonoid'_closure -> Submonoid.toAddSubmonoid'_closure is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid'_closure Submonoid.toAddSubmonoid'_closureₓ'. -/
 theorem Submonoid.toAddSubmonoid'_closure (S : Set (Multiplicative A)) :
     (Submonoid.closure S).toAddSubmonoid' = AddSubmonoid.closure (Additive.ofMul ⁻¹' S) :=
@@ -1328,10 +1316,7 @@ noncomputable def equivMapOfInjective (f : M →* N) (hf : Function.Injective f)
 #align add_submonoid.equiv_map_of_injective AddSubmonoid.equivMapOfInjective
 
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 Case conversion may be inaccurate. Consider using '#align submonoid.coe_equiv_map_of_injective_apply Submonoid.coe_equivMapOfInjective_applyₓ'. -/
 @[simp, to_additive]
 theorem coe_equivMapOfInjective_apply (f : M →* N) (hf : Function.Injective f) (x : S) :
@@ -1799,10 +1784,7 @@ def restrict {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M] (
 -/
 
 /- warning: monoid_hom.restrict_apply -> MonoidHom.restrict_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align monoid_hom.restrict_apply MonoidHom.restrict_applyₓ'. -/
 @[simp, to_additive]
 theorem restrict_apply {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M]
@@ -1855,10 +1837,7 @@ def mrangeRestrict {N} [MulOneClass N] (f : M →* N) : M →* f.mrange :=
 #align add_monoid_hom.mrange_restrict AddMonoidHom.mrangeRestrict
 
 /- warning: monoid_hom.coe_mrange_restrict -> MonoidHom.coe_mrangeRestrict is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align monoid_hom.coe_mrange_restrict MonoidHom.coe_mrangeRestrictₓ'. -/
 @[simp, to_additive]
 theorem coe_mrangeRestrict {N} [MulOneClass N] (f : M →* N) (x : M) :
@@ -2087,10 +2066,7 @@ def submonoidMap (f : M →* N) (M' : Submonoid M) : M' →* M'.map f
 #align add_monoid_hom.add_submonoid_map AddMonoidHom.addSubmonoidMap
 
 /- warning: monoid_hom.submonoid_map_surjective -> MonoidHom.submonoidMap_surjective is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align monoid_hom.submonoid_map_surjective MonoidHom.submonoidMap_surjectiveₓ'. -/
 @[to_additive]
 theorem submonoidMap_surjective (f : M →* N) (M' : Submonoid M) :
@@ -2370,10 +2346,7 @@ def submonoidMap (e : M ≃* N) (S : Submonoid M) : S ≃* S.map e.toMonoidHom :
 #align add_equiv.add_submonoid_map AddEquiv.addSubmonoidMap
 
 /- warning: mul_equiv.coe_submonoid_map_apply -> MulEquiv.coe_submonoidMap_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mul_equiv.coe_submonoid_map_apply MulEquiv.coe_submonoidMap_applyₓ'. -/
 @[simp, to_additive]
 theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
@@ -2383,10 +2356,7 @@ theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
 #align add_equiv.coe_add_submonoid_map_apply AddEquiv.coe_addSubmonoidMap_apply
 
 /- warning: mul_equiv.submonoid_map_symm_apply -> MulEquiv.submonoidMap_symm_apply is a dubious translation:
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(MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulEquivClass.toEquivLike.{max u1 u2, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1) (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1))))) (MulEquiv.symm.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) S) (SetLike.mem_coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => M) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (EquivLike.toEmbeddingLike.{max (succ u1) (succ u2), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulEquivClass.toEquivLike.{max u1 u2, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1) (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1))))) (MulEquiv.symm.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g))) (Iff.mp (Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g) (Set.image.{u2, u1} M N (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} M N) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => N) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} M N) (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e)) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S))) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : N) => M) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Set.{u2} M) (Set.instMembershipSet.{u2} M) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} N M) N (fun (_x : N) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : N) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} N M) (Equiv.symm.{succ u2, succ u1} M N (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e)) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) (Set.mem_image_equiv.{u1, u2} M N (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S) (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Subtype.property.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S)) g))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mul_equiv.submonoid_map_symm_apply MulEquiv.submonoidMap_symm_applyₓ'. -/
 @[simp, to_additive AddEquiv.add_submonoid_map_symm_apply]
 theorem submonoidMap_symm_apply (e : M ≃* N) (S : Submonoid M) (g : S.map (e : M →* N)) :

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

@@ -118,7 +118,7 @@ abbrev AddSubmonoid.toSubmonoid' : AddSubmonoid (Additive M) ≃o Submonoid M :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (fun (_x : RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))) => (Submonoid.{u1} M _inst_1) -> (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))) (Submonoid.toAddSubmonoid.{u1} M _inst_1) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (fun (_x : Equiv.{succ u1, succ u1} (Additive.{u1} M) M) => (Additive.{u1} M) -> M) (Equiv.hasCoeToFun.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} M _inst_1) (fun (_x : Submonoid.{u1} M _inst_1) => AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Submonoid.toAddSubmonoid.{u1} M _inst_1) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.{u1} M) (fun (_x : Additive.{u1} M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Additive.{u1} M) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Submonoid.{u1} M _inst_1) (fun (_x : Submonoid.{u1} M _inst_1) => AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Submonoid.toAddSubmonoid.{u1} M _inst_1) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.{u1} M) (fun (_x : Additive.{u1} M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Additive.{u1} M) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid_closure Submonoid.toAddSubmonoid_closureₓ'. -/
 theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
     (Submonoid.closure S).toAddSubmonoid = AddSubmonoid.closure (Additive.toMul ⁻¹' S) :=
@@ -131,7 +131,7 @@ theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))))) => (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) -> (Submonoid.{u1} M _inst_1)) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))))) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (fun (_x : Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) => M -> (Multiplicative.{u1} M)) (Equiv.hasCoeToFun.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (_x : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => Submonoid.{u1} M _inst_1) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => Multiplicative.{u1} M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (_x : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => Submonoid.{u1} M _inst_1) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => Multiplicative.{u1} M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid'_closure AddSubmonoid.toSubmonoid'_closureₓ'. -/
 theorem AddSubmonoid.toSubmonoid'_closure (S : Set (Additive M)) :
     (AddSubmonoid.closure S).toSubmonoid' = Submonoid.closure (Multiplicative.ofAdd ⁻¹' S) :=
@@ -186,7 +186,7 @@ abbrev Submonoid.toAddSubmonoid' : Submonoid (Multiplicative A) ≃o AddSubmonoi
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))) => (AddSubmonoid.{u1} A _inst_4) -> (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))) (AddSubmonoid.toSubmonoid.{u1} A _inst_4) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (fun (_x : Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) => (Multiplicative.{u1} A) -> A) (Equiv.hasCoeToFun.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
 but is expected to have type
-  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} A _inst_4) (fun (_x : AddSubmonoid.{u1} A _inst_4) => Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toSubmonoid.{u1} A _inst_4) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.{u1} A) (fun (_x : Multiplicative.{u1} A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Multiplicative.{u1} A) => A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
+  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} A _inst_4) (fun (_x : AddSubmonoid.{u1} A _inst_4) => Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (AddSubmonoid.toSubmonoid.{u1} A _inst_4) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.{u1} A) (fun (_x : Multiplicative.{u1} A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Multiplicative.{u1} A) => A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid_closure AddSubmonoid.toSubmonoid_closureₓ'. -/
 theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
     (AddSubmonoid.closure S).toSubmonoid = Submonoid.closure (Multiplicative.toAdd ⁻¹' S) :=
@@ -200,7 +200,7 @@ theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} (AddSubmonoid.{u1} A _inst_4) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (fun (_x : RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))))) => (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) -> (AddSubmonoid.{u1} A _inst_4)) (RelIso.hasCoeToFun.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))))) (Submonoid.toAddSubmonoid'.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) (fun (_x : Equiv.{succ u1, succ u1} A (Additive.{u1} A)) => A -> (Additive.{u1} A)) (Equiv.hasCoeToFun.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
 but is expected to have type
-  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} (AddSubmonoid.{u1} A _inst_4) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (_x : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => AddSubmonoid.{u1} A _inst_4) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Submonoid.toAddSubmonoid'.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : A) => Additive.{u1} A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
+  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} (AddSubmonoid.{u1} A _inst_4) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (_x : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => AddSubmonoid.{u1} A _inst_4) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (Submonoid.toAddSubmonoid'.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => Additive.{u1} A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid'_closure Submonoid.toAddSubmonoid'_closureₓ'. -/
 theorem Submonoid.toAddSubmonoid'_closure (S : Set (Multiplicative A)) :
     (Submonoid.closure S).toAddSubmonoid' = AddSubmonoid.closure (Additive.ofMul ⁻¹' S) :=
@@ -242,7 +242,7 @@ def comap (f : F) (S : Submonoid N) : Submonoid M
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (S : Submonoid.{u2} N _inst_2) (f : F), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} M _inst_1) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submonoid.{u2} N _inst_2) (Set.{u2} N) (HasLiftT.mk.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (CoeTCₓ.coe.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (SetLike.Set.hasCoeT.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) S))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (S : Submonoid.{u3} N _inst_2) (f : F), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) S))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (S : Submonoid.{u3} N _inst_2) (f : F), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_comap Submonoid.coe_comapₓ'. -/
 @[simp, to_additive]
 theorem coe_comap (S : Submonoid N) (f : F) : (S.comap f : Set M) = f ⁻¹' S :=
@@ -254,7 +254,7 @@ theorem coe_comap (S : Submonoid N) (f : F) : (S.comap f : Set M) = f ⁻¹' S :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {S : Submonoid.{u2} N _inst_2} {f : F} {x : M}, Iff (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) S)
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {S : Submonoid.{u3} N _inst_2} {f : F} {x : M}, Iff (Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) S)
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {S : Submonoid.{u3} N _inst_2} {f : F} {x : M}, Iff (Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) x) (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) S)
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_comap Submonoid.mem_comapₓ'. -/
 @[simp, to_additive]
 theorem mem_comap {S : Submonoid N} {f : F} {x : M} : x ∈ S.comap f ↔ f x ∈ S :=
@@ -301,7 +301,7 @@ def map (f : F) (S : Submonoid M) : Submonoid N
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u1} M _inst_1), Eq.{succ u2} (Set.{u2} N) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submonoid.{u2} N _inst_2) (Set.{u2} N) (HasLiftT.mk.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (CoeTCₓ.coe.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (SetLike.Set.hasCoeT.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Set.image.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} M _inst_1) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1), Eq.{succ u2} (Set.{u2} N) (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1), Eq.{succ u2} (Set.{u2} N) (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_map Submonoid.coe_mapₓ'. -/
 @[simp, to_additive]
 theorem coe_map (f : F) (S : Submonoid M) : (S.map f : Set N) = f '' S :=
@@ -313,7 +313,7 @@ theorem coe_map (f : F) (S : Submonoid M) : (S.map f : Set N) = f '' S :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u1} M _inst_1} {y : N}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) y (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Exists.{succ u1} M (fun (x : M) => Exists.{0} (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S) (fun (H : Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S) => Eq.{succ u2} N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) y)))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u3} M _inst_1} {y : N}, Iff (Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) y (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Exists.{succ u3} M (fun (x : M) => And (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) a) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) y)))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u3} M _inst_1} {y : N}, Iff (Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) y (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Exists.{succ u3} M (fun (x : M) => And (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) a) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) y)))
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map Submonoid.mem_mapₓ'. -/
 @[simp, to_additive]
 theorem mem_map {f : F} {S : Submonoid M} {y : N} : y ∈ S.map f ↔ ∃ x ∈ S, f x = y :=
@@ -325,7 +325,7 @@ theorem mem_map {f : F} {S : Submonoid M} {y : N} : y ∈ S.map f ↔ ∃ x ∈
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) {S : Submonoid.{u1} M _inst_1} {x : M}, (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S) -> (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {S : Submonoid.{u3} M _inst_1} {x : M}, (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {S : Submonoid.{u3} M _inst_1} {x : M}, (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S))
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map_of_mem Submonoid.mem_map_of_memₓ'. -/
 @[to_additive]
 theorem mem_map_of_mem (f : F) {S : Submonoid M} {x : M} (hx : x ∈ S) : f x ∈ S.map f :=
@@ -337,7 +337,7 @@ theorem mem_map_of_mem (f : F) {S : Submonoid M} {x : M} (hx : x ∈ S) : f x 
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u1} M _inst_1) (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S), Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) 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} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))))) x)) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1) (x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S)), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1) (x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S)), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)
 Case conversion may be inaccurate. Consider using '#align submonoid.apply_coe_mem_map Submonoid.apply_coe_mem_mapₓ'. -/
 @[to_additive]
 theorem apply_coe_mem_map (f : F) (S : Submonoid M) (x : S) : f x ∈ S.map f :=
@@ -365,7 +365,7 @@ include mc
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u1} M _inst_1} {x : M}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {x : M}, Iff (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {x : M}, Iff (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S))
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map_iff_mem Submonoid.mem_map_iff_memₓ'. -/
 @[to_additive]
 theorem mem_map_iff_mem {f : F} (hf : Function.Injective f) {S : Submonoid M} {x : M} :
@@ -587,7 +587,7 @@ include hf
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (GaloisCoinsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisCoinsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisCoinsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.gci_map_comap Submonoid.gciMapComapₓ'. -/
 /-- `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. -/
 @[to_additive " `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. "]
@@ -600,7 +600,7 @@ def gciMapComap : GaloisCoinsertion (map f) (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) S)
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) S)
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) S)
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_map_eq_of_injective Submonoid.comap_map_eq_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_map_eq_of_injective (S : Submonoid M) : (S.map f).comap f = S :=
@@ -612,7 +612,7 @@ theorem comap_map_eq_of_injective (S : Submonoid M) : (S.map f).comap f = S :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Surjective.{succ u2, succ u1} (Submonoid.{u2} N _inst_2) (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_surjective_of_injective Submonoid.comap_surjective_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
@@ -624,7 +624,7 @@ theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Injective.{succ u1, succ u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_injective_of_injective Submonoid.map_injective_of_injectiveₓ'. -/
 @[to_additive]
 theorem map_injective_of_injective : Function.Injective (map f) :=
@@ -636,7 +636,7 @@ theorem map_injective_of_injective : Function.Injective (map f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instInfSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSubmonoid.{u3} M _inst_1) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instInfSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSubmonoid.{u3} M _inst_1) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_inf_map_of_injective Submonoid.comap_inf_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_inf_map_of_injective (S T : Submonoid M) : (S.map f ⊓ T.map f).comap f = S ⊓ T :=
@@ -648,7 +648,7 @@ theorem comap_inf_map_of_injective (S T : Submonoid M) : (S.map f ⊓ T.map f).c
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (iInf.{u2, succ u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (iInf.{u1, succ u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι S))
 but is expected to have type
-  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (iInf.{u3, succ u1} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSetSubmonoid.{u3} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iInf.{u4, succ u1} (Submonoid.{u4} M _inst_1) (Submonoid.instInfSetSubmonoid.{u4} M _inst_1) ι S))
+  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (iInf.{u3, succ u1} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSetSubmonoid.{u3} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iInf.{u4, succ u1} (Submonoid.{u4} M _inst_1) (Submonoid.instInfSetSubmonoid.{u4} M _inst_1) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_infi_map_of_injective Submonoid.comap_iInf_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_iInf_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).map f).comap f = iInf S :=
@@ -660,7 +660,7 @@ theorem comap_iInf_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).map
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} M _inst_1) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} M _inst_1) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} M _inst_1) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} M _inst_1) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_sup_map_of_injective Submonoid.comap_sup_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_sup_map_of_injective (S T : Submonoid M) : (S.map f ⊔ T.map f).comap f = S ⊔ T :=
@@ -672,7 +672,7 @@ theorem comap_sup_map_of_injective (S T : Submonoid M) : (S.map f ⊔ T.map f).c
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (iSup.{u2, succ u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (iSup.{u1, succ u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι S))
 but is expected to have type
-  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (iSup.{u3, succ u1} (Submonoid.{u3} N _inst_2) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iSup.{u4, succ u1} (Submonoid.{u4} M _inst_1) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u4} M _inst_1)) ι S))
+  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (iSup.{u3, succ u1} (Submonoid.{u3} N _inst_2) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iSup.{u4, succ u1} (Submonoid.{u4} M _inst_1) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u4} M _inst_1)) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_supr_map_of_injective Submonoid.comap_iSup_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_iSup_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).map f).comap f = iSup S :=
@@ -684,7 +684,7 @@ theorem comap_iSup_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).map
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u1} M _inst_1} {T : Submonoid.{u1} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toHasLe.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {T : Submonoid.{u3} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2))))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} M _inst_1) (Preorder.toLE.{u3} (Submonoid.{u3} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1))))) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {T : Submonoid.{u3} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2))))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} M _inst_1) (Preorder.toLE.{u3} (Submonoid.{u3} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1))))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_le_map_iff_of_injective Submonoid.map_le_map_iff_of_injectiveₓ'. -/
 @[to_additive]
 theorem map_le_map_iff_of_injective {S T : Submonoid M} : S.map f ≤ T.map f ↔ S ≤ T :=
@@ -696,7 +696,7 @@ theorem map_le_map_iff_of_injective {S T : Submonoid M} : S.map f ≤ T.map f 
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (StrictMono.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_strict_mono_of_injective Submonoid.map_strictMono_of_injectiveₓ'. -/
 @[to_additive]
 theorem map_strictMono_of_injective : StrictMono (map f) :=
@@ -716,7 +716,7 @@ include hf
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (GaloisInsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisInsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisInsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.gi_map_comap Submonoid.giMapComapₓ'. -/
 /-- `map f` and `comap f` form a `galois_insertion` when `f` is surjective. -/
 @[to_additive " `map f` and `comap f` form a `galois_insertion` when `f` is surjective. "]
@@ -731,7 +731,7 @@ def giMapComap : GaloisInsertion (map f) (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) S)
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) S)
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) S)
 Case conversion may be inaccurate. Consider using '#align submonoid.map_comap_eq_of_surjective Submonoid.map_comap_eq_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_comap_eq_of_surjective (S : Submonoid N) : (S.comap f).map f = S :=
@@ -743,7 +743,7 @@ theorem map_comap_eq_of_surjective (S : Submonoid N) : (S.comap f).map f = S :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Surjective.{succ u1, succ u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_surjective_of_surjective Submonoid.map_surjective_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_surjective_of_surjective : Function.Surjective (map f) :=
@@ -755,7 +755,7 @@ theorem map_surjective_of_surjective : Function.Surjective (map f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Injective.{succ u2, succ u1} (Submonoid.{u2} N _inst_2) (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_injective_of_surjective Submonoid.comap_injective_of_surjectiveₓ'. -/
 @[to_additive]
 theorem comap_injective_of_surjective : Function.Injective (comap f) :=
@@ -767,7 +767,7 @@ theorem comap_injective_of_surjective : Function.Injective (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Inf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instInfSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSubmonoid.{u3} N _inst_2) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instInfSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSubmonoid.{u3} N _inst_2) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_inf_comap_of_surjective Submonoid.map_inf_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_inf_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊓ T.comap f).map f = S ⊓ T :=
@@ -779,7 +779,7 @@ theorem map_inf_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊓ T.comap
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (iInf.{u1, succ u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (iInf.{u2, succ u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (iInf.{u3, succ u1} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSetSubmonoid.{u3} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iInf.{u4, succ u1} (Submonoid.{u4} N _inst_2) (Submonoid.instInfSetSubmonoid.{u4} N _inst_2) ι S))
+  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (iInf.{u3, succ u1} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSetSubmonoid.{u3} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iInf.{u4, succ u1} (Submonoid.{u4} N _inst_2) (Submonoid.instInfSetSubmonoid.{u4} N _inst_2) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_infi_comap_of_surjective Submonoid.map_iInf_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_iInf_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).comap f).map f = iInf S :=
@@ -791,7 +791,7 @@ theorem map_iInf_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).co
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Sup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} M _inst_1) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} M _inst_1) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} N _inst_2) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} N _inst_2) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} M _inst_1) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} M _inst_1) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} N _inst_2) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} N _inst_2) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_sup_comap_of_surjective Submonoid.map_sup_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_sup_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊔ T.comap f).map f = S ⊔ T :=
@@ -803,7 +803,7 @@ theorem map_sup_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊔ T.comap
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (iSup.{u1, succ u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (iSup.{u2, succ u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (iSup.{u3, succ u1} (Submonoid.{u3} M _inst_1) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iSup.{u4, succ u1} (Submonoid.{u4} N _inst_2) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u4} N _inst_2)) ι S))
+  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (iSup.{u3, succ u1} (Submonoid.{u3} M _inst_1) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iSup.{u4, succ u1} (Submonoid.{u4} N _inst_2) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u4} N _inst_2)) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_supr_comap_of_surjective Submonoid.map_iSup_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_iSup_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).comap f).map f = iSup S :=
@@ -815,7 +815,7 @@ theorem map_iSup_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).co
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u2} N _inst_2} {T : Submonoid.{u2} N _inst_2}, Iff (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toHasLe.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} N _inst_2} {T : Submonoid.{u3} N _inst_2}, Iff (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} N _inst_2) (Preorder.toLE.{u3} (Submonoid.{u3} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2))))) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} N _inst_2} {T : Submonoid.{u3} N _inst_2}, Iff (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} N _inst_2) (Preorder.toLE.{u3} (Submonoid.{u3} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2))))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_le_comap_iff_of_surjective Submonoid.comap_le_comap_iff_of_surjectiveₓ'. -/
 @[to_additive]
 theorem comap_le_comap_iff_of_surjective {S T : Submonoid N} : S.comap f ≤ T.comap f ↔ S ≤ T :=
@@ -827,7 +827,7 @@ theorem comap_le_comap_iff_of_surjective {S T : Submonoid N} : S.comap f ≤ T.c
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (StrictMono.{u2, u1} (Submonoid.{u2} N _inst_2) (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_strict_mono_of_surjective Submonoid.comap_strictMono_of_surjectiveₓ'. -/
 @[to_additive]
 theorem comap_strictMono_of_surjective : StrictMono (comap f) :=
@@ -1031,7 +1031,7 @@ def Subtype : S' →* M :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {A : Type.{u2}} [_inst_4 : SetLike.{u2, u1} A M] [hA : SubmonoidClass.{u2, u1} A M _inst_1 _inst_4] (S' : A), Eq.{succ u1} ((fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) => (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') -> M) (SubmonoidClass.Subtype.{u1, u2} M _inst_1 A _inst_4 hA S')) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) => (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') -> M) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) (SubmonoidClass.Subtype.{u1, u2} M _inst_1 A _inst_4 hA S')) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (coeBase.{succ u1, succ u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u2} M A (SetLike.hasMem.{u2, u1} A M _inst_4) x S'))))))
 but is expected to have type
-  forall {M : Type.{u2}} [_inst_1 : MulOneClass.{u2} M] {A : Type.{u1}} [_inst_4 : SetLike.{u1, u2} A M] [hA : SubmonoidClass.{u1, u2} A M _inst_1 _inst_4] (S' : A), Eq.{succ u2} (forall (a : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S')) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1 (MonoidHom.monoidHomClass.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1))) (SubmonoidClass.Subtype.{u2, u1} M _inst_1 A _inst_4 hA S')) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S'))
+  forall {M : Type.{u2}} [_inst_1 : MulOneClass.{u2} M] {A : Type.{u1}} [_inst_4 : SetLike.{u1, u2} A M] [hA : SubmonoidClass.{u1, u2} A M _inst_1 _inst_4] (S' : A), Eq.{succ u2} (forall (a : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S')) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1 (MonoidHom.monoidHomClass.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1))) (SubmonoidClass.Subtype.{u2, u1} M _inst_1 A _inst_4 hA S')) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S'))
 Case conversion may be inaccurate. Consider using '#align submonoid_class.coe_subtype SubmonoidClass.coe_subtypeₓ'. -/
 @[simp, to_additive]
 theorem coe_subtype : (SubmonoidClass.Subtype S' : S' → M) = coe :=
@@ -1275,7 +1275,7 @@ def subtype : S →* M :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} ((coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) -> M) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) -> M) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Submonoid.subtype.{u1} M _inst_1 S)) ((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} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))))))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u1} M _inst_1 S)) (MulOneClass.toMul.{u1} M _inst_1) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1 (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1))) (Submonoid.subtype.{u1} M _inst_1 S)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u1} M _inst_1 S)) (MulOneClass.toMul.{u1} M _inst_1) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1 (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1))) (Submonoid.subtype.{u1} M _inst_1 S)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_subtype Submonoid.coe_subtypeₓ'. -/
 @[simp, to_additive]
 theorem coe_subtype : ⇑S.Subtype = coe :=
@@ -1316,7 +1316,7 @@ theorem topEquiv_toMonoidHom : (topEquiv : _ ≃* M).toMonoidHom = (⊤ : Submon
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), (Function.Injective.{succ u1, succ u2} M N (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f)) -> (MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))
 Case conversion may be inaccurate. Consider using '#align submonoid.equiv_map_of_injective Submonoid.equivMapOfInjectiveₓ'. -/
 /-- A subgroup is isomorphic to its image under an injective function. If you have an isomorphism,
 use `mul_equiv.submonoid_map` for better definitional equalities. -/
@@ -1331,7 +1331,7 @@ noncomputable def equivMapOfInjective (f : M →* N) (hf : Function.Injective f)
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (hf : Function.Injective.{succ u1, succ u2} M N (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f)) (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S), Eq.{succ u2} N ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (coeSubtype.{succ u2} N (fun (x : N) => Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (fun (_x : MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, 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 but is expected to have type
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(SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 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(Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (MulEquivClass.toEquivLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) 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(MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) x))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (S : Submonoid.{u2} M _inst_1) (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2) (hf : Function.Injective.{succ u2, succ u1} M N (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f)) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (MulEquivClass.toEquivLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)))))) (Submonoid.equivMapOfInjective.{u2, u1} M N _inst_1 _inst_2 S f hf) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) x))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_equiv_map_of_injective_apply Submonoid.coe_equivMapOfInjective_applyₓ'. -/
 @[simp, to_additive]
 theorem coe_equivMapOfInjective_apply (f : M →* N) (hf : Function.Injective f) (x : S) :
@@ -1682,7 +1682,7 @@ def mrange (f : F) : Submonoid N :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u2} (Set.{u2} N) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submonoid.{u2} N _inst_2) (Set.{u2} N) (HasLiftT.mk.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (CoeTCₓ.coe.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (SetLike.Set.hasCoeT.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Set.range.{u2, succ u1} N M (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} N) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Set.range.{u3, succ u2} N M (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} N) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Set.range.{u3, succ u2} N M (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.coe_mrange MonoidHom.coe_mrangeₓ'. -/
 @[simp, to_additive]
 theorem coe_mrange (f : F) : (mrange f : Set N) = Set.range f :=
@@ -1694,7 +1694,7 @@ theorem coe_mrange (f : F) : (mrange f : Set N) = Set.range f :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F} {y : N}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) y (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Exists.{succ u1} M (fun (x : M) => Eq.{succ u2} N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) y))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F} {y : N}, Iff (Membership.mem.{u3, u3} N (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) y (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Exists.{succ u2} M (fun (x : M) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) y))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F} {y : N}, Iff (Membership.mem.{u3, u3} N (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) y (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Exists.{succ u2} M (fun (x : M) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) x) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) y))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mem_mrange MonoidHom.mem_mrangeₓ'. -/
 @[simp, to_additive]
 theorem mem_mrange {f : F} {y : N} : y ∈ mrange f ↔ ∃ x, f x = y :=
@@ -1734,7 +1734,7 @@ include mc
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, Iff (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasTop.{u2} N _inst_2))) (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, Iff (Eq.{succ u3} (Submonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instTopSubmonoid.{u3} N _inst_2))) (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, Iff (Eq.{succ u3} (Submonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instTopSubmonoid.{u3} N _inst_2))) (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mrange_top_iff_surjective MonoidHom.mrange_top_iff_surjectiveₓ'. -/
 @[to_additive]
 theorem mrange_top_iff_surjective {f : F} : mrange f = (⊤ : Submonoid N) ↔ Function.Surjective f :=
@@ -1746,7 +1746,7 @@ theorem mrange_top_iff_surjective {f : F} : mrange f = (⊤ : Submonoid N) ↔ F
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F), (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasTop.{u2} N _inst_2)))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u3, u2, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instTopSubmonoid.{u2} N _inst_2)))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u3, u2, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instTopSubmonoid.{u2} N _inst_2)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mrange_top_of_surjective MonoidHom.mrange_top_of_surjectiveₓ'. -/
 /-- The range of a surjective monoid hom is the whole of the codomain. -/
 @[to_additive "The range of a surjective `add_monoid` hom is the whole of the codomain."]
@@ -1760,7 +1760,7 @@ theorem mrange_top_of_surjective (f : F) (hf : Function.Surjective f) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u2} N), LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) s)) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u2} N _inst_2 s))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} N), LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.closure.{u2} M _inst_1 (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) s)) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} N _inst_2 s))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} N), LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.closure.{u2} M _inst_1 (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) s)) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} N _inst_2 s))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mclosure_preimage_le MonoidHom.mclosure_preimage_leₓ'. -/
 @[to_additive]
 theorem mclosure_preimage_le (f : F) (s : Set N) : closure (f ⁻¹' s) ≤ (closure s).comap f :=
@@ -1772,7 +1772,7 @@ theorem mclosure_preimage_le (f : F) (s : Set N) : closure (f ⁻¹' s) ≤ (clo
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u1} M), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u1} M _inst_1 s)) (Submonoid.closure.{u2} N _inst_2 (Set.image.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) s))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} M), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} M _inst_1 s)) (Submonoid.closure.{u2} N _inst_2 (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) s))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} M), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} M _inst_1 s)) (Submonoid.closure.{u2} N _inst_2 (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) s))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_mclosure MonoidHom.map_mclosureₓ'. -/
 /-- The image under a monoid hom of the submonoid generated by a set equals the submonoid generated
     by the image of the set. -/
@@ -1802,7 +1802,7 @@ def restrict {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M] (
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} {S : Type.{u3}} [_inst_4 : MulOneClass.{u2} N] [_inst_5 : SetLike.{u3, u1} S M] [_inst_6 : SubmonoidClass.{u3, u1} S M _inst_1 _inst_5] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (s : S) (x : coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s), Eq.{succ u2} N (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) N (SubmonoidClass.toMulOneClass.{u1, u3} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) N (SubmonoidClass.toMulOneClass.{u1, u3} M _inst_1 S _inst_5 _inst_6 s) _inst_4) => (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) -> N) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) N (SubmonoidClass.toMulOneClass.{u1, u3} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (MonoidHom.restrict.{u1, u2, u3} M _inst_1 N S _inst_4 _inst_5 _inst_6 f s) x) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_4) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_4) f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (coeBase.{succ u1, succ u1} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u3} M S (SetLike.hasMem.{u3, u1} S M _inst_5) x s))))) x))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u3}} {S : Type.{u2}} [_inst_4 : MulOneClass.{u3} N] [_inst_5 : SetLike.{u2, u1} S M] [_inst_6 : SubmonoidClass.{u2, u1} S M _inst_1 _inst_5] (f : MonoidHom.{u1, u3} M N _inst_1 _inst_4) (s : S) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s)) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4 (MonoidHom.monoidHomClass.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4))) (MonoidHom.restrict.{u1, u3, u2} M _inst_1 N S _inst_4 _inst_5 _inst_6 f s) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u3} M N _inst_1 _inst_4))) f (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u2, u1} S M _inst_5 s)) x))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u3}} {S : Type.{u2}} [_inst_4 : MulOneClass.{u3} N] [_inst_5 : SetLike.{u2, u1} S M] [_inst_6 : SubmonoidClass.{u2, u1} S M _inst_1 _inst_5] (f : MonoidHom.{u1, u3} M N _inst_1 _inst_4) (s : S) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s)) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4 (MonoidHom.monoidHomClass.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4))) (MonoidHom.restrict.{u1, u3, u2} M _inst_1 N S _inst_4 _inst_5 _inst_6 f s) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u3} M N _inst_1 _inst_4))) f (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u2, u1} S M _inst_5 s)) x))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.restrict_apply MonoidHom.restrict_applyₓ'. -/
 @[simp, to_additive]
 theorem restrict_apply {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M]
@@ -1828,7 +1828,7 @@ theorem restrict_mrange (f : M →* N) : (f.restrict S).mrange = S.map f := by
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {S : Type.{u3}} [_inst_4 : SetLike.{u3, u2} S N] [_inst_5 : SubmonoidClass.{u3, u2} S N _inst_2 _inst_4] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (s : S), (forall (x : M), Membership.Mem.{u2, u3} N S (SetLike.hasMem.{u3, u2} S N _inst_4) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f x) s) -> (MonoidHom.{u1, u2} M (coeSort.{succ u3, succ (succ u2)} S Type.{u2} (SetLike.hasCoeToSort.{u3, u2} S N _inst_4) s) _inst_1 (SubmonoidClass.toMulOneClass.{u2, u3} N _inst_2 S _inst_4 _inst_5 s))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {S : Type.{u3}} [_inst_4 : SetLike.{u3, u2} S N] [_inst_5 : SubmonoidClass.{u3, u2} S N _inst_2 _inst_4] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (s : S), (forall (x : M), Membership.mem.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) S (SetLike.instMembership.{u3, u2} S N _inst_4) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f x) s) -> (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u3} N S (SetLike.instMembership.{u3, u2} S N _inst_4) x s)) _inst_1 (SubmonoidClass.toMulOneClass.{u2, u3} N _inst_2 S _inst_4 _inst_5 s))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {S : Type.{u3}} [_inst_4 : SetLike.{u3, u2} S N] [_inst_5 : SubmonoidClass.{u3, u2} S N _inst_2 _inst_4] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (s : S), (forall (x : M), Membership.mem.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) x) S (SetLike.instMembership.{u3, u2} S N _inst_4) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f x) s) -> (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u3} N S (SetLike.instMembership.{u3, u2} S N _inst_4) x s)) _inst_1 (SubmonoidClass.toMulOneClass.{u2, u3} N _inst_2 S _inst_4 _inst_5 s))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.cod_restrict MonoidHom.codRestrictₓ'. -/
 /-- Restriction of a monoid hom to a submonoid of the codomain. -/
 @[to_additive "Restriction of an `add_monoid` hom to an `add_submonoid` of the codomain.",
@@ -1858,7 +1858,7 @@ def mrangeRestrict {N} [MulOneClass N] (f : M →* N) : M →* f.mrange :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} [_inst_4 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (x : M), Eq.{succ u2} N ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (coeSubtype.{succ u2} N (fun (x : N) => Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)))))) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (fun (_x : MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) => M -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHom.hasCoeToFun.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_4 f) x)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_4) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_4) f x)
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} [_inst_4 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (x : M), Eq.{succ u2} N (Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4) (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) (MonoidHom.monoidHomClass.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_4 f) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4))) f x)
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} [_inst_4 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (x : M), Eq.{succ u2} N (Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4) (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) (MonoidHom.monoidHomClass.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_4 f) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4))) f x)
 Case conversion may be inaccurate. Consider using '#align monoid_hom.coe_mrange_restrict MonoidHom.coe_mrangeRestrictₓ'. -/
 @[simp, to_additive]
 theorem coe_mrangeRestrict {N} [MulOneClass N] (f : M →* N) (x : M) :
@@ -1871,7 +1871,7 @@ theorem coe_mrangeRestrict {N} [MulOneClass N] (f : M →* N) (x : M) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), Function.Surjective.{succ u1, succ u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (fun (_x : MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) => M -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MonoidHom.hasCoeToFun.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_2 f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2), Function.Surjective.{succ u2, succ u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f)) (MonoidHom.monoidHomClass.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))))) (MonoidHom.mrangeRestrict.{u2, u1} M _inst_1 N _inst_2 f))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2), Function.Surjective.{succ u2, succ u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f)) (MonoidHom.monoidHomClass.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))))) (MonoidHom.mrangeRestrict.{u2, u1} M _inst_1 N _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mrange_restrict_surjective MonoidHom.mrangeRestrict_surjectiveₓ'. -/
 @[to_additive]
 theorem mrangeRestrict_surjective (f : M →* N) : Function.Surjective f.mrangeRestrict :=
@@ -1896,7 +1896,7 @@ def mker (f : F) : Submonoid M :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) {x : M}, Iff (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x (MonoidHom.mker.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Eq.{succ u2} N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) (OfNat.ofNat.{u2} N 1 (OfNat.mk.{u2} N 1 (One.one.{u2} N (MulOneClass.toHasOne.{u2} N _inst_2)))))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {x : M}, Iff (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) 1 (One.toOfNat1.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (MulOneClass.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) _inst_2))))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {x : M}, Iff (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) x) 1 (One.toOfNat1.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) x) (MulOneClass.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) x) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mem_mker MonoidHom.mem_mkerₓ'. -/
 @[to_additive]
 theorem mem_mker (f : F) {x : M} : x ∈ mker f ↔ f x = 1 :=
@@ -1908,7 +1908,7 @@ theorem mem_mker (f : F) {x : M} : x ∈ mker f ↔ f x = 1 :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} M _inst_1) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (MonoidHom.mker.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.hasSingleton.{u2} N) (OfNat.ofNat.{u2} N 1 (OfNat.mk.{u2} N 1 (One.one.{u2} N (MulOneClass.toHasOne.{u2} N _inst_2))))))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Set.preimage.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.instSingletonSet.{u2} N) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (MulOneClass.toOne.{u2} N _inst_2)))))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Set.preimage.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.instSingletonSet.{u2} N) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (MulOneClass.toOne.{u2} N _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.coe_mker MonoidHom.coe_mkerₓ'. -/
 @[to_additive]
 theorem coe_mker (f : F) : (mker f : Set M) = (f : M → N) ⁻¹' {1} :=
@@ -2090,7 +2090,7 @@ def submonoidMap (f : M →* N) (M' : Submonoid M) : M' →* M'.map f
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (M' : Submonoid.{u1} M _inst_1), Function.Surjective.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (Submonoid.toMulOneClass.{u1} M _inst_1 M') (Submonoid.toMulOneClass.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (Submonoid.toMulOneClass.{u1} M _inst_1 M') (Submonoid.toMulOneClass.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (Submonoid.toMulOneClass.{u1} M _inst_1 M') (Submonoid.toMulOneClass.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) (MonoidHom.submonoidMap.{u1, u2} M N _inst_1 _inst_2 f M'))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2) (M' : Submonoid.{u2} M _inst_1), Function.Surjective.{succ u2, succ u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Submonoid.toMulOneClass.{u2} M _inst_1 M')) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M')) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))))) (MonoidHom.submonoidMap.{u2, u1} M N _inst_1 _inst_2 f M'))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2) (M' : Submonoid.{u2} M _inst_1), Function.Surjective.{succ u2, succ u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Submonoid.toMulOneClass.{u2} M _inst_1 M')) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M')) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))))) (MonoidHom.submonoidMap.{u2, u1} M N _inst_1 _inst_2 f M'))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.submonoid_map_surjective MonoidHom.submonoidMap_surjectiveₓ'. -/
 @[to_additive]
 theorem submonoidMap_surjective (f : M →* N) (M' : Submonoid M) :
@@ -2331,7 +2331,7 @@ def submonoidCongr (h : S = T) : S ≃* T :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) {g : N -> M}, (Function.LeftInverse.{succ u1, succ u2} M N g (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f)) -> (MulEquiv.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) (MulOneClass.toHasMul.{u1} M _inst_1) (Submonoid.mul.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) {g : N -> M}, (Function.LeftInverse.{succ u1, succ u2} M N g (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u1} M _inst_1) (Submonoid.mul.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) {g : N -> M}, (Function.LeftInverse.{succ u1, succ u2} M N g (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u1} M _inst_1) (Submonoid.mul.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)))
 Case conversion may be inaccurate. Consider using '#align mul_equiv.of_left_inverse' MulEquiv.ofLeftInverse'ₓ'. -/
 -- this name is primed so that the version to `f.range` instead of `f.mrange` can be unprimed.
 /-- A monoid homomorphism `f : M →* N` with a left-inverse `g : N → M` defines a multiplicative
@@ -2386,7 +2386,7 @@ theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (e : MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) (S : Submonoid.{u1} M _inst_1) (g : coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) ((fun (a : Sort.{max (succ u1) (succ u2)}) (b : Sort.{max (succ u2) (succ u1)}) [self : HasLiftT.{max (succ u1) (succ u2), max (succ u2) (succ u1)} a b] => self.0) (MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (HasLiftT.mk.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (CoeTCₓ.coe.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.hasCoeT.{u1, u2, max u1 u2} M N (MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.monoidHomClass.{max u1 u2, u1, u2} (MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.mulEquivClass.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)))))) e) S)), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (MulEquiv.{u2, u1} 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(Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) (Submonoid.mul.{u1} M _inst_1 S)) => (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) -> (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S)) (MulEquiv.hasCoeToFun.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N 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_inst_2 e S)) g) (Subtype.mk.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (MulEquiv.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) (fun (_x : MulEquiv.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) => N -> M) (MulEquiv.hasCoeToFun.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) (MulEquiv.symm.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) e) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N 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 but is expected to have type
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(Subtype.property.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S)) g))))
 Case conversion may be inaccurate. Consider using '#align mul_equiv.submonoid_map_symm_apply MulEquiv.submonoidMap_symm_applyₓ'. -/
 @[simp, to_additive AddEquiv.add_submonoid_map_symm_apply]
 theorem submonoidMap_symm_apply (e : M ≃* N) (S : Submonoid M) (g : S.map (e : M →* N)) :

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

@@ -82,7 +82,7 @@ section
 
 /- warning: submonoid.to_add_submonoid -> Submonoid.toAddSubmonoid is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M], OrderIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M], OrderIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M], OrderIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid Submonoid.toAddSubmonoidₓ'. -/
@@ -105,7 +105,7 @@ def Submonoid.toAddSubmonoid : Submonoid M ≃o AddSubmonoid (Additive M)
 
 /- warning: add_submonoid.to_submonoid' -> AddSubmonoid.toSubmonoid' is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M], OrderIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M], OrderIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M], OrderIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid' AddSubmonoid.toSubmonoid'ₓ'. -/
@@ -116,7 +116,7 @@ abbrev AddSubmonoid.toSubmonoid' : AddSubmonoid (Additive M) ≃o Submonoid M :=
 
 /- warning: submonoid.to_add_submonoid_closure -> Submonoid.toAddSubmonoid_closure is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (fun (_x : RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))) => (Submonoid.{u1} M _inst_1) -> (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))) (Submonoid.toAddSubmonoid.{u1} M _inst_1) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (fun (_x : Equiv.{succ u1, succ u1} (Additive.{u1} M) M) => (Additive.{u1} M) -> M) (Equiv.hasCoeToFun.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (fun (_x : RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))) => (Submonoid.{u1} M _inst_1) -> (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))) (Submonoid.toAddSubmonoid.{u1} M _inst_1) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (fun (_x : Equiv.{succ u1, succ u1} (Additive.{u1} M) M) => (Additive.{u1} M) -> M) (Equiv.hasCoeToFun.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} M _inst_1) (fun (_x : Submonoid.{u1} M _inst_1) => AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Submonoid.toAddSubmonoid.{u1} M _inst_1) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.{u1} M) (fun (_x : Additive.{u1} M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Additive.{u1} M) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid_closure Submonoid.toAddSubmonoid_closureₓ'. -/
@@ -129,7 +129,7 @@ theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
 
 /- warning: add_submonoid.to_submonoid'_closure -> AddSubmonoid.toSubmonoid'_closure is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))))) => (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) -> (Submonoid.{u1} M _inst_1)) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))))) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (fun (_x : Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) => M -> (Multiplicative.{u1} M)) (Equiv.hasCoeToFun.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))))) => (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) -> (Submonoid.{u1} M _inst_1)) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))))) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (fun (_x : Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) => M -> (Multiplicative.{u1} M)) (Equiv.hasCoeToFun.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (_x : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => Submonoid.{u1} M _inst_1) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => Multiplicative.{u1} M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid'_closure AddSubmonoid.toSubmonoid'_closureₓ'. -/
@@ -149,7 +149,7 @@ variable {A : Type _} [AddZeroClass A]
 
 /- warning: add_submonoid.to_submonoid -> AddSubmonoid.toSubmonoid is a dubious translation:
 lean 3 declaration is
-  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A], OrderIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))
+  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A], OrderIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))
 but is expected to have type
   forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A], OrderIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid AddSubmonoid.toSubmonoidₓ'. -/
@@ -173,7 +173,7 @@ def AddSubmonoid.toSubmonoid : AddSubmonoid A ≃o Submonoid (Multiplicative A)
 
 /- warning: submonoid.to_add_submonoid' -> Submonoid.toAddSubmonoid' is a dubious translation:
 lean 3 declaration is
-  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A], OrderIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))
+  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A], OrderIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))
 but is expected to have type
   forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A], OrderIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid' Submonoid.toAddSubmonoid'ₓ'. -/
@@ -184,7 +184,7 @@ abbrev Submonoid.toAddSubmonoid' : Submonoid (Multiplicative A) ≃o AddSubmonoi
 
 /- warning: add_submonoid.to_submonoid_closure -> AddSubmonoid.toSubmonoid_closure is a dubious translation:
 lean 3 declaration is
-  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))) => (AddSubmonoid.{u1} A _inst_4) -> (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))) (AddSubmonoid.toSubmonoid.{u1} A _inst_4) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (fun (_x : Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) => (Multiplicative.{u1} A) -> A) (Equiv.hasCoeToFun.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
+  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))) => (AddSubmonoid.{u1} A _inst_4) -> (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))) (AddSubmonoid.toSubmonoid.{u1} A _inst_4) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (fun (_x : Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) => (Multiplicative.{u1} A) -> A) (Equiv.hasCoeToFun.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
 but is expected to have type
   forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} A _inst_4) (fun (_x : AddSubmonoid.{u1} A _inst_4) => Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toSubmonoid.{u1} A _inst_4) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.{u1} A) (fun (_x : Multiplicative.{u1} A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Multiplicative.{u1} A) => A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid_closure AddSubmonoid.toSubmonoid_closureₓ'. -/
@@ -198,7 +198,7 @@ theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
 
 /- warning: submonoid.to_add_submonoid'_closure -> Submonoid.toAddSubmonoid'_closure is a dubious translation:
 lean 3 declaration is
-  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} (AddSubmonoid.{u1} A _inst_4) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (fun (_x : RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))))) => (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) -> (AddSubmonoid.{u1} A _inst_4)) (RelIso.hasCoeToFun.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))))) (Submonoid.toAddSubmonoid'.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) (fun (_x : Equiv.{succ u1, succ u1} A (Additive.{u1} A)) => A -> (Additive.{u1} A)) (Equiv.hasCoeToFun.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
+  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} (AddSubmonoid.{u1} A _inst_4) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (fun (_x : RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))))) => (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) -> (AddSubmonoid.{u1} A _inst_4)) (RelIso.hasCoeToFun.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toHasLe.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))))) (Submonoid.toAddSubmonoid'.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) (fun (_x : Equiv.{succ u1, succ u1} A (Additive.{u1} A)) => A -> (Additive.{u1} A)) (Equiv.hasCoeToFun.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
 but is expected to have type
   forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} (AddSubmonoid.{u1} A _inst_4) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (_x : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => AddSubmonoid.{u1} A _inst_4) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Submonoid.toAddSubmonoid'.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : A) => Additive.{u1} A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid'_closure Submonoid.toAddSubmonoid'_closureₓ'. -/
@@ -376,7 +376,7 @@ theorem mem_map_iff_mem {f : F} (hf : Function.Injective f) {S : Submonoid M} {x
 
 /- warning: submonoid.map_le_iff_le_comap -> Submonoid.map_le_iff_le_comap is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u1} M _inst_1} {T : Submonoid.{u2} N _inst_2}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) T) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u1} M _inst_1} {T : Submonoid.{u2} N _inst_2}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toHasLe.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) T) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))
 but is expected to have type
   forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u3} M _inst_1} {T : Submonoid.{u2} N _inst_2}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2))))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) T) (LE.le.{u3} (Submonoid.{u3} M _inst_1) (Preorder.toLE.{u3} (Submonoid.{u3} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1))))) S (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_le_iff_le_comap Submonoid.map_le_iff_le_comapₓ'. -/
@@ -400,7 +400,7 @@ theorem gc_map_comap (f : F) : GaloisConnection (map f) (comap f) := fun S T =>
 
 /- warning: submonoid.map_le_of_le_comap -> Submonoid.map_le_of_le_comap is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {T : Submonoid.{u2} N _inst_2} {f : F}, (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) -> (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) T)
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {T : Submonoid.{u2} N _inst_2} {f : F}, (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) -> (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toHasLe.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) T)
 but is expected to have type
   forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] (S : Submonoid.{u2} M _inst_1) {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {T : Submonoid.{u3} N _inst_2} {f : F}, (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) S (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T)) -> (LE.le.{u3} (Submonoid.{u3} N _inst_2) (Preorder.toLE.{u3} (Submonoid.{u3} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2))))) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) T)
 Case conversion may be inaccurate. Consider using '#align submonoid.map_le_of_le_comap Submonoid.map_le_of_le_comapₓ'. -/
@@ -412,7 +412,7 @@ theorem map_le_of_le_comap {T : Submonoid N} {f : F} : S ≤ T.comap f → S.map
 
 /- warning: submonoid.le_comap_of_map_le -> Submonoid.le_comap_of_map_le is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {T : Submonoid.{u2} N _inst_2} {f : F}, (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) T) -> (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {T : Submonoid.{u2} N _inst_2} {f : F}, (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toHasLe.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) T) -> (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))
 but is expected to have type
   forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] (S : Submonoid.{u2} M _inst_1) {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {T : Submonoid.{u3} N _inst_2} {f : F}, (LE.le.{u3} (Submonoid.{u3} N _inst_2) (Preorder.toLE.{u3} (Submonoid.{u3} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2))))) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) T) -> (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) S (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))
 Case conversion may be inaccurate. Consider using '#align submonoid.le_comap_of_map_le Submonoid.le_comap_of_map_leₓ'. -/
@@ -424,7 +424,7 @@ theorem le_comap_of_map_le {T : Submonoid N} {f : F} : S.map f ≤ T → S ≤ T
 
 /- warning: submonoid.le_comap_map -> Submonoid.le_comap_map is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S))
 but is expected to have type
   forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u3} M _inst_1) {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, LE.le.{u3} (Submonoid.{u3} M _inst_1) (Preorder.toLE.{u3} (Submonoid.{u3} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1))))) S (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S))
 Case conversion may be inaccurate. Consider using '#align submonoid.le_comap_map Submonoid.le_comap_mapₓ'. -/
@@ -436,7 +436,7 @@ theorem le_comap_map {f : F} : S ≤ (S.map f).comap f :=
 
 /- warning: submonoid.map_comap_le -> Submonoid.map_comap_le is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {S : Submonoid.{u2} N _inst_2} {f : F}, LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) S
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {S : Submonoid.{u2} N _inst_2} {f : F}, LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toHasLe.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) S
 but is expected to have type
   forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {S : Submonoid.{u3} N _inst_2} {f : F}, LE.le.{u3} (Submonoid.{u3} N _inst_2) (Preorder.toLE.{u3} (Submonoid.{u3} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2))))) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) S
 Case conversion may be inaccurate. Consider using '#align submonoid.map_comap_le Submonoid.map_comap_leₓ'. -/
@@ -682,7 +682,7 @@ theorem comap_iSup_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).map
 
 /- warning: submonoid.map_le_map_iff_of_injective -> Submonoid.map_le_map_iff_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u1} M _inst_1} {T : Submonoid.{u1} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S T))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u1} M _inst_1} {T : Submonoid.{u1} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toHasLe.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S T))
 but is expected to have type
   forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {T : Submonoid.{u3} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2))))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} M _inst_1) (Preorder.toLE.{u3} (Submonoid.{u3} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1))))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_le_map_iff_of_injective Submonoid.map_le_map_iff_of_injectiveₓ'. -/
@@ -813,7 +813,7 @@ theorem map_iSup_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).co
 
 /- warning: submonoid.comap_le_comap_iff_of_surjective -> Submonoid.comap_le_comap_iff_of_surjective is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u2} N _inst_2} {T : Submonoid.{u2} N _inst_2}, Iff (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) S T))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u2} N _inst_2} {T : Submonoid.{u2} N _inst_2}, Iff (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toHasLe.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) S T))
 but is expected to have type
   forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} N _inst_2} {T : Submonoid.{u3} N _inst_2}, Iff (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} N _inst_2) (Preorder.toLE.{u3} (Submonoid.{u3} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2))))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_le_comap_iff_of_surjective Submonoid.comap_le_comap_iff_of_surjectiveₓ'. -/
@@ -1405,7 +1405,7 @@ theorem mem_prod {s : Submonoid M} {t : Submonoid N} {p : M × N} :
 
 /- warning: submonoid.prod_mono -> Submonoid.prod_mono is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {s₁ : Submonoid.{u1} M _inst_1} {s₂ : Submonoid.{u1} M _inst_1} {t₁ : Submonoid.{u2} N _inst_2} {t₂ : Submonoid.{u2} N _inst_2}, (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) s₁ s₂) -> (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) t₁ t₂) -> (LE.le.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Preorder.toLE.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Prod.{u1, u2} M N) (Submonoid.setLike.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s₁ t₁) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s₂ t₂))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {s₁ : Submonoid.{u1} M _inst_1} {s₂ : Submonoid.{u1} M _inst_1} {t₁ : Submonoid.{u2} N _inst_2} {t₂ : Submonoid.{u2} N _inst_2}, (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) s₁ s₂) -> (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toHasLe.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) t₁ t₂) -> (LE.le.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Preorder.toHasLe.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Prod.{u1, u2} M N) (Submonoid.setLike.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s₁ t₁) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s₂ t₂))
 but is expected to have type
   forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] {s₁ : Submonoid.{u2} M _inst_1} {s₂ : Submonoid.{u2} M _inst_1} {t₁ : Submonoid.{u1} N _inst_2} {t₂ : Submonoid.{u1} N _inst_2}, (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) s₁ s₂) -> (LE.le.{u1} (Submonoid.{u1} N _inst_2) (Preorder.toLE.{u1} (Submonoid.{u1} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u1} N _inst_2))))) t₁ t₂) -> (LE.le.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Preorder.toLE.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instCompleteLatticeSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)))))) (Submonoid.prod.{u2, u1} M N _inst_1 _inst_2 s₁ t₁) (Submonoid.prod.{u2, u1} M N _inst_1 _inst_2 s₂ t₂))
 Case conversion may be inaccurate. Consider using '#align submonoid.prod_mono Submonoid.prod_monoₓ'. -/
@@ -1577,7 +1577,7 @@ theorem map_equiv_top (f : M ≃* N) : (⊤ : Submonoid M).map f.toMonoidHom = 
 
 /- warning: submonoid.le_prod_iff -> Submonoid.le_prod_iff is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {s : Submonoid.{u1} M _inst_1} {t : Submonoid.{u2} N _inst_2} {u : Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)}, Iff (LE.le.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Preorder.toLE.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Prod.{u1, u2} M N) (Submonoid.setLike.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) u (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s t)) (And (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.map.{max u1 u2, u1, max u1 u2} (Prod.{u1, u2} M N) M (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_1 (MonoidHom.{max u1 u2, u1} (Prod.{u1, u2} M N) M (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_1) (MonoidHom.monoidHomClass.{max u1 u2, u1} (Prod.{u1, u2} M N) M (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_1) (MonoidHom.fst.{u1, u2} M N _inst_1 _inst_2) u) s) (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{max u1 u2, u2, max u1 u2} (Prod.{u1, u2} M N) N (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_2 (MonoidHom.{max u1 u2, u2} (Prod.{u1, u2} M N) N (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_2) (MonoidHom.monoidHomClass.{max u1 u2, u2} (Prod.{u1, u2} M N) N (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_2) (MonoidHom.snd.{u1, u2} M N _inst_1 _inst_2) u) t))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {s : Submonoid.{u1} M _inst_1} {t : Submonoid.{u2} N _inst_2} {u : Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)}, Iff (LE.le.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Preorder.toHasLe.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Prod.{u1, u2} M N) (Submonoid.setLike.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) u (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s t)) (And (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.map.{max u1 u2, u1, max u1 u2} (Prod.{u1, u2} M N) M (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_1 (MonoidHom.{max u1 u2, u1} (Prod.{u1, u2} M N) M (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_1) (MonoidHom.monoidHomClass.{max u1 u2, u1} (Prod.{u1, u2} M N) M (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_1) (MonoidHom.fst.{u1, u2} M N _inst_1 _inst_2) u) s) (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toHasLe.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{max u1 u2, u2, max u1 u2} (Prod.{u1, u2} M N) N (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_2 (MonoidHom.{max u1 u2, u2} (Prod.{u1, u2} M N) N (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_2) (MonoidHom.monoidHomClass.{max u1 u2, u2} (Prod.{u1, u2} M N) N (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) _inst_2) (MonoidHom.snd.{u1, u2} M N _inst_1 _inst_2) u) t))
 but is expected to have type
   forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] {s : Submonoid.{u2} M _inst_1} {t : Submonoid.{u1} N _inst_2} {u : Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)}, Iff (LE.le.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Preorder.toLE.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instCompleteLatticeSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)))))) u (Submonoid.prod.{u2, u1} M N _inst_1 _inst_2 s t)) (And (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.map.{max u2 u1, u2, max u2 u1} (Prod.{u2, u1} M N) M (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) _inst_1 (MonoidHom.{max u1 u2, u2} (Prod.{u2, u1} M N) M (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) _inst_1) (MonoidHom.monoidHomClass.{max u2 u1, u2} (Prod.{u2, u1} M N) M (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) _inst_1) (MonoidHom.fst.{u2, u1} M N _inst_1 _inst_2) u) s) (LE.le.{u1} (Submonoid.{u1} N _inst_2) (Preorder.toLE.{u1} (Submonoid.{u1} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u1} N _inst_2))))) (Submonoid.map.{max u2 u1, u1, max u2 u1} (Prod.{u2, u1} M N) N (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) _inst_2 (MonoidHom.{max u1 u2, u1} (Prod.{u2, u1} M N) N (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) _inst_2) (MonoidHom.monoidHomClass.{max u2 u1, u1} (Prod.{u2, u1} M N) N (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) _inst_2) (MonoidHom.snd.{u2, u1} M N _inst_1 _inst_2) u) t))
 Case conversion may be inaccurate. Consider using '#align submonoid.le_prod_iff Submonoid.le_prod_iffₓ'. -/
@@ -1599,7 +1599,7 @@ theorem le_prod_iff {s : Submonoid M} {t : Submonoid N} {u : Submonoid (M × N)}
 
 /- warning: submonoid.prod_le_iff -> Submonoid.prod_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {s : Submonoid.{u1} M _inst_1} {t : Submonoid.{u2} N _inst_2} {u : Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)}, Iff (LE.le.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Preorder.toLE.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Prod.{u1, u2} M N) (Submonoid.setLike.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s t) u) (And (LE.le.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Preorder.toLE.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Prod.{u1, u2} M N) (Submonoid.setLike.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (Submonoid.map.{u1, max u1 u2, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.{u1, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u1, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.inl.{u1, u2} M N _inst_1 _inst_2) s) u) (LE.le.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Preorder.toLE.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Prod.{u1, u2} M N) (Submonoid.setLike.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (Submonoid.map.{u2, max u1 u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.{u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.inr.{u1, u2} M N _inst_1 _inst_2) t) u))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {s : Submonoid.{u1} M _inst_1} {t : Submonoid.{u2} N _inst_2} {u : Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)}, Iff (LE.le.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Preorder.toHasLe.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Prod.{u1, u2} M N) (Submonoid.setLike.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s t) u) (And (LE.le.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Preorder.toHasLe.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Prod.{u1, u2} M N) (Submonoid.setLike.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (Submonoid.map.{u1, max u1 u2, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.{u1, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u1, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.inl.{u1, u2} M N _inst_1 _inst_2) s) u) (LE.le.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Preorder.toHasLe.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SetLike.partialOrder.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Prod.{u1, u2} M N) (Submonoid.setLike.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (Submonoid.map.{u2, max u1 u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.{u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.inr.{u1, u2} M N _inst_1 _inst_2) t) u))
 but is expected to have type
   forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] {s : Submonoid.{u2} M _inst_1} {t : Submonoid.{u1} N _inst_2} {u : Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)}, Iff (LE.le.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Preorder.toLE.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instCompleteLatticeSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)))))) (Submonoid.prod.{u2, u1} M N _inst_1 _inst_2 s t) u) (And (LE.le.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Preorder.toLE.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instCompleteLatticeSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)))))) (Submonoid.map.{u2, max u2 u1, max u2 u1} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.{u2, max u1 u2} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u2, max u2 u1} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.inl.{u2, u1} M N _inst_1 _inst_2) s) u) (LE.le.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Preorder.toLE.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (PartialOrder.toPreorder.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instCompleteLatticeSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)))))) (Submonoid.map.{u1, max u2 u1, max u2 u1} N (Prod.{u2, u1} M N) _inst_2 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.{u1, max u1 u2} N (Prod.{u2, u1} M N) _inst_2 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (Prod.{u2, u1} M N) _inst_2 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.inr.{u2, u1} M N _inst_1 _inst_2) t) u))
 Case conversion may be inaccurate. Consider using '#align submonoid.prod_le_iff Submonoid.prod_le_iffₓ'. -/
@@ -1758,7 +1758,7 @@ theorem mrange_top_of_surjective (f : F) (hf : Function.Surjective f) :
 
 /- warning: monoid_hom.mclosure_preimage_le -> MonoidHom.mclosure_preimage_le is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u2} N), LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) s)) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u2} N _inst_2 s))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u2} N), LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) s)) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u2} N _inst_2 s))
 but is expected to have type
   forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} N), LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.closure.{u2} M _inst_1 (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) s)) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} N _inst_2 s))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mclosure_preimage_le MonoidHom.mclosure_preimage_leₓ'. -/
@@ -2216,7 +2216,7 @@ theorem mrange_inl_sup_mrange_inr : (inl M N).mrange ⊔ (inr M N).mrange = ⊤
 
 /- warning: submonoid.inclusion -> Submonoid.inclusion is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {S : Submonoid.{u1} M _inst_1} {T : Submonoid.{u1} M _inst_1}, (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S T) -> (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) T) (Submonoid.toMulOneClass.{u1} M _inst_1 S) (Submonoid.toMulOneClass.{u1} M _inst_1 T))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {S : Submonoid.{u1} M _inst_1} {T : Submonoid.{u1} M _inst_1}, (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toHasLe.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S T) -> (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) T) (Submonoid.toMulOneClass.{u1} M _inst_1 S) (Submonoid.toMulOneClass.{u1} M _inst_1 T))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {S : Submonoid.{u1} M _inst_1} {T : Submonoid.{u1} M _inst_1}, (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) S T) -> (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x T)) (Submonoid.toMulOneClass.{u1} M _inst_1 S) (Submonoid.toMulOneClass.{u1} M _inst_1 T))
 Case conversion may be inaccurate. Consider using '#align submonoid.inclusion Submonoid.inclusionₓ'. -/

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

@@ -1331,7 +1331,7 @@ noncomputable def equivMapOfInjective (f : M →* N) (hf : Function.Injective f)
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (hf : Function.Injective.{succ u1, succ u2} M N (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f)) (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S), Eq.{succ u2} N ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, 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 but is expected to have type
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(SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 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(Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)))))) (Submonoid.equivMapOfInjective.{u2, u1} M N _inst_1 _inst_2 S f hf) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) x))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (S : Submonoid.{u2} M _inst_1) (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2) (hf : Function.Injective.{succ u2, succ u1} M N (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f)) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (MulEquivClass.toEquivLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)))))) (Submonoid.equivMapOfInjective.{u2, u1} M N _inst_1 _inst_2 S f hf) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) x))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_equiv_map_of_injective_apply Submonoid.coe_equivMapOfInjective_applyₓ'. -/
 @[simp, to_additive]
 theorem coe_equivMapOfInjective_apply (f : M →* N) (hf : Function.Injective f) (x : S) :
@@ -1528,7 +1528,7 @@ theorem prod_bot_sup_bot_prod (s : Submonoid M) (t : Submonoid N) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {f : MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)} {K : Submonoid.{u1} M _inst_1} {x : N}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 f) K)) (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (MulEquiv.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) (fun (_x : MulEquiv.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) => N -> M) (MulEquiv.hasCoeToFun.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) (MulEquiv.symm.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) f) x) K)
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] {f : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)} {K : Submonoid.{u2} M _inst_1} {x : N}, Iff (Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 f) K)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => M) x) (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquivClass.instMonoidHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1))))) (MulEquiv.symm.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) f) x) K)
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] {f : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)} {K : Submonoid.{u2} M _inst_1} {x : N}, Iff (Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 f) K)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => M) x) (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => M) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (EquivLike.toEmbeddingLike.{max (succ u1) (succ u2), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulEquivClass.toEquivLike.{max u1 u2, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1) (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1))))) (MulEquiv.symm.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) f) x) K)
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map_equiv Submonoid.mem_map_equivₓ'. -/
 @[to_additive]
 theorem mem_map_equiv {f : M ≃* N} {K : Submonoid M} {x : N} :
@@ -2373,7 +2373,7 @@ def submonoidMap (e : M ≃* N) (S : Submonoid M) : S ≃* S.map e.toMonoidHom :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (e : MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) (S : Submonoid.{u1} M _inst_1) (g : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S), Eq.{succ u2} N ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) N (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) 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M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) N (coeSubtype.{succ u2} N (fun (x : N) => Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S))) (fun (_x : MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S))) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S))) (MulEquiv.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M 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(MulOneClass.toHasMul.{u2} N _inst_2)) => M -> N) (MulEquiv.hasCoeToFun.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) e ((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} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))))) g))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (e : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) (S : Submonoid.{u2} M _inst_1) (g : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => 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u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (MulEquivClass.toEquivLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) 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(MulEquiv.submonoidMap.{u2, u1} M N _inst_1 _inst_2 e S) g)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M (fun (_x : M) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N (MulEquivClass.toEquivLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))))) e (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) g))
 Case conversion may be inaccurate. Consider using '#align mul_equiv.coe_submonoid_map_apply MulEquiv.coe_submonoidMap_applyₓ'. -/
 @[simp, to_additive]
 theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
@@ -2386,7 +2386,7 @@ theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (e : MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) (S : Submonoid.{u1} M _inst_1) (g : coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) ((fun (a : Sort.{max (succ u1) (succ u2)}) (b : Sort.{max (succ u2) (succ u1)}) [self : HasLiftT.{max (succ u1) (succ u2), max (succ u2) (succ u1)} a b] => self.0) (MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (HasLiftT.mk.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) 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 but is expected to have type
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(MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g) (Set.image.{u2, u1} M N (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} M N) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => N) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} M N) (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e)) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S))) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : N) => M) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Set.{u2} M) (Set.instMembershipSet.{u2} M) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} N M) N (fun (_x : N) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : N) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} N M) (Equiv.symm.{succ u2, succ u1} M N (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e)) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) (Set.mem_image_equiv.{u1, u2} M N (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S) (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Subtype.property.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S)) g))))
 Case conversion may be inaccurate. Consider using '#align mul_equiv.submonoid_map_symm_apply MulEquiv.submonoidMap_symm_applyₓ'. -/
 @[simp, to_additive AddEquiv.add_submonoid_map_symm_apply]
 theorem submonoidMap_symm_apply (e : M ≃* N) (S : Submonoid M) (g : S.map (e : M →* N)) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -506,17 +506,17 @@ theorem map_sup (S T : Submonoid M) (f : F) : (S ⊔ T).map f = S.map f ⊔ T.ma
 #align submonoid.map_sup Submonoid.map_sup
 #align add_submonoid.map_sup AddSubmonoid.map_sup
 
-/- warning: submonoid.map_supr -> Submonoid.map_supᵢ is a dubious translation:
+/- warning: submonoid.map_supr -> Submonoid.map_iSup is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Sort.{u4}} (f : F) (s : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (supᵢ.{u1, u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι s)) (supᵢ.{u2, u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (s i)))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Sort.{u4}} (f : F) (s : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (iSup.{u1, u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι s)) (iSup.{u2, u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (s i)))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {ι : Sort.{u4}} (f : F) (s : ι -> (Submonoid.{u3} M _inst_1)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, u4} (Submonoid.{u3} M _inst_1) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)) ι s)) (supᵢ.{u2, u4} (Submonoid.{u2} N _inst_2) (CompleteLattice.toSupSet.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)) ι (fun (i : ι) => Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (s i)))
-Case conversion may be inaccurate. Consider using '#align submonoid.map_supr Submonoid.map_supᵢₓ'. -/
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {ι : Sort.{u4}} (f : F) (s : ι -> (Submonoid.{u3} M _inst_1)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (iSup.{u3, u4} (Submonoid.{u3} M _inst_1) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)) ι s)) (iSup.{u2, u4} (Submonoid.{u2} N _inst_2) (CompleteLattice.toSupSet.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)) ι (fun (i : ι) => Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (s i)))
+Case conversion may be inaccurate. Consider using '#align submonoid.map_supr Submonoid.map_iSupₓ'. -/
 @[to_additive]
-theorem map_supᵢ {ι : Sort _} (f : F) (s : ι → Submonoid M) : (supᵢ s).map f = ⨆ i, (s i).map f :=
-  (gc_map_comap f : GaloisConnection (map f) (comap f)).l_supᵢ
-#align submonoid.map_supr Submonoid.map_supᵢ
-#align add_submonoid.map_supr AddSubmonoid.map_supᵢ
+theorem map_iSup {ι : Sort _} (f : F) (s : ι → Submonoid M) : (iSup s).map f = ⨆ i, (s i).map f :=
+  (gc_map_comap f : GaloisConnection (map f) (comap f)).l_iSup
+#align submonoid.map_supr Submonoid.map_iSup
+#align add_submonoid.map_supr AddSubmonoid.map_iSup
 
 /- warning: submonoid.comap_inf -> Submonoid.comap_inf is a dubious translation:
 lean 3 declaration is
@@ -530,18 +530,18 @@ theorem comap_inf (S T : Submonoid N) (f : F) : (S ⊓ T).comap f = S.comap f 
 #align submonoid.comap_inf Submonoid.comap_inf
 #align add_submonoid.comap_inf AddSubmonoid.comap_inf
 
-/- warning: submonoid.comap_infi -> Submonoid.comap_infᵢ is a dubious translation:
+/- warning: submonoid.comap_infi -> Submonoid.comap_iInf is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Sort.{u4}} (f : F) (s : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (infᵢ.{u2, u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι s)) (infᵢ.{u1, u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (s i)))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Sort.{u4}} (f : F) (s : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (iInf.{u2, u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι s)) (iInf.{u1, u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (s i)))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {ι : Sort.{u4}} (f : F) (s : ι -> (Submonoid.{u3} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, u4} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSetSubmonoid.{u3} N _inst_2) ι s)) (infᵢ.{u2, u4} (Submonoid.{u2} M _inst_1) (Submonoid.instInfSetSubmonoid.{u2} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (s i)))
-Case conversion may be inaccurate. Consider using '#align submonoid.comap_infi Submonoid.comap_infᵢₓ'. -/
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {ι : Sort.{u4}} (f : F) (s : ι -> (Submonoid.{u3} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (iInf.{u3, u4} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSetSubmonoid.{u3} N _inst_2) ι s)) (iInf.{u2, u4} (Submonoid.{u2} M _inst_1) (Submonoid.instInfSetSubmonoid.{u2} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (s i)))
+Case conversion may be inaccurate. Consider using '#align submonoid.comap_infi Submonoid.comap_iInfₓ'. -/
 @[to_additive]
-theorem comap_infᵢ {ι : Sort _} (f : F) (s : ι → Submonoid N) :
-    (infᵢ s).comap f = ⨅ i, (s i).comap f :=
-  (gc_map_comap f : GaloisConnection (map f) (comap f)).u_infᵢ
-#align submonoid.comap_infi Submonoid.comap_infᵢ
-#align add_submonoid.comap_infi AddSubmonoid.comap_infᵢ
+theorem comap_iInf {ι : Sort _} (f : F) (s : ι → Submonoid N) :
+    (iInf s).comap f = ⨅ i, (s i).comap f :=
+  (gc_map_comap f : GaloisConnection (map f) (comap f)).u_iInf
+#align submonoid.comap_infi Submonoid.comap_iInf
+#align add_submonoid.comap_infi AddSubmonoid.comap_iInf
 
 /- warning: submonoid.map_bot -> Submonoid.map_bot is a dubious translation:
 lean 3 declaration is
@@ -644,17 +644,17 @@ theorem comap_inf_map_of_injective (S T : Submonoid M) : (S.map f ⊓ T.map f).c
 #align submonoid.comap_inf_map_of_injective Submonoid.comap_inf_map_of_injective
 #align add_submonoid.comap_inf_map_of_injective AddSubmonoid.comap_inf_map_of_injective
 
-/- warning: submonoid.comap_infi_map_of_injective -> Submonoid.comap_infᵢ_map_of_injective is a dubious translation:
+/- warning: submonoid.comap_infi_map_of_injective -> Submonoid.comap_iInf_map_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (infᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι S))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (iInf.{u2, succ u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (iInf.{u1, succ u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι S))
 but is expected to have type
-  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, succ u1} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSetSubmonoid.{u3} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u4, succ u1} (Submonoid.{u4} M _inst_1) (Submonoid.instInfSetSubmonoid.{u4} M _inst_1) ι S))
-Case conversion may be inaccurate. Consider using '#align submonoid.comap_infi_map_of_injective Submonoid.comap_infᵢ_map_of_injectiveₓ'. -/
+  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (iInf.{u3, succ u1} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSetSubmonoid.{u3} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iInf.{u4, succ u1} (Submonoid.{u4} M _inst_1) (Submonoid.instInfSetSubmonoid.{u4} M _inst_1) ι S))
+Case conversion may be inaccurate. Consider using '#align submonoid.comap_infi_map_of_injective Submonoid.comap_iInf_map_of_injectiveₓ'. -/
 @[to_additive]
-theorem comap_infᵢ_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).map f).comap f = infᵢ S :=
-  (gciMapComap hf).u_infᵢ_l _
-#align submonoid.comap_infi_map_of_injective Submonoid.comap_infᵢ_map_of_injective
-#align add_submonoid.comap_infi_map_of_injective AddSubmonoid.comap_infᵢ_map_of_injective
+theorem comap_iInf_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).map f).comap f = iInf S :=
+  (gciMapComap hf).u_iInf_l _
+#align submonoid.comap_infi_map_of_injective Submonoid.comap_iInf_map_of_injective
+#align add_submonoid.comap_infi_map_of_injective AddSubmonoid.comap_iInf_map_of_injective
 
 /- warning: submonoid.comap_sup_map_of_injective -> Submonoid.comap_sup_map_of_injective is a dubious translation:
 lean 3 declaration is
@@ -668,17 +668,17 @@ theorem comap_sup_map_of_injective (S T : Submonoid M) : (S.map f ⊔ T.map f).c
 #align submonoid.comap_sup_map_of_injective Submonoid.comap_sup_map_of_injective
 #align add_submonoid.comap_sup_map_of_injective AddSubmonoid.comap_sup_map_of_injective
 
-/- warning: submonoid.comap_supr_map_of_injective -> Submonoid.comap_supᵢ_map_of_injective is a dubious translation:
+/- warning: submonoid.comap_supr_map_of_injective -> Submonoid.comap_iSup_map_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (supᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι S))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (iSup.{u2, succ u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (iSup.{u1, succ u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι S))
 but is expected to have type
-  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, succ u1} (Submonoid.{u3} N _inst_2) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u4, succ u1} (Submonoid.{u4} M _inst_1) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u4} M _inst_1)) ι S))
-Case conversion may be inaccurate. Consider using '#align submonoid.comap_supr_map_of_injective Submonoid.comap_supᵢ_map_of_injectiveₓ'. -/
+  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (iSup.{u3, succ u1} (Submonoid.{u3} N _inst_2) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iSup.{u4, succ u1} (Submonoid.{u4} M _inst_1) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u4} M _inst_1)) ι S))
+Case conversion may be inaccurate. Consider using '#align submonoid.comap_supr_map_of_injective Submonoid.comap_iSup_map_of_injectiveₓ'. -/
 @[to_additive]
-theorem comap_supᵢ_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).map f).comap f = supᵢ S :=
-  (gciMapComap hf).u_supᵢ_l _
-#align submonoid.comap_supr_map_of_injective Submonoid.comap_supᵢ_map_of_injective
-#align add_submonoid.comap_supr_map_of_injective AddSubmonoid.comap_supᵢ_map_of_injective
+theorem comap_iSup_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).map f).comap f = iSup S :=
+  (gciMapComap hf).u_iSup_l _
+#align submonoid.comap_supr_map_of_injective Submonoid.comap_iSup_map_of_injective
+#align add_submonoid.comap_supr_map_of_injective AddSubmonoid.comap_iSup_map_of_injective
 
 /- warning: submonoid.map_le_map_iff_of_injective -> Submonoid.map_le_map_iff_of_injective is a dubious translation:
 lean 3 declaration is
@@ -775,17 +775,17 @@ theorem map_inf_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊓ T.comap
 #align submonoid.map_inf_comap_of_surjective Submonoid.map_inf_comap_of_surjective
 #align add_submonoid.map_inf_comap_of_surjective AddSubmonoid.map_inf_comap_of_surjective
 
-/- warning: submonoid.map_infi_comap_of_surjective -> Submonoid.map_infᵢ_comap_of_surjective is a dubious translation:
+/- warning: submonoid.map_infi_comap_of_surjective -> Submonoid.map_iInf_comap_of_surjective is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (infᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι S))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (iInf.{u1, succ u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (iInf.{u2, succ u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, succ u1} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSetSubmonoid.{u3} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u4, succ u1} (Submonoid.{u4} N _inst_2) (Submonoid.instInfSetSubmonoid.{u4} N _inst_2) ι S))
-Case conversion may be inaccurate. Consider using '#align submonoid.map_infi_comap_of_surjective Submonoid.map_infᵢ_comap_of_surjectiveₓ'. -/
+  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (iInf.{u3, succ u1} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSetSubmonoid.{u3} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iInf.{u4, succ u1} (Submonoid.{u4} N _inst_2) (Submonoid.instInfSetSubmonoid.{u4} N _inst_2) ι S))
+Case conversion may be inaccurate. Consider using '#align submonoid.map_infi_comap_of_surjective Submonoid.map_iInf_comap_of_surjectiveₓ'. -/
 @[to_additive]
-theorem map_infᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).comap f).map f = infᵢ S :=
-  (giMapComap hf).l_infᵢ_u _
-#align submonoid.map_infi_comap_of_surjective Submonoid.map_infᵢ_comap_of_surjective
-#align add_submonoid.map_infi_comap_of_surjective AddSubmonoid.map_infᵢ_comap_of_surjective
+theorem map_iInf_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).comap f).map f = iInf S :=
+  (giMapComap hf).l_iInf_u _
+#align submonoid.map_infi_comap_of_surjective Submonoid.map_iInf_comap_of_surjective
+#align add_submonoid.map_infi_comap_of_surjective AddSubmonoid.map_iInf_comap_of_surjective
 
 /- warning: submonoid.map_sup_comap_of_surjective -> Submonoid.map_sup_comap_of_surjective is a dubious translation:
 lean 3 declaration is
@@ -799,17 +799,17 @@ theorem map_sup_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊔ T.comap
 #align submonoid.map_sup_comap_of_surjective Submonoid.map_sup_comap_of_surjective
 #align add_submonoid.map_sup_comap_of_surjective AddSubmonoid.map_sup_comap_of_surjective
 
-/- warning: submonoid.map_supr_comap_of_surjective -> Submonoid.map_supᵢ_comap_of_surjective is a dubious translation:
+/- warning: submonoid.map_supr_comap_of_surjective -> Submonoid.map_iSup_comap_of_surjective is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (supᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι S))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (iSup.{u1, succ u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (iSup.{u2, succ u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, succ u1} (Submonoid.{u3} M _inst_1) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u4, succ u1} (Submonoid.{u4} N _inst_2) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u4} N _inst_2)) ι S))
-Case conversion may be inaccurate. Consider using '#align submonoid.map_supr_comap_of_surjective Submonoid.map_supᵢ_comap_of_surjectiveₓ'. -/
+  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (iSup.{u3, succ u1} (Submonoid.{u3} M _inst_1) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (iSup.{u4, succ u1} (Submonoid.{u4} N _inst_2) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u4} N _inst_2)) ι S))
+Case conversion may be inaccurate. Consider using '#align submonoid.map_supr_comap_of_surjective Submonoid.map_iSup_comap_of_surjectiveₓ'. -/
 @[to_additive]
-theorem map_supᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).comap f).map f = supᵢ S :=
-  (giMapComap hf).l_supᵢ_u _
-#align submonoid.map_supr_comap_of_surjective Submonoid.map_supᵢ_comap_of_surjective
-#align add_submonoid.map_supr_comap_of_surjective AddSubmonoid.map_supᵢ_comap_of_surjective
+theorem map_iSup_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).comap f).map f = iSup S :=
+  (giMapComap hf).l_iSup_u _
+#align submonoid.map_supr_comap_of_surjective Submonoid.map_iSup_comap_of_surjective
+#align add_submonoid.map_supr_comap_of_surjective AddSubmonoid.map_iSup_comap_of_surjective
 
 /- warning: submonoid.comap_le_comap_iff_of_surjective -> Submonoid.comap_le_comap_iff_of_surjective is a dubious translation:
 lean 3 declaration is

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

@@ -118,7 +118,7 @@ abbrev AddSubmonoid.toSubmonoid' : AddSubmonoid (Additive M) ≃o Submonoid M :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (fun (_x : RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))) => (Submonoid.{u1} M _inst_1) -> (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))) (Submonoid.toAddSubmonoid.{u1} M _inst_1) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (fun (_x : Equiv.{succ u1, succ u1} (Additive.{u1} M) M) => (Additive.{u1} M) -> M) (Equiv.hasCoeToFun.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} M _inst_1) => AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.closure.{u1} M _inst_1 S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (Submonoid.{u1} M _inst_1) (fun (_x : Submonoid.{u1} M _inst_1) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} M _inst_1) => AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))) (RelEmbedding.toEmbedding.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Submonoid.toAddSubmonoid.{u1} M _inst_1))) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.{u1} M) (fun (_x : Additive.{u1} M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Additive.{u1} M) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} M _inst_1) (fun (_x : Submonoid.{u1} M _inst_1) => AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Submonoid.toAddSubmonoid.{u1} M _inst_1) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.{u1} M) (fun (_x : Additive.{u1} M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Additive.{u1} M) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid_closure Submonoid.toAddSubmonoid_closureₓ'. -/
 theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
     (Submonoid.closure S).toAddSubmonoid = AddSubmonoid.closure (Additive.toMul ⁻¹' S) :=
@@ -131,7 +131,7 @@ theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))))) => (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) -> (Submonoid.{u1} M _inst_1)) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))))) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (fun (_x : Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) => M -> (Multiplicative.{u1} M)) (Equiv.hasCoeToFun.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => Submonoid.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (_x : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => Submonoid.{u1} M _inst_1) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1))) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => Multiplicative.{u1} M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (_x : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => Submonoid.{u1} M _inst_1) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => Multiplicative.{u1} M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid'_closure AddSubmonoid.toSubmonoid'_closureₓ'. -/
 theorem AddSubmonoid.toSubmonoid'_closure (S : Set (Additive M)) :
     (AddSubmonoid.closure S).toSubmonoid' = Submonoid.closure (Multiplicative.ofAdd ⁻¹' S) :=
@@ -186,7 +186,7 @@ abbrev Submonoid.toAddSubmonoid' : Submonoid (Multiplicative A) ≃o AddSubmonoi
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))) => (AddSubmonoid.{u1} A _inst_4) -> (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))) (AddSubmonoid.toSubmonoid.{u1} A _inst_4) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (fun (_x : Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) => (Multiplicative.{u1} A) -> A) (Equiv.hasCoeToFun.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
 but is expected to have type
-  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} A _inst_4) => Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.closure.{u1} A _inst_4 S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (AddSubmonoid.{u1} A _inst_4) (fun (_x : AddSubmonoid.{u1} A _inst_4) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} A _inst_4) => Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toSubmonoid.{u1} A _inst_4))) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.{u1} A) (fun (_x : Multiplicative.{u1} A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Multiplicative.{u1} A) => A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
+  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} A _inst_4) (fun (_x : AddSubmonoid.{u1} A _inst_4) => Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toSubmonoid.{u1} A _inst_4) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.{u1} A) (fun (_x : Multiplicative.{u1} A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Multiplicative.{u1} A) => A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid_closure AddSubmonoid.toSubmonoid_closureₓ'. -/
 theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
     (AddSubmonoid.closure S).toSubmonoid = Submonoid.closure (Multiplicative.toAdd ⁻¹' S) :=
@@ -200,7 +200,7 @@ theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} (AddSubmonoid.{u1} A _inst_4) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (fun (_x : RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))))) => (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) -> (AddSubmonoid.{u1} A _inst_4)) (RelIso.hasCoeToFun.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))))) (Submonoid.toAddSubmonoid'.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) (fun (_x : Equiv.{succ u1, succ u1} A (Additive.{u1} A)) => A -> (Additive.{u1} A)) (Equiv.hasCoeToFun.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
 but is expected to have type
-  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => AddSubmonoid.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (_x : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => AddSubmonoid.{u1} A _inst_4) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4))) (RelEmbedding.toEmbedding.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Submonoid.toAddSubmonoid'.{u1} A _inst_4))) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : A) => Additive.{u1} A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
+  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} (AddSubmonoid.{u1} A _inst_4) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (_x : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => AddSubmonoid.{u1} A _inst_4) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (Submonoid.toAddSubmonoid'.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : A) => Additive.{u1} A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid'_closure Submonoid.toAddSubmonoid'_closureₓ'. -/
 theorem Submonoid.toAddSubmonoid'_closure (S : Set (Multiplicative A)) :
     (Submonoid.closure S).toAddSubmonoid' = AddSubmonoid.closure (Additive.ofMul ⁻¹' S) :=

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

@@ -118,7 +118,7 @@ abbrev AddSubmonoid.toSubmonoid' : AddSubmonoid (Additive M) ≃o Submonoid M :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (fun (_x : RelIso.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))) => (Submonoid.{u1} M _inst_1) -> (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))))) (Submonoid.toAddSubmonoid.{u1} M _inst_1) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (fun (_x : Equiv.{succ u1, succ u1} (Additive.{u1} M) M) => (Additive.{u1} M) -> M) (Equiv.hasCoeToFun.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} M _inst_1) => AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.closure.{u1} M _inst_1 S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (Submonoid.{u1} M _inst_1) (fun (_x : Submonoid.{u1} M _inst_1) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} M _inst_1) => AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))) (RelEmbedding.toEmbedding.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Submonoid.toAddSubmonoid.{u1} M _inst_1))) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.{u1} M) (fun (_x : Additive.{u1} M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Additive.{u1} M) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} M), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} M _inst_1) => AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.closure.{u1} M _inst_1 S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (Submonoid.{u1} M _inst_1) (fun (_x : Submonoid.{u1} M _inst_1) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} M _inst_1) => AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))) (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))) (RelEmbedding.toEmbedding.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (Submonoid.{u1} M _inst_1) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Submonoid.toAddSubmonoid.{u1} M _inst_1))) (Submonoid.closure.{u1} M _inst_1 S)) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) (Set.preimage.{u1, u1} (Additive.{u1} M) M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.{u1} M) (fun (_x : Additive.{u1} M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Additive.{u1} M) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Additive.{u1} M) M) (Additive.toMul.{u1} M)) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid_closure Submonoid.toAddSubmonoid_closureₓ'. -/
 theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
     (Submonoid.closure S).toAddSubmonoid = AddSubmonoid.closure (Additive.toMul ⁻¹' S) :=
@@ -131,7 +131,7 @@ theorem Submonoid.toAddSubmonoid_closure (S : Set M) :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))))) => (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) -> (Submonoid.{u1} M _inst_1)) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Additive.{u1} M) (AddSubmonoid.setLike.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))))) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (fun (_x : Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) => M -> (Multiplicative.{u1} M)) (Equiv.hasCoeToFun.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => Submonoid.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (_x : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => Submonoid.{u1} M _inst_1) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1))) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : M) => Multiplicative.{u1} M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Set.{u1} (Additive.{u1} M)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => Submonoid.{u1} M _inst_1) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (fun (_x : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => Submonoid.{u1} M _inst_1) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1)) (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Submonoid.{u1} M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) => LE.le.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} M _inst_1) => LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toSubmonoid'.{u1} M _inst_1))) (AddSubmonoid.closure.{u1} (Additive.{u1} M) (Additive.addZeroClass.{u1} M _inst_1) S)) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u1} M (Multiplicative.{u1} M) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => Multiplicative.{u1} M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} M (Multiplicative.{u1} M)) (Multiplicative.ofAdd.{u1} M)) S))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid'_closure AddSubmonoid.toSubmonoid'_closureₓ'. -/
 theorem AddSubmonoid.toSubmonoid'_closure (S : Set (Additive M)) :
     (AddSubmonoid.closure S).toSubmonoid' = Submonoid.closure (Multiplicative.ofAdd ⁻¹' S) :=
@@ -186,7 +186,7 @@ abbrev Submonoid.toAddSubmonoid' : Submonoid (Multiplicative A) ≃o AddSubmonoi
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))) => (AddSubmonoid.{u1} A _inst_4) -> (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))))) (AddSubmonoid.toSubmonoid.{u1} A _inst_4) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (fun (_x : Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) => (Multiplicative.{u1} A) -> A) (Equiv.hasCoeToFun.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
 but is expected to have type
-  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} A _inst_4) => Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.closure.{u1} A _inst_4 S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (AddSubmonoid.{u1} A _inst_4) (fun (_x : AddSubmonoid.{u1} A _inst_4) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} A _inst_4) => Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toSubmonoid.{u1} A _inst_4))) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.{u1} A) (fun (_x : Multiplicative.{u1} A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Multiplicative.{u1} A) => A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
+  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} A), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} A _inst_4) => Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.closure.{u1} A _inst_4 S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (AddSubmonoid.{u1} A _inst_4) (fun (_x : AddSubmonoid.{u1} A _inst_4) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} A _inst_4) => Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))) (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} A _inst_4) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toSubmonoid.{u1} A _inst_4))) (AddSubmonoid.closure.{u1} A _inst_4 S)) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) (Set.preimage.{u1, u1} (Multiplicative.{u1} A) A (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.{u1} A) (fun (_x : Multiplicative.{u1} A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Multiplicative.{u1} A) => A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Multiplicative.{u1} A) A) (Multiplicative.toAdd.{u1} A)) S))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_submonoid_closure AddSubmonoid.toSubmonoid_closureₓ'. -/
 theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
     (AddSubmonoid.closure S).toSubmonoid = Submonoid.closure (Multiplicative.toAdd ⁻¹' S) :=
@@ -200,7 +200,7 @@ theorem AddSubmonoid.toSubmonoid_closure (S : Set A) :
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} (AddSubmonoid.{u1} A _inst_4) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4))))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4))))) (fun (_x : RelIso.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))))) => (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) -> (AddSubmonoid.{u1} A _inst_4)) (RelIso.hasCoeToFun.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Multiplicative.{u1} A) (Submonoid.setLike.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) (LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (SetLike.partialOrder.{u1, u1} (AddSubmonoid.{u1} A _inst_4) A (AddSubmonoid.setLike.{u1} A _inst_4)))))) (Submonoid.toAddSubmonoid'.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) (fun (_x : Equiv.{succ u1, succ u1} A (Additive.{u1} A)) => A -> (Additive.{u1} A)) (Equiv.hasCoeToFun.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
 but is expected to have type
-  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => AddSubmonoid.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (_x : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => AddSubmonoid.{u1} A _inst_4) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4))) (RelEmbedding.toEmbedding.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Submonoid.toAddSubmonoid'.{u1} A _inst_4))) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : A) => Additive.{u1} A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
+  forall {A : Type.{u1}} [_inst_4 : AddZeroClass.{u1} A] (S : Set.{u1} (Multiplicative.{u1} A)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => AddSubmonoid.{u1} A _inst_4) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (fun (_x : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => AddSubmonoid.{u1} A _inst_4) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4)) (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4))) (RelEmbedding.toEmbedding.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (AddSubmonoid.{u1} A _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) => LE.le.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Preorder.toLE.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)) (Submonoid.instCompleteLatticeSubmonoid.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} A _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} A _inst_4) => LE.le.{u1} (AddSubmonoid.{u1} A _inst_4) (Preorder.toLE.{u1} (AddSubmonoid.{u1} A _inst_4) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} A _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} A _inst_4) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} A _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (Submonoid.toAddSubmonoid'.{u1} A _inst_4))) (Submonoid.closure.{u1} (Multiplicative.{u1} A) (Multiplicative.mulOneClass.{u1} A _inst_4) S)) (AddSubmonoid.closure.{u1} A _inst_4 (Set.preimage.{u1, u1} A (Additive.{u1} A) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} A (Additive.{u1} A)) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : A) => Additive.{u1} A) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} A (Additive.{u1} A)) (Additive.ofMul.{u1} A)) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.to_add_submonoid'_closure Submonoid.toAddSubmonoid'_closureₓ'. -/
 theorem Submonoid.toAddSubmonoid'_closure (S : Set (Multiplicative A)) :
     (Submonoid.closure S).toAddSubmonoid' = AddSubmonoid.closure (Additive.ofMul ⁻¹' S) :=
@@ -242,7 +242,7 @@ def comap (f : F) (S : Submonoid N) : Submonoid M
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (S : Submonoid.{u2} N _inst_2) (f : F), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} M _inst_1) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submonoid.{u2} N _inst_2) (Set.{u2} N) (HasLiftT.mk.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (CoeTCₓ.coe.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (SetLike.Set.hasCoeT.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) S))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (S : Submonoid.{u3} N _inst_2) (f : F), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) S))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (S : Submonoid.{u3} N _inst_2) (f : F), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_comap Submonoid.coe_comapₓ'. -/
 @[simp, to_additive]
 theorem coe_comap (S : Submonoid N) (f : F) : (S.comap f : Set M) = f ⁻¹' S :=
@@ -254,7 +254,7 @@ theorem coe_comap (S : Submonoid N) (f : F) : (S.comap f : Set M) = f ⁻¹' S :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {S : Submonoid.{u2} N _inst_2} {f : F} {x : M}, Iff (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) S)
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {S : Submonoid.{u3} N _inst_2} {f : F} {x : M}, Iff (Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) S)
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {S : Submonoid.{u3} N _inst_2} {f : F} {x : M}, Iff (Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) S)
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_comap Submonoid.mem_comapₓ'. -/
 @[simp, to_additive]
 theorem mem_comap {S : Submonoid N} {f : F} {x : M} : x ∈ S.comap f ↔ f x ∈ S :=
@@ -301,7 +301,7 @@ def map (f : F) (S : Submonoid M) : Submonoid N
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u1} M _inst_1), Eq.{succ u2} (Set.{u2} N) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submonoid.{u2} N _inst_2) (Set.{u2} N) (HasLiftT.mk.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (CoeTCₓ.coe.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (SetLike.Set.hasCoeT.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Set.image.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} M _inst_1) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1), Eq.{succ u2} (Set.{u2} N) (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1), Eq.{succ u2} (Set.{u2} N) (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_map Submonoid.coe_mapₓ'. -/
 @[simp, to_additive]
 theorem coe_map (f : F) (S : Submonoid M) : (S.map f : Set N) = f '' S :=
@@ -313,7 +313,7 @@ theorem coe_map (f : F) (S : Submonoid M) : (S.map f : Set N) = f '' S :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u1} M _inst_1} {y : N}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) y (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Exists.{succ u1} M (fun (x : M) => Exists.{0} (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S) (fun (H : Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S) => Eq.{succ u2} N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) y)))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u3} M _inst_1} {y : N}, Iff (Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) y (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Exists.{succ u3} M (fun (x : M) => And (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) a) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) y)))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u3} M _inst_1} {y : N}, Iff (Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) y (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Exists.{succ u3} M (fun (x : M) => And (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) a) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) y)))
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map Submonoid.mem_mapₓ'. -/
 @[simp, to_additive]
 theorem mem_map {f : F} {S : Submonoid M} {y : N} : y ∈ S.map f ↔ ∃ x ∈ S, f x = y :=
@@ -325,7 +325,7 @@ theorem mem_map {f : F} {S : Submonoid M} {y : N} : y ∈ S.map f ↔ ∃ x ∈
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) {S : Submonoid.{u1} M _inst_1} {x : M}, (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S) -> (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {S : Submonoid.{u3} M _inst_1} {x : M}, (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {S : Submonoid.{u3} M _inst_1} {x : M}, (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S))
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map_of_mem Submonoid.mem_map_of_memₓ'. -/
 @[to_additive]
 theorem mem_map_of_mem (f : F) {S : Submonoid M} {x : M} (hx : x ∈ S) : f x ∈ S.map f :=
@@ -337,7 +337,7 @@ theorem mem_map_of_mem (f : F) {S : Submonoid M} {x : M} (hx : x ∈ S) : f x 
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u1} M _inst_1) (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S), Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) 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} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))))) x)) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1) (x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S)), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1) (x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S)), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)
 Case conversion may be inaccurate. Consider using '#align submonoid.apply_coe_mem_map Submonoid.apply_coe_mem_mapₓ'. -/
 @[to_additive]
 theorem apply_coe_mem_map (f : F) (S : Submonoid M) (x : S) : f x ∈ S.map f :=
@@ -365,7 +365,7 @@ include mc
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u1} M _inst_1} {x : M}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {x : M}, Iff (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {x : M}, Iff (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S))
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map_iff_mem Submonoid.mem_map_iff_memₓ'. -/
 @[to_additive]
 theorem mem_map_iff_mem {f : F} (hf : Function.Injective f) {S : Submonoid M} {x : M} :
@@ -587,7 +587,7 @@ include hf
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (GaloisCoinsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisCoinsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisCoinsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.gci_map_comap Submonoid.gciMapComapₓ'. -/
 /-- `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. -/
 @[to_additive " `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. "]
@@ -600,7 +600,7 @@ def gciMapComap : GaloisCoinsertion (map f) (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) S)
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) S)
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) S)
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_map_eq_of_injective Submonoid.comap_map_eq_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_map_eq_of_injective (S : Submonoid M) : (S.map f).comap f = S :=
@@ -612,7 +612,7 @@ theorem comap_map_eq_of_injective (S : Submonoid M) : (S.map f).comap f = S :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Surjective.{succ u2, succ u1} (Submonoid.{u2} N _inst_2) (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_surjective_of_injective Submonoid.comap_surjective_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
@@ -624,7 +624,7 @@ theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Injective.{succ u1, succ u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_injective_of_injective Submonoid.map_injective_of_injectiveₓ'. -/
 @[to_additive]
 theorem map_injective_of_injective : Function.Injective (map f) :=
@@ -636,7 +636,7 @@ theorem map_injective_of_injective : Function.Injective (map f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instInfSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSubmonoid.{u3} M _inst_1) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instInfSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSubmonoid.{u3} M _inst_1) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_inf_map_of_injective Submonoid.comap_inf_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_inf_map_of_injective (S T : Submonoid M) : (S.map f ⊓ T.map f).comap f = S ⊓ T :=
@@ -648,7 +648,7 @@ theorem comap_inf_map_of_injective (S T : Submonoid M) : (S.map f ⊓ T.map f).c
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (infᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι S))
 but is expected to have type
-  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, succ u1} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSetSubmonoid.{u3} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u4, succ u1} (Submonoid.{u4} M _inst_1) (Submonoid.instInfSetSubmonoid.{u4} M _inst_1) ι S))
+  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, succ u1} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSetSubmonoid.{u3} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u4, succ u1} (Submonoid.{u4} M _inst_1) (Submonoid.instInfSetSubmonoid.{u4} M _inst_1) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_infi_map_of_injective Submonoid.comap_infᵢ_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_infᵢ_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).map f).comap f = infᵢ S :=
@@ -660,7 +660,7 @@ theorem comap_infᵢ_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).m
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} M _inst_1) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} M _inst_1) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} M _inst_1) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} M _inst_1) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_sup_map_of_injective Submonoid.comap_sup_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_sup_map_of_injective (S T : Submonoid M) : (S.map f ⊔ T.map f).comap f = S ⊔ T :=
@@ -672,7 +672,7 @@ theorem comap_sup_map_of_injective (S T : Submonoid M) : (S.map f ⊔ T.map f).c
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (supᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι S))
 but is expected to have type
-  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, succ u1} (Submonoid.{u3} N _inst_2) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u4, succ u1} (Submonoid.{u4} M _inst_1) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u4} M _inst_1)) ι S))
+  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, succ u1} (Submonoid.{u3} N _inst_2) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u4, succ u1} (Submonoid.{u4} M _inst_1) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u4} M _inst_1)) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_supr_map_of_injective Submonoid.comap_supᵢ_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_supᵢ_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).map f).comap f = supᵢ S :=
@@ -684,7 +684,7 @@ theorem comap_supᵢ_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).m
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u1} M _inst_1} {T : Submonoid.{u1} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {T : Submonoid.{u3} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2))))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} M _inst_1) (Preorder.toLE.{u3} (Submonoid.{u3} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1))))) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {T : Submonoid.{u3} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2))))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} M _inst_1) (Preorder.toLE.{u3} (Submonoid.{u3} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1))))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_le_map_iff_of_injective Submonoid.map_le_map_iff_of_injectiveₓ'. -/
 @[to_additive]
 theorem map_le_map_iff_of_injective {S T : Submonoid M} : S.map f ≤ T.map f ↔ S ≤ T :=
@@ -696,7 +696,7 @@ theorem map_le_map_iff_of_injective {S T : Submonoid M} : S.map f ≤ T.map f 
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (StrictMono.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_strict_mono_of_injective Submonoid.map_strictMono_of_injectiveₓ'. -/
 @[to_additive]
 theorem map_strictMono_of_injective : StrictMono (map f) :=
@@ -716,7 +716,7 @@ include hf
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (GaloisInsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisInsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisInsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.gi_map_comap Submonoid.giMapComapₓ'. -/
 /-- `map f` and `comap f` form a `galois_insertion` when `f` is surjective. -/
 @[to_additive " `map f` and `comap f` form a `galois_insertion` when `f` is surjective. "]
@@ -731,7 +731,7 @@ def giMapComap : GaloisInsertion (map f) (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) S)
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) S)
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) S)
 Case conversion may be inaccurate. Consider using '#align submonoid.map_comap_eq_of_surjective Submonoid.map_comap_eq_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_comap_eq_of_surjective (S : Submonoid N) : (S.comap f).map f = S :=
@@ -743,7 +743,7 @@ theorem map_comap_eq_of_surjective (S : Submonoid N) : (S.comap f).map f = S :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Surjective.{succ u1, succ u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_surjective_of_surjective Submonoid.map_surjective_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_surjective_of_surjective : Function.Surjective (map f) :=
@@ -755,7 +755,7 @@ theorem map_surjective_of_surjective : Function.Surjective (map f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Injective.{succ u2, succ u1} (Submonoid.{u2} N _inst_2) (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_injective_of_surjective Submonoid.comap_injective_of_surjectiveₓ'. -/
 @[to_additive]
 theorem comap_injective_of_surjective : Function.Injective (comap f) :=
@@ -767,7 +767,7 @@ theorem comap_injective_of_surjective : Function.Injective (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Inf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instInfSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSubmonoid.{u3} N _inst_2) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instInfSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSubmonoid.{u3} N _inst_2) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_inf_comap_of_surjective Submonoid.map_inf_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_inf_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊓ T.comap f).map f = S ⊓ T :=
@@ -779,7 +779,7 @@ theorem map_inf_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊓ T.comap
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (infᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, succ u1} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSetSubmonoid.{u3} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u4, succ u1} (Submonoid.{u4} N _inst_2) (Submonoid.instInfSetSubmonoid.{u4} N _inst_2) ι S))
+  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, succ u1} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSetSubmonoid.{u3} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u4, succ u1} (Submonoid.{u4} N _inst_2) (Submonoid.instInfSetSubmonoid.{u4} N _inst_2) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_infi_comap_of_surjective Submonoid.map_infᵢ_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_infᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).comap f).map f = infᵢ S :=
@@ -791,7 +791,7 @@ theorem map_infᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Sup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} M _inst_1) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} M _inst_1) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} N _inst_2) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} N _inst_2) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} M _inst_1) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} M _inst_1) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} N _inst_2) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} N _inst_2) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_sup_comap_of_surjective Submonoid.map_sup_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_sup_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊔ T.comap f).map f = S ⊔ T :=
@@ -803,7 +803,7 @@ theorem map_sup_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊔ T.comap
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (supᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, succ u1} (Submonoid.{u3} M _inst_1) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u4, succ u1} (Submonoid.{u4} N _inst_2) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u4} N _inst_2)) ι S))
+  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, succ u1} (Submonoid.{u3} M _inst_1) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u4, succ u1} (Submonoid.{u4} N _inst_2) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u4} N _inst_2)) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_supr_comap_of_surjective Submonoid.map_supᵢ_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_supᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).comap f).map f = supᵢ S :=
@@ -815,7 +815,7 @@ theorem map_supᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u2} N _inst_2} {T : Submonoid.{u2} N _inst_2}, Iff (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} N _inst_2} {T : Submonoid.{u3} N _inst_2}, Iff (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} N _inst_2) (Preorder.toLE.{u3} (Submonoid.{u3} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2))))) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} N _inst_2} {T : Submonoid.{u3} N _inst_2}, Iff (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} N _inst_2) (Preorder.toLE.{u3} (Submonoid.{u3} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2))))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_le_comap_iff_of_surjective Submonoid.comap_le_comap_iff_of_surjectiveₓ'. -/
 @[to_additive]
 theorem comap_le_comap_iff_of_surjective {S T : Submonoid N} : S.comap f ≤ T.comap f ↔ S ≤ T :=
@@ -827,7 +827,7 @@ theorem comap_le_comap_iff_of_surjective {S T : Submonoid N} : S.comap f ≤ T.c
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (StrictMono.{u2, u1} (Submonoid.{u2} N _inst_2) (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_strict_mono_of_surjective Submonoid.comap_strictMono_of_surjectiveₓ'. -/
 @[to_additive]
 theorem comap_strictMono_of_surjective : StrictMono (comap f) :=
@@ -1031,7 +1031,7 @@ def Subtype : S' →* M :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {A : Type.{u2}} [_inst_4 : SetLike.{u2, u1} A M] [hA : SubmonoidClass.{u2, u1} A M _inst_1 _inst_4] (S' : A), Eq.{succ u1} ((fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) => (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') -> M) (SubmonoidClass.Subtype.{u1, u2} M _inst_1 A _inst_4 hA S')) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) => (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') -> M) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) (SubmonoidClass.Subtype.{u1, u2} M _inst_1 A _inst_4 hA S')) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (coeBase.{succ u1, succ u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u2} M A (SetLike.hasMem.{u2, u1} A M _inst_4) x S'))))))
 but is expected to have type
-  forall {M : Type.{u2}} [_inst_1 : MulOneClass.{u2} M] {A : Type.{u1}} [_inst_4 : SetLike.{u1, u2} A M] [hA : SubmonoidClass.{u1, u2} A M _inst_1 _inst_4] (S' : A), Eq.{succ u2} (forall (a : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S')) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1 (MonoidHom.monoidHomClass.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1))) (SubmonoidClass.Subtype.{u2, u1} M _inst_1 A _inst_4 hA S')) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S'))
+  forall {M : Type.{u2}} [_inst_1 : MulOneClass.{u2} M] {A : Type.{u1}} [_inst_4 : SetLike.{u1, u2} A M] [hA : SubmonoidClass.{u1, u2} A M _inst_1 _inst_4] (S' : A), Eq.{succ u2} (forall (a : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S')) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1 (MonoidHom.monoidHomClass.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1))) (SubmonoidClass.Subtype.{u2, u1} M _inst_1 A _inst_4 hA S')) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S'))
 Case conversion may be inaccurate. Consider using '#align submonoid_class.coe_subtype SubmonoidClass.coe_subtypeₓ'. -/
 @[simp, to_additive]
 theorem coe_subtype : (SubmonoidClass.Subtype S' : S' → M) = coe :=
@@ -1275,7 +1275,7 @@ def subtype : S →* M :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} ((coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) -> M) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) -> M) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Submonoid.subtype.{u1} M _inst_1 S)) ((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} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))))))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u1} M _inst_1 S)) (MulOneClass.toMul.{u1} M _inst_1) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1 (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1))) (Submonoid.subtype.{u1} M _inst_1 S)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u1} M _inst_1 S)) (MulOneClass.toMul.{u1} M _inst_1) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1 (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1))) (Submonoid.subtype.{u1} M _inst_1 S)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_subtype Submonoid.coe_subtypeₓ'. -/
 @[simp, to_additive]
 theorem coe_subtype : ⇑S.Subtype = coe :=
@@ -1316,7 +1316,7 @@ theorem topEquiv_toMonoidHom : (topEquiv : _ ≃* M).toMonoidHom = (⊤ : Submon
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), (Function.Injective.{succ u1, succ u2} M N (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f)) -> (MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))
 Case conversion may be inaccurate. Consider using '#align submonoid.equiv_map_of_injective Submonoid.equivMapOfInjectiveₓ'. -/
 /-- A subgroup is isomorphic to its image under an injective function. If you have an isomorphism,
 use `mul_equiv.submonoid_map` for better definitional equalities. -/
@@ -1331,7 +1331,7 @@ noncomputable def equivMapOfInjective (f : M →* N) (hf : Function.Injective f)
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (hf : Function.Injective.{succ u1, succ u2} M N (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f)) (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S), Eq.{succ u2} N ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (coeSubtype.{succ u2} N (fun (x : N) => Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (fun (_x : MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, 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 but is expected to have type
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(Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) 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Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)))))) (Submonoid.equivMapOfInjective.{u2, u1} M N _inst_1 _inst_2 S f hf) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) x))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (S : Submonoid.{u2} M _inst_1) (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2) (hf : Function.Injective.{succ u2, succ u1} M N (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f)) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u2} M _inst_1 S)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)))))) (Submonoid.equivMapOfInjective.{u2, u1} M N _inst_1 _inst_2 S f hf) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) x))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_equiv_map_of_injective_apply Submonoid.coe_equivMapOfInjective_applyₓ'. -/
 @[simp, to_additive]
 theorem coe_equivMapOfInjective_apply (f : M →* N) (hf : Function.Injective f) (x : S) :
@@ -1528,7 +1528,7 @@ theorem prod_bot_sup_bot_prod (s : Submonoid M) (t : Submonoid N) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {f : MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)} {K : Submonoid.{u1} M _inst_1} {x : N}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 f) K)) (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (MulEquiv.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) (fun (_x : MulEquiv.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) => N -> M) (MulEquiv.hasCoeToFun.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) (MulEquiv.symm.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) f) x) K)
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] {f : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)} {K : Submonoid.{u2} M _inst_1} {x : N}, Iff (Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 f) K)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => M) x) (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquivClass.instMonoidHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1))))) (MulEquiv.symm.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) f) x) K)
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] {f : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)} {K : Submonoid.{u2} M _inst_1} {x : N}, Iff (Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 f) K)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => M) x) (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquivClass.instMonoidHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1))))) (MulEquiv.symm.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) f) x) K)
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map_equiv Submonoid.mem_map_equivₓ'. -/
 @[to_additive]
 theorem mem_map_equiv {f : M ≃* N} {K : Submonoid M} {x : N} :
@@ -1682,7 +1682,7 @@ def mrange (f : F) : Submonoid N :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u2} (Set.{u2} N) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submonoid.{u2} N _inst_2) (Set.{u2} N) (HasLiftT.mk.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (CoeTCₓ.coe.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (SetLike.Set.hasCoeT.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Set.range.{u2, succ u1} N M (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} N) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Set.range.{u3, succ u2} N M (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} N) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Set.range.{u3, succ u2} N M (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.coe_mrange MonoidHom.coe_mrangeₓ'. -/
 @[simp, to_additive]
 theorem coe_mrange (f : F) : (mrange f : Set N) = Set.range f :=
@@ -1694,7 +1694,7 @@ theorem coe_mrange (f : F) : (mrange f : Set N) = Set.range f :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F} {y : N}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) y (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Exists.{succ u1} M (fun (x : M) => Eq.{succ u2} N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) y))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F} {y : N}, Iff (Membership.mem.{u3, u3} N (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) y (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Exists.{succ u2} M (fun (x : M) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) y))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F} {y : N}, Iff (Membership.mem.{u3, u3} N (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) y (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Exists.{succ u2} M (fun (x : M) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) y))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mem_mrange MonoidHom.mem_mrangeₓ'. -/
 @[simp, to_additive]
 theorem mem_mrange {f : F} {y : N} : y ∈ mrange f ↔ ∃ x, f x = y :=
@@ -1734,7 +1734,7 @@ include mc
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, Iff (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasTop.{u2} N _inst_2))) (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, Iff (Eq.{succ u3} (Submonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instTopSubmonoid.{u3} N _inst_2))) (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, Iff (Eq.{succ u3} (Submonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instTopSubmonoid.{u3} N _inst_2))) (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mrange_top_iff_surjective MonoidHom.mrange_top_iff_surjectiveₓ'. -/
 @[to_additive]
 theorem mrange_top_iff_surjective {f : F} : mrange f = (⊤ : Submonoid N) ↔ Function.Surjective f :=
@@ -1746,7 +1746,7 @@ theorem mrange_top_iff_surjective {f : F} : mrange f = (⊤ : Submonoid N) ↔ F
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F), (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasTop.{u2} N _inst_2)))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u3, u2, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instTopSubmonoid.{u2} N _inst_2)))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u3, u2, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instTopSubmonoid.{u2} N _inst_2)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mrange_top_of_surjective MonoidHom.mrange_top_of_surjectiveₓ'. -/
 /-- The range of a surjective monoid hom is the whole of the codomain. -/
 @[to_additive "The range of a surjective `add_monoid` hom is the whole of the codomain."]
@@ -1760,7 +1760,7 @@ theorem mrange_top_of_surjective (f : F) (hf : Function.Surjective f) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u2} N), LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) s)) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u2} N _inst_2 s))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} N), LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.closure.{u2} M _inst_1 (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) s)) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} N _inst_2 s))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} N), LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.closure.{u2} M _inst_1 (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) s)) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} N _inst_2 s))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mclosure_preimage_le MonoidHom.mclosure_preimage_leₓ'. -/
 @[to_additive]
 theorem mclosure_preimage_le (f : F) (s : Set N) : closure (f ⁻¹' s) ≤ (closure s).comap f :=
@@ -1772,7 +1772,7 @@ theorem mclosure_preimage_le (f : F) (s : Set N) : closure (f ⁻¹' s) ≤ (clo
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u1} M), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u1} M _inst_1 s)) (Submonoid.closure.{u2} N _inst_2 (Set.image.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) s))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} M), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} M _inst_1 s)) (Submonoid.closure.{u2} N _inst_2 (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) s))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} M), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} M _inst_1 s)) (Submonoid.closure.{u2} N _inst_2 (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) s))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_mclosure MonoidHom.map_mclosureₓ'. -/
 /-- The image under a monoid hom of the submonoid generated by a set equals the submonoid generated
     by the image of the set. -/
@@ -1802,7 +1802,7 @@ def restrict {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M] (
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} {S : Type.{u3}} [_inst_4 : MulOneClass.{u2} N] [_inst_5 : SetLike.{u3, u1} S M] [_inst_6 : SubmonoidClass.{u3, u1} S M _inst_1 _inst_5] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (s : S) (x : coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s), Eq.{succ u2} N (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) N (SubmonoidClass.toMulOneClass.{u1, u3} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) N (SubmonoidClass.toMulOneClass.{u1, u3} M _inst_1 S _inst_5 _inst_6 s) _inst_4) => (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) -> N) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) N (SubmonoidClass.toMulOneClass.{u1, u3} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (MonoidHom.restrict.{u1, u2, u3} M _inst_1 N S _inst_4 _inst_5 _inst_6 f s) x) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_4) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_4) f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (coeBase.{succ u1, succ u1} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u3} M S (SetLike.hasMem.{u3, u1} S M _inst_5) x s))))) x))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u3}} {S : Type.{u2}} [_inst_4 : MulOneClass.{u3} N] [_inst_5 : SetLike.{u2, u1} S M] [_inst_6 : SubmonoidClass.{u2, u1} S M _inst_1 _inst_5] (f : MonoidHom.{u1, u3} M N _inst_1 _inst_4) (s : S) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s)) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4 (MonoidHom.monoidHomClass.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4))) (MonoidHom.restrict.{u1, u3, u2} M _inst_1 N S _inst_4 _inst_5 _inst_6 f s) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u3} M N _inst_1 _inst_4))) f (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u2, u1} S M _inst_5 s)) x))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u3}} {S : Type.{u2}} [_inst_4 : MulOneClass.{u3} N] [_inst_5 : SetLike.{u2, u1} S M] [_inst_6 : SubmonoidClass.{u2, u1} S M _inst_1 _inst_5] (f : MonoidHom.{u1, u3} M N _inst_1 _inst_4) (s : S) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s)) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4 (MonoidHom.monoidHomClass.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4))) (MonoidHom.restrict.{u1, u3, u2} M _inst_1 N S _inst_4 _inst_5 _inst_6 f s) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u3} M N _inst_1 _inst_4))) f (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u2, u1} S M _inst_5 s)) x))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.restrict_apply MonoidHom.restrict_applyₓ'. -/
 @[simp, to_additive]
 theorem restrict_apply {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M]
@@ -1828,7 +1828,7 @@ theorem restrict_mrange (f : M →* N) : (f.restrict S).mrange = S.map f := by
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {S : Type.{u3}} [_inst_4 : SetLike.{u3, u2} S N] [_inst_5 : SubmonoidClass.{u3, u2} S N _inst_2 _inst_4] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (s : S), (forall (x : M), Membership.Mem.{u2, u3} N S (SetLike.hasMem.{u3, u2} S N _inst_4) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f x) s) -> (MonoidHom.{u1, u2} M (coeSort.{succ u3, succ (succ u2)} S Type.{u2} (SetLike.hasCoeToSort.{u3, u2} S N _inst_4) s) _inst_1 (SubmonoidClass.toMulOneClass.{u2, u3} N _inst_2 S _inst_4 _inst_5 s))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {S : Type.{u3}} [_inst_4 : SetLike.{u3, u2} S N] [_inst_5 : SubmonoidClass.{u3, u2} S N _inst_2 _inst_4] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (s : S), (forall (x : M), Membership.mem.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) S (SetLike.instMembership.{u3, u2} S N _inst_4) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f x) s) -> (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u3} N S (SetLike.instMembership.{u3, u2} S N _inst_4) x s)) _inst_1 (SubmonoidClass.toMulOneClass.{u2, u3} N _inst_2 S _inst_4 _inst_5 s))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {S : Type.{u3}} [_inst_4 : SetLike.{u3, u2} S N] [_inst_5 : SubmonoidClass.{u3, u2} S N _inst_2 _inst_4] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (s : S), (forall (x : M), Membership.mem.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) S (SetLike.instMembership.{u3, u2} S N _inst_4) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f x) s) -> (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u3} N S (SetLike.instMembership.{u3, u2} S N _inst_4) x s)) _inst_1 (SubmonoidClass.toMulOneClass.{u2, u3} N _inst_2 S _inst_4 _inst_5 s))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.cod_restrict MonoidHom.codRestrictₓ'. -/
 /-- Restriction of a monoid hom to a submonoid of the codomain. -/
 @[to_additive "Restriction of an `add_monoid` hom to an `add_submonoid` of the codomain.",
@@ -1858,7 +1858,7 @@ def mrangeRestrict {N} [MulOneClass N] (f : M →* N) : M →* f.mrange :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} [_inst_4 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (x : M), Eq.{succ u2} N ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (coeSubtype.{succ u2} N (fun (x : N) => Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)))))) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (fun (_x : MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) => M -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHom.hasCoeToFun.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_4 f) x)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_4) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_4) f x)
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} [_inst_4 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (x : M), Eq.{succ u2} N (Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4) (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) (MonoidHom.monoidHomClass.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_4 f) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4))) f x)
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} [_inst_4 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (x : M), Eq.{succ u2} N (Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4) (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) (MonoidHom.monoidHomClass.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_4 f) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4))) f x)
 Case conversion may be inaccurate. Consider using '#align monoid_hom.coe_mrange_restrict MonoidHom.coe_mrangeRestrictₓ'. -/
 @[simp, to_additive]
 theorem coe_mrangeRestrict {N} [MulOneClass N] (f : M →* N) (x : M) :
@@ -1871,7 +1871,7 @@ theorem coe_mrangeRestrict {N} [MulOneClass N] (f : M →* N) (x : M) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), Function.Surjective.{succ u1, succ u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (fun (_x : MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) => M -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MonoidHom.hasCoeToFun.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_2 f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2), Function.Surjective.{succ u2, succ u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f)) (MonoidHom.monoidHomClass.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))))) (MonoidHom.mrangeRestrict.{u2, u1} M _inst_1 N _inst_2 f))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2), Function.Surjective.{succ u2, succ u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f)) (MonoidHom.monoidHomClass.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))))) (MonoidHom.mrangeRestrict.{u2, u1} M _inst_1 N _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mrange_restrict_surjective MonoidHom.mrangeRestrict_surjectiveₓ'. -/
 @[to_additive]
 theorem mrangeRestrict_surjective (f : M →* N) : Function.Surjective f.mrangeRestrict :=
@@ -1896,7 +1896,7 @@ def mker (f : F) : Submonoid M :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) {x : M}, Iff (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x (MonoidHom.mker.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Eq.{succ u2} N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) (OfNat.ofNat.{u2} N 1 (OfNat.mk.{u2} N 1 (One.one.{u2} N (MulOneClass.toHasOne.{u2} N _inst_2)))))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {x : M}, Iff (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) 1 (One.toOfNat1.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (MulOneClass.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) _inst_2))))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {x : M}, Iff (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) 1 (One.toOfNat1.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) (MulOneClass.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) x) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mem_mker MonoidHom.mem_mkerₓ'. -/
 @[to_additive]
 theorem mem_mker (f : F) {x : M} : x ∈ mker f ↔ f x = 1 :=
@@ -1908,7 +1908,7 @@ theorem mem_mker (f : F) {x : M} : x ∈ mker f ↔ f x = 1 :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} M _inst_1) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (MonoidHom.mker.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.hasSingleton.{u2} N) (OfNat.ofNat.{u2} N 1 (OfNat.mk.{u2} N 1 (One.one.{u2} N (MulOneClass.toHasOne.{u2} N _inst_2))))))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Set.preimage.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.instSingletonSet.{u2} N) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (MulOneClass.toOne.{u2} N _inst_2)))))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Set.preimage.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.instSingletonSet.{u2} N) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (MulOneClass.toOne.{u2} N _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.coe_mker MonoidHom.coe_mkerₓ'. -/
 @[to_additive]
 theorem coe_mker (f : F) : (mker f : Set M) = (f : M → N) ⁻¹' {1} :=
@@ -2090,7 +2090,7 @@ def submonoidMap (f : M →* N) (M' : Submonoid M) : M' →* M'.map f
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (M' : Submonoid.{u1} M _inst_1), Function.Surjective.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (Submonoid.toMulOneClass.{u1} M _inst_1 M') (Submonoid.toMulOneClass.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (Submonoid.toMulOneClass.{u1} M _inst_1 M') (Submonoid.toMulOneClass.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (Submonoid.toMulOneClass.{u1} M _inst_1 M') (Submonoid.toMulOneClass.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) (MonoidHom.submonoidMap.{u1, u2} M N _inst_1 _inst_2 f M'))
 but is expected to have type
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(Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Submonoid.toMulOneClass.{u2} M _inst_1 M')) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M')) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))))) (MonoidHom.submonoidMap.{u2, u1} M N _inst_1 _inst_2 f M'))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2) (M' : Submonoid.{u2} M _inst_1), Function.Surjective.{succ u2, succ u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Submonoid.toMulOneClass.{u2} M _inst_1 M')) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M')) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))))) (MonoidHom.submonoidMap.{u2, u1} M N _inst_1 _inst_2 f M'))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.submonoid_map_surjective MonoidHom.submonoidMap_surjectiveₓ'. -/
 @[to_additive]
 theorem submonoidMap_surjective (f : M →* N) (M' : Submonoid M) :
@@ -2331,7 +2331,7 @@ def submonoidCongr (h : S = T) : S ≃* T :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) {g : N -> M}, (Function.LeftInverse.{succ u1, succ u2} M N g (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f)) -> (MulEquiv.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) (MulOneClass.toHasMul.{u1} M _inst_1) (Submonoid.mul.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) {g : N -> M}, (Function.LeftInverse.{succ u1, succ u2} M N g (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u1} M _inst_1) (Submonoid.mul.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) {g : N -> M}, (Function.LeftInverse.{succ u1, succ u2} M N g (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u1} M _inst_1) (Submonoid.mul.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)))
 Case conversion may be inaccurate. Consider using '#align mul_equiv.of_left_inverse' MulEquiv.ofLeftInverse'ₓ'. -/
 -- this name is primed so that the version to `f.range` instead of `f.mrange` can be unprimed.
 /-- A monoid homomorphism `f : M →* N` with a left-inverse `g : N → M` defines a multiplicative
@@ -2373,7 +2373,7 @@ def submonoidMap (e : M ≃* N) (S : Submonoid M) : S ≃* S.map e.toMonoidHom :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (e : MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) (S : Submonoid.{u1} M _inst_1) (g : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S), Eq.{succ u2} N ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) N (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) N (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) N (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) N (coeSubtype.{succ u2} N (fun (x : N) => Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 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 but is expected to have type
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_inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)))))) (MulEquiv.submonoidMap.{u2, u1} M N _inst_1 _inst_2 e S) g)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))))) e (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) g))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (e : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) (S : Submonoid.{u2} M _inst_1) (g : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u2} M _inst_1 S)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)))))) (MulEquiv.submonoidMap.{u2, u1} M N _inst_1 _inst_2 e S) g)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))))) e (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) g))
 Case conversion may be inaccurate. Consider using '#align mul_equiv.coe_submonoid_map_apply MulEquiv.coe_submonoidMap_applyₓ'. -/
 @[simp, to_additive]
 theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
@@ -2386,7 +2386,7 @@ theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
 lean 3 declaration is
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 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (e : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) (S : Submonoid.{u2} M _inst_1) (g : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) g) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (Submonoid.mul.{u2} M _inst_1 S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (fun (_x : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (Submonoid.mul.{u2} M _inst_1 S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) 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(Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (MulEquivClass.instMonoidHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (Submonoid.mul.{u2} M _inst_1 S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) 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(Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (MulEquiv.submonoidMap.{u2, u1} M N _inst_1 _inst_2 e S)) g) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun 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(Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Iff.mp (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => M) _x) 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_inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g) (Set.image.{u2, u1} M N (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} M N) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : M) => N) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} M N) (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e)) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S))) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : N) => M) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Set.{u2} M) 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(MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) (Set.mem_image_equiv.{u1, u2} M N (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S) (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Subtype.property.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S)) g))))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (e : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) (S : Submonoid.{u2} M _inst_1) (g : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) g) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N 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(MulHomClass.toFunLike.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquivClass.instMonoidHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1))))) (MulEquiv.symm.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, 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(SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) S) (SetLike.mem_coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquivClass.instMonoidHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1))))) (MulEquiv.symm.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g))) (Iff.mp (Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g) (Set.image.{u2, u1} M N (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} M N) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => N) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} M N) (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e)) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S))) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : N) => M) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Set.{u2} M) (Set.instMembershipSet.{u2} M) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} N M) N (fun (_x : N) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : N) => M) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} N M) (Equiv.symm.{succ u2, succ u1} M N (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e)) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) (Set.mem_image_equiv.{u1, u2} M N (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S) (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Subtype.property.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S)) g))))
 Case conversion may be inaccurate. Consider using '#align mul_equiv.submonoid_map_symm_apply MulEquiv.submonoidMap_symm_applyₓ'. -/
 @[simp, to_additive AddEquiv.add_submonoid_map_symm_apply]
 theorem submonoidMap_symm_apply (e : M ≃* N) (S : Submonoid M) (g : S.map (e : M →* N)) :

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

@@ -242,7 +242,7 @@ def comap (f : F) (S : Submonoid N) : Submonoid M
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (S : Submonoid.{u2} N _inst_2) (f : F), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} M _inst_1) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submonoid.{u2} N _inst_2) (Set.{u2} N) (HasLiftT.mk.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (CoeTCₓ.coe.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (SetLike.Set.hasCoeT.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) S))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (S : Submonoid.{u3} N _inst_2) (f : F), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) S))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (S : Submonoid.{u3} N _inst_2) (f : F), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_comap Submonoid.coe_comapₓ'. -/
 @[simp, to_additive]
 theorem coe_comap (S : Submonoid N) (f : F) : (S.comap f : Set M) = f ⁻¹' S :=
@@ -254,7 +254,7 @@ theorem coe_comap (S : Submonoid N) (f : F) : (S.comap f : Set M) = f ⁻¹' S :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {S : Submonoid.{u2} N _inst_2} {f : F} {x : M}, Iff (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) S)
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {S : Submonoid.{u3} N _inst_2} {f : F} {x : M}, Iff (Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) x) (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) S)
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {S : Submonoid.{u3} N _inst_2} {f : F} {x : M}, Iff (Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) S)
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_comap Submonoid.mem_comapₓ'. -/
 @[simp, to_additive]
 theorem mem_comap {S : Submonoid N} {f : F} {x : M} : x ∈ S.comap f ↔ f x ∈ S :=
@@ -301,7 +301,7 @@ def map (f : F) (S : Submonoid M) : Submonoid N
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u1} M _inst_1), Eq.{succ u2} (Set.{u2} N) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submonoid.{u2} N _inst_2) (Set.{u2} N) (HasLiftT.mk.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (CoeTCₓ.coe.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (SetLike.Set.hasCoeT.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Set.image.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} M _inst_1) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1), Eq.{succ u2} (Set.{u2} N) (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1), Eq.{succ u2} (Set.{u2} N) (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_map Submonoid.coe_mapₓ'. -/
 @[simp, to_additive]
 theorem coe_map (f : F) (S : Submonoid M) : (S.map f : Set N) = f '' S :=
@@ -313,7 +313,7 @@ theorem coe_map (f : F) (S : Submonoid M) : (S.map f : Set N) = f '' S :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u1} M _inst_1} {y : N}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) y (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Exists.{succ u1} M (fun (x : M) => Exists.{0} (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S) (fun (H : Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S) => Eq.{succ u2} N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) y)))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u3} M _inst_1} {y : N}, Iff (Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) y (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Exists.{succ u3} M (fun (x : M) => And (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) a) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) y)))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F} {S : Submonoid.{u3} M _inst_1} {y : N}, Iff (Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) y (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Exists.{succ u3} M (fun (x : M) => And (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) a) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) y)))
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map Submonoid.mem_mapₓ'. -/
 @[simp, to_additive]
 theorem mem_map {f : F} {S : Submonoid M} {y : N} : y ∈ S.map f ↔ ∃ x ∈ S, f x = y :=
@@ -325,7 +325,7 @@ theorem mem_map {f : F} {S : Submonoid M} {y : N} : y ∈ S.map f ↔ ∃ x ∈
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) {S : Submonoid.{u1} M _inst_1} {x : M}, (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S) -> (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {S : Submonoid.{u3} M _inst_1} {x : M}, (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {S : Submonoid.{u3} M _inst_1} {x : M}, (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S))
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map_of_mem Submonoid.mem_map_of_memₓ'. -/
 @[to_additive]
 theorem mem_map_of_mem (f : F) {S : Submonoid M} {x : M} (hx : x ∈ S) : f x ∈ S.map f :=
@@ -337,7 +337,7 @@ theorem mem_map_of_mem (f : F) {S : Submonoid M} {x : M} (hx : x ∈ S) : f x 
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u1} M _inst_1) (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S), Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) 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} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))))) x)) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1) (x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S)), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (S : Submonoid.{u3} M _inst_1) (x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S)), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) S)) x)) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)
 Case conversion may be inaccurate. Consider using '#align submonoid.apply_coe_mem_map Submonoid.apply_coe_mem_mapₓ'. -/
 @[to_additive]
 theorem apply_coe_mem_map (f : F) (S : Submonoid M) (x : S) : f x ∈ S.map f :=
@@ -365,7 +365,7 @@ include mc
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u1} M _inst_1} {x : M}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {x : M}, Iff (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {x : M}, Iff (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x S))
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map_iff_mem Submonoid.mem_map_iff_memₓ'. -/
 @[to_additive]
 theorem mem_map_iff_mem {f : F} (hf : Function.Injective f) {S : Submonoid M} {x : M} :
@@ -587,7 +587,7 @@ include hf
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (GaloisCoinsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisCoinsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisCoinsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.gci_map_comap Submonoid.gciMapComapₓ'. -/
 /-- `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. -/
 @[to_additive " `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. "]
@@ -600,7 +600,7 @@ def gciMapComap : GaloisCoinsertion (map f) (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) S)
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) S)
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S)) S)
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_map_eq_of_injective Submonoid.comap_map_eq_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_map_eq_of_injective (S : Submonoid M) : (S.map f).comap f = S :=
@@ -612,7 +612,7 @@ theorem comap_map_eq_of_injective (S : Submonoid M) : (S.map f).comap f = S :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Surjective.{succ u2, succ u1} (Submonoid.{u2} N _inst_2) (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_surjective_of_injective Submonoid.comap_surjective_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
@@ -624,7 +624,7 @@ theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Injective.{succ u1, succ u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_injective_of_injective Submonoid.map_injective_of_injectiveₓ'. -/
 @[to_additive]
 theorem map_injective_of_injective : Function.Injective (map f) :=
@@ -636,7 +636,7 @@ theorem map_injective_of_injective : Function.Injective (map f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instInfSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSubmonoid.{u3} M _inst_1) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instInfSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSubmonoid.{u3} M _inst_1) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_inf_map_of_injective Submonoid.comap_inf_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_inf_map_of_injective (S T : Submonoid M) : (S.map f ⊓ T.map f).comap f = S ⊓ T :=
@@ -648,7 +648,7 @@ theorem comap_inf_map_of_injective (S T : Submonoid M) : (S.map f ⊓ T.map f).c
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (infᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι S))
 but is expected to have type
-  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, succ u1} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSetSubmonoid.{u3} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u4, succ u1} (Submonoid.{u4} M _inst_1) (Submonoid.instInfSetSubmonoid.{u4} M _inst_1) ι S))
+  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, succ u1} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSetSubmonoid.{u3} N _inst_2) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u4, succ u1} (Submonoid.{u4} M _inst_1) (Submonoid.instInfSetSubmonoid.{u4} M _inst_1) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_infi_map_of_injective Submonoid.comap_infᵢ_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_infᵢ_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).map f).comap f = infᵢ S :=
@@ -660,7 +660,7 @@ theorem comap_infᵢ_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).m
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} M _inst_1) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} M _inst_1) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} M _inst_1) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} M _inst_1) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_sup_map_of_injective Submonoid.comap_sup_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_sup_map_of_injective (S T : Submonoid M) : (S.map f ⊔ T.map f).comap f = S ⊔ T :=
@@ -672,7 +672,7 @@ theorem comap_sup_map_of_injective (S T : Submonoid M) : (S.map f ⊔ T.map f).c
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u1} M _inst_1)), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (supᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι (fun (i : ι) => Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι S))
 but is expected to have type
-  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, succ u1} (Submonoid.{u3} N _inst_2) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u4, succ u1} (Submonoid.{u4} M _inst_1) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u4} M _inst_1)) ι S))
+  forall {M : Type.{u4}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u4} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u4, u3} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Injective.{succ u4, succ u3} M N (FunLike.coe.{succ u2, succ u4, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u2, u4, u3} F M N (MulOneClass.toMul.{u4} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u4, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} M _inst_1)), Eq.{succ u4} (Submonoid.{u4} M _inst_1) (Submonoid.comap.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, succ u1} (Submonoid.{u3} N _inst_2) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)) ι (fun (i : ι) => Submonoid.map.{u4, u3, u2} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u4, succ u1} (Submonoid.{u4} M _inst_1) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u4} M _inst_1)) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_supr_map_of_injective Submonoid.comap_supᵢ_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_supᵢ_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).map f).comap f = supᵢ S :=
@@ -684,7 +684,7 @@ theorem comap_supᵢ_map_of_injective (S : ι → Submonoid M) : (⨆ i, (S i).m
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u1} M _inst_1} {T : Submonoid.{u1} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {T : Submonoid.{u3} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2))))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} M _inst_1) (Preorder.toLE.{u3} (Submonoid.{u3} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1))))) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} M _inst_1} {T : Submonoid.{u3} M _inst_1}, Iff (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2))))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} M _inst_1) (Preorder.toLE.{u3} (Submonoid.{u3} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1))))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_le_map_iff_of_injective Submonoid.map_le_map_iff_of_injectiveₓ'. -/
 @[to_additive]
 theorem map_le_map_iff_of_injective {S T : Submonoid M} : S.map f ≤ T.map f ↔ S ≤ T :=
@@ -696,7 +696,7 @@ theorem map_le_map_iff_of_injective {S T : Submonoid M} : S.map f ≤ T.map f 
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (StrictMono.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_strict_mono_of_injective Submonoid.map_strictMono_of_injectiveₓ'. -/
 @[to_additive]
 theorem map_strictMono_of_injective : StrictMono (map f) :=
@@ -716,7 +716,7 @@ include hf
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (GaloisInsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisInsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (FunLike.coe.{succ u3, succ u1, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc)) f)) -> (GaloisInsertion.{u1, u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u1} M _inst_1)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.gi_map_comap Submonoid.giMapComapₓ'. -/
 /-- `map f` and `comap f` form a `galois_insertion` when `f` is surjective. -/
 @[to_additive " `map f` and `comap f` form a `galois_insertion` when `f` is surjective. "]
@@ -731,7 +731,7 @@ def giMapComap : GaloisInsertion (map f) (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S)) S)
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) S)
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S)) S)
 Case conversion may be inaccurate. Consider using '#align submonoid.map_comap_eq_of_surjective Submonoid.map_comap_eq_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_comap_eq_of_surjective (S : Submonoid N) : (S.comap f).map f = S :=
@@ -743,7 +743,7 @@ theorem map_comap_eq_of_surjective (S : Submonoid N) : (S.comap f).map f = S :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Surjective.{succ u1, succ u2} (Submonoid.{u1} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Surjective.{succ u3, succ u2} (Submonoid.{u3} M _inst_1) (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_surjective_of_surjective Submonoid.map_surjective_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_surjective_of_surjective : Function.Surjective (map f) :=
@@ -755,7 +755,7 @@ theorem map_surjective_of_surjective : Function.Surjective (map f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Function.Injective.{succ u2, succ u1} (Submonoid.{u2} N _inst_2) (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (Function.Injective.{succ u3, succ u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_injective_of_surjective Submonoid.comap_injective_of_surjectiveₓ'. -/
 @[to_additive]
 theorem comap_injective_of_surjective : Function.Injective (comap f) :=
@@ -767,7 +767,7 @@ theorem comap_injective_of_surjective : Function.Injective (comap f) :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Inf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instInfSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSubmonoid.{u3} N _inst_2) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instInfSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSubmonoid.{u3} N _inst_2) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_inf_comap_of_surjective Submonoid.map_inf_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_inf_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊓ T.comap f).map f = S ⊓ T :=
@@ -779,7 +779,7 @@ theorem map_inf_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊓ T.comap
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (infᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) ι S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, succ u1} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSetSubmonoid.{u3} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u4, succ u1} (Submonoid.{u4} N _inst_2) (Submonoid.instInfSetSubmonoid.{u4} N _inst_2) ι S))
+  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (infᵢ.{u3, succ u1} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSetSubmonoid.{u3} M _inst_1) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (infᵢ.{u4, succ u1} (Submonoid.{u4} N _inst_2) (Submonoid.instInfSetSubmonoid.{u4} N _inst_2) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_infi_comap_of_surjective Submonoid.map_infᵢ_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_infᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).comap f).map f = infᵢ S :=
@@ -791,7 +791,7 @@ theorem map_infᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Sup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} M _inst_1) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} M _inst_1) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} N _inst_2) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} N _inst_2) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} M _inst_1) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} M _inst_1) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} N _inst_2) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} N _inst_2) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_sup_comap_of_surjective Submonoid.map_sup_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_sup_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊔ T.comap f).map f = S ⊔ T :=
@@ -803,7 +803,7 @@ theorem map_sup_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊔ T.comap
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {ι : Type.{u4}} {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : ι -> (Submonoid.{u2} N _inst_2)), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (supᵢ.{u1, succ u4} (Submonoid.{u1} M _inst_1) (CompleteSemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toCompleteSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1))) ι (fun (i : ι) => Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u2, succ u4} (Submonoid.{u2} N _inst_2) (CompleteSemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2))) ι S))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, succ u1} (Submonoid.{u3} M _inst_1) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u4, succ u1} (Submonoid.{u4} N _inst_2) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u4} N _inst_2)) ι S))
+  forall {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u4} N] {F : Type.{u2}} [mc : MonoidHomClass.{u2, u3, u4} F M N _inst_1 _inst_2] {ι : Type.{u1}} {f : F}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{succ u2, succ u3, succ u4} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u2, u3, u4} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u4} N _inst_2) (MonoidHomClass.toMulHomClass.{u2, u3, u4} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : ι -> (Submonoid.{u4} N _inst_2)), Eq.{succ u4} (Submonoid.{u4} N _inst_2) (Submonoid.map.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (supᵢ.{u3, succ u1} (Submonoid.{u3} M _inst_1) (CompleteLattice.toSupSet.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)) ι (fun (i : ι) => Submonoid.comap.{u3, u4, u2} M N _inst_1 _inst_2 F mc f (S i)))) (supᵢ.{u4, succ u1} (Submonoid.{u4} N _inst_2) (CompleteLattice.toSupSet.{u4} (Submonoid.{u4} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u4} N _inst_2)) ι S))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_supr_comap_of_surjective Submonoid.map_supᵢ_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_supᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).comap f).map f = supᵢ S :=
@@ -815,7 +815,7 @@ theorem map_supᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨆ i, (S i).
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall {S : Submonoid.{u2} N _inst_2} {T : Submonoid.{u2} N _inst_2}, Iff (LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u2} (Submonoid.{u2} N _inst_2) (Preorder.toLE.{u2} (Submonoid.{u2} N _inst_2) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} N _inst_2} {T : Submonoid.{u3} N _inst_2}, Iff (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} N _inst_2) (Preorder.toLE.{u3} (Submonoid.{u3} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2))))) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall {S : Submonoid.{u3} N _inst_2} {T : Submonoid.{u3} N _inst_2}, Iff (LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T)) (LE.le.{u3} (Submonoid.{u3} N _inst_2) (Preorder.toLE.{u3} (Submonoid.{u3} N _inst_2) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2))))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_le_comap_iff_of_surjective Submonoid.comap_le_comap_iff_of_surjectiveₓ'. -/
 @[to_additive]
 theorem comap_le_comap_iff_of_surjective {S T : Submonoid N} : S.comap f ≤ T.comap f ↔ S ≤ T :=
@@ -827,7 +827,7 @@ theorem comap_le_comap_iff_of_surjective {S T : Submonoid N} : S.comap f ≤ T.c
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (StrictMono.{u2, u1} (Submonoid.{u2} N _inst_2) (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} N _inst_2) (SetLike.partialOrder.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (StrictMono.{u3, u2} (Submonoid.{u3} N _inst_2) (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_strict_mono_of_surjective Submonoid.comap_strictMono_of_surjectiveₓ'. -/
 @[to_additive]
 theorem comap_strictMono_of_surjective : StrictMono (comap f) :=
@@ -1031,7 +1031,7 @@ def Subtype : S' →* M :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {A : Type.{u2}} [_inst_4 : SetLike.{u2, u1} A M] [hA : SubmonoidClass.{u2, u1} A M _inst_1 _inst_4] (S' : A), Eq.{succ u1} ((fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) => (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') -> M) (SubmonoidClass.Subtype.{u1, u2} M _inst_1 A _inst_4 hA S')) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) => (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') -> M) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 A _inst_4 hA S') _inst_1) (SubmonoidClass.Subtype.{u1, u2} M _inst_1 A _inst_4 hA S')) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (coeBase.{succ u1, succ u1} (coeSort.{succ u2, succ (succ u1)} A Type.{u1} (SetLike.hasCoeToSort.{u2, u1} A M _inst_4) S') M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u2} M A (SetLike.hasMem.{u2, u1} A M _inst_4) x S'))))))
 but is expected to have type
-  forall {M : Type.{u2}} [_inst_1 : MulOneClass.{u2} M] {A : Type.{u1}} [_inst_4 : SetLike.{u1, u2} A M] [hA : SubmonoidClass.{u1, u2} A M _inst_1 _inst_4] (S' : A), Eq.{succ u2} (forall (a : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S')) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1 (MonoidHom.monoidHomClass.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1))) (SubmonoidClass.Subtype.{u2, u1} M _inst_1 A _inst_4 hA S')) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S'))
+  forall {M : Type.{u2}} [_inst_1 : MulOneClass.{u2} M] {A : Type.{u1}} [_inst_4 : SetLike.{u1, u2} A M] [hA : SubmonoidClass.{u1, u2} A M _inst_1 _inst_4] (S' : A), Eq.{succ u2} (forall (a : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) => M) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S')) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1 (MonoidHom.monoidHomClass.{u2, u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S')) M (SubmonoidClass.toMulOneClass.{u2, u1} M _inst_1 A _inst_4 hA S') _inst_1))) (SubmonoidClass.Subtype.{u2, u1} M _inst_1 A _inst_4 hA S')) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M A (SetLike.instMembership.{u1, u2} A M _inst_4) x S'))
 Case conversion may be inaccurate. Consider using '#align submonoid_class.coe_subtype SubmonoidClass.coe_subtypeₓ'. -/
 @[simp, to_additive]
 theorem coe_subtype : (SubmonoidClass.Subtype S' : S' → M) = coe :=
@@ -1275,7 +1275,7 @@ def subtype : S →* M :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} ((coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) -> M) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) -> M) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Submonoid.subtype.{u1} M _inst_1 S)) ((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} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))))))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u1} M _inst_1 S)) (MulOneClass.toMul.{u1} M _inst_1) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1 (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1))) (Submonoid.subtype.{u1} M _inst_1 S)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] (S : Submonoid.{u1} M _inst_1), Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) => M) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u1} M _inst_1 S)) (MulOneClass.toMul.{u1} M _inst_1) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1 (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) M (Submonoid.toMulOneClass.{u1} M _inst_1 S) _inst_1))) (Submonoid.subtype.{u1} M _inst_1 S)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_subtype Submonoid.coe_subtypeₓ'. -/
 @[simp, to_additive]
 theorem coe_subtype : ⇑S.Subtype = coe :=
@@ -1316,7 +1316,7 @@ theorem topEquiv_toMonoidHom : (topEquiv : _ ≃* M).toMonoidHom = (⊤ : Submon
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), (Function.Injective.{succ u1, succ u2} M N (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f)) -> (MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u1} M _inst_1)) x S)) (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))
 Case conversion may be inaccurate. Consider using '#align submonoid.equiv_map_of_injective Submonoid.equivMapOfInjectiveₓ'. -/
 /-- A subgroup is isomorphic to its image under an injective function. If you have an isomorphism,
 use `mul_equiv.submonoid_map` for better definitional equalities. -/
@@ -1331,7 +1331,7 @@ noncomputable def equivMapOfInjective (f : M →* N) (hf : Function.Injective f)
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (S : Submonoid.{u1} M _inst_1) (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (hf : Function.Injective.{succ u1, succ u2} M N (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f)) (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S), Eq.{succ u2} N ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) N (coeSubtype.{succ u2} N (fun (x : N) => Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (fun (_x : MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (MulEquiv.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f S))) (Submonoid.equivMapOfInjective.{u1, u2} M N _inst_1 _inst_2 S f hf) x)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) 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} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x S))))) x))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (S : Submonoid.{u2} M _inst_1) (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2) (hf : Function.Injective.{succ u2, succ u1} M N (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f)) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u2} M _inst_1 S)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)))))) (Submonoid.equivMapOfInjective.{u2, u1} M N _inst_1 _inst_2 S f hf) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) x))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (S : Submonoid.{u2} M _inst_1) (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2) (hf : Function.Injective.{succ u2, succ u1} M N (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f)) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u2} M _inst_1 S)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f S)))))) (Submonoid.equivMapOfInjective.{u2, u1} M N _inst_1 _inst_2 S f hf) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2))) f (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) x))
 Case conversion may be inaccurate. Consider using '#align submonoid.coe_equiv_map_of_injective_apply Submonoid.coe_equivMapOfInjective_applyₓ'. -/
 @[simp, to_additive]
 theorem coe_equivMapOfInjective_apply (f : M →* N) (hf : Function.Injective f) (x : S) :
@@ -1528,7 +1528,7 @@ theorem prod_bot_sup_bot_prod (s : Submonoid M) (t : Submonoid N) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {f : MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)} {K : Submonoid.{u1} M _inst_1} {x : N}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 f) K)) (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (MulEquiv.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) (fun (_x : MulEquiv.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) => N -> M) (MulEquiv.hasCoeToFun.{u2, u1} N M (MulOneClass.toHasMul.{u2} N _inst_2) (MulOneClass.toHasMul.{u1} M _inst_1)) (MulEquiv.symm.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) f) x) K)
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] {f : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)} {K : Submonoid.{u2} M _inst_1} {x : N}, Iff (Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 f) K)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => M) x) (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquivClass.instMonoidHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1))))) (MulEquiv.symm.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) f) x) K)
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] {f : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)} {K : Submonoid.{u2} M _inst_1} {x : N}, Iff (Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 f) K)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => M) x) (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquivClass.instMonoidHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N M _inst_2 _inst_1 (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1))))) (MulEquiv.symm.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) f) x) K)
 Case conversion may be inaccurate. Consider using '#align submonoid.mem_map_equiv Submonoid.mem_map_equivₓ'. -/
 @[to_additive]
 theorem mem_map_equiv {f : M ≃* N} {K : Submonoid M} {x : N} :
@@ -1682,7 +1682,7 @@ def mrange (f : F) : Submonoid N :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u2} (Set.{u2} N) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submonoid.{u2} N _inst_2) (Set.{u2} N) (HasLiftT.mk.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (CoeTCₓ.coe.{succ u2, succ u2} (Submonoid.{u2} N _inst_2) (Set.{u2} N) (SetLike.Set.hasCoeT.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)))) (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Set.range.{u2, succ u1} N M (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} N) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Set.range.{u3, succ u2} N M (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} N) (SetLike.coe.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Set.range.{u3, succ u2} N M (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.coe_mrange MonoidHom.coe_mrangeₓ'. -/
 @[simp, to_additive]
 theorem coe_mrange (f : F) : (mrange f : Set N) = Set.range f :=
@@ -1694,7 +1694,7 @@ theorem coe_mrange (f : F) : (mrange f : Set N) = Set.range f :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F} {y : N}, Iff (Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) y (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Exists.{succ u1} M (fun (x : M) => Eq.{succ u2} N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) y))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F} {y : N}, Iff (Membership.mem.{u3, u3} N (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) y (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Exists.{succ u2} M (fun (x : M) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) x) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) y))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F} {y : N}, Iff (Membership.mem.{u3, u3} N (Submonoid.{u3} N _inst_2) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u3} N _inst_2)) y (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f)) (Exists.{succ u2} M (fun (x : M) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f x) y))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mem_mrange MonoidHom.mem_mrangeₓ'. -/
 @[simp, to_additive]
 theorem mem_mrange {f : F} {y : N} : y ∈ mrange f ↔ ∃ x, f x = y :=
@@ -1734,7 +1734,7 @@ include mc
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, Iff (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasTop.{u2} N _inst_2))) (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, Iff (Eq.{succ u3} (Submonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instTopSubmonoid.{u3} N _inst_2))) (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, Iff (Eq.{succ u3} (Submonoid.{u3} N _inst_2) (MonoidHom.mrange.{u2, u3, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instTopSubmonoid.{u3} N _inst_2))) (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mrange_top_iff_surjective MonoidHom.mrange_top_iff_surjectiveₓ'. -/
 @[to_additive]
 theorem mrange_top_iff_surjective {f : F} : mrange f = (⊤ : Submonoid N) ↔ Function.Surjective f :=
@@ -1746,7 +1746,7 @@ theorem mrange_top_iff_surjective {f : F} : mrange f = (⊤ : Submonoid N) ↔ F
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F), (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u1, u2, u3} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasTop.{u2} N _inst_2)))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u3, u2, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instTopSubmonoid.{u2} N _inst_2)))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), (Function.Surjective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (Eq.{succ u2} (Submonoid.{u2} N _inst_2) (MonoidHom.mrange.{u3, u2, u1} M N _inst_1 _inst_2 F mc f) (Top.top.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instTopSubmonoid.{u2} N _inst_2)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mrange_top_of_surjective MonoidHom.mrange_top_of_surjectiveₓ'. -/
 /-- The range of a surjective monoid hom is the whole of the codomain. -/
 @[to_additive "The range of a surjective `add_monoid` hom is the whole of the codomain."]
@@ -1760,7 +1760,7 @@ theorem mrange_top_of_surjective (f : F) (hf : Function.Surjective f) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u2} N), LE.le.{u1} (Submonoid.{u1} M _inst_1) (Preorder.toLE.{u1} (Submonoid.{u1} M _inst_1) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M _inst_1) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (Submonoid.closure.{u1} M _inst_1 (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) s)) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u2} N _inst_2 s))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} N), LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.closure.{u2} M _inst_1 (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) s)) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} N _inst_2 s))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} N), LE.le.{u2} (Submonoid.{u2} M _inst_1) (Preorder.toLE.{u2} (Submonoid.{u2} M _inst_1) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1))))) (Submonoid.closure.{u2} M _inst_1 (Set.preimage.{u2, u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f) s)) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} N _inst_2 s))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mclosure_preimage_le MonoidHom.mclosure_preimage_leₓ'. -/
 @[to_additive]
 theorem mclosure_preimage_le (f : F) (s : Set N) : closure (f ⁻¹' s) ≤ (closure s).comap f :=
@@ -1772,7 +1772,7 @@ theorem mclosure_preimage_le (f : F) (s : Set N) : closure (f ⁻¹' s) ≤ (clo
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u1} M), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u1} M _inst_1 s)) (Submonoid.closure.{u2} N _inst_2 (Set.image.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) s))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} M), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} M _inst_1 s)) (Submonoid.closure.{u2} N _inst_2 (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) s))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) (s : Set.{u3} M), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Submonoid.closure.{u3} M _inst_1 s)) (Submonoid.closure.{u2} N _inst_2 (Set.image.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) s))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.map_mclosure MonoidHom.map_mclosureₓ'. -/
 /-- The image under a monoid hom of the submonoid generated by a set equals the submonoid generated
     by the image of the set. -/
@@ -1802,7 +1802,7 @@ def restrict {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M] (
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} {S : Type.{u3}} [_inst_4 : MulOneClass.{u2} N] [_inst_5 : SetLike.{u3, u1} S M] [_inst_6 : SubmonoidClass.{u3, u1} S M _inst_1 _inst_5] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (s : S) (x : coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s), Eq.{succ u2} N (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) N (SubmonoidClass.toMulOneClass.{u1, u3} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) N (SubmonoidClass.toMulOneClass.{u1, u3} M _inst_1 S _inst_5 _inst_6 s) _inst_4) => (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) -> N) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) N (SubmonoidClass.toMulOneClass.{u1, u3} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (MonoidHom.restrict.{u1, u2, u3} M _inst_1 N S _inst_4 _inst_5 _inst_6 f s) x) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_4) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_4) f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (coeBase.{succ u1, succ u1} (coeSort.{succ u3, succ (succ u1)} S Type.{u1} (SetLike.hasCoeToSort.{u3, u1} S M _inst_5) s) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u3} M S (SetLike.hasMem.{u3, u1} S M _inst_5) x s))))) x))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u3}} {S : Type.{u2}} [_inst_4 : MulOneClass.{u3} N] [_inst_5 : SetLike.{u2, u1} S M] [_inst_6 : SubmonoidClass.{u2, u1} S M _inst_1 _inst_5] (f : MonoidHom.{u1, u3} M N _inst_1 _inst_4) (s : S) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s)) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4 (MonoidHom.monoidHomClass.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4))) (MonoidHom.restrict.{u1, u3, u2} M _inst_1 N S _inst_4 _inst_5 _inst_6 f s) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u3} M N _inst_1 _inst_4))) f (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u2, u1} S M _inst_5 s)) x))
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u3}} {S : Type.{u2}} [_inst_4 : MulOneClass.{u3} N] [_inst_5 : SetLike.{u2, u1} S M] [_inst_6 : SubmonoidClass.{u2, u1} S M _inst_1 _inst_5] (f : MonoidHom.{u1, u3} M N _inst_1 _inst_4) (s : S) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (MulOneClass.toMul.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s)) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4 (MonoidHom.monoidHomClass.{u1, u3} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u2} M S (SetLike.instMembership.{u2, u1} S M _inst_5) x s)) N (SubmonoidClass.toMulOneClass.{u1, u2} M _inst_1 S _inst_5 _inst_6 s) _inst_4))) (MonoidHom.restrict.{u1, u3, u2} M _inst_1 N S _inst_4 _inst_5 _inst_6 f s) x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u3} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u3} M N _inst_1 _inst_4))) f (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u2, u1} S M _inst_5 s)) x))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.restrict_apply MonoidHom.restrict_applyₓ'. -/
 @[simp, to_additive]
 theorem restrict_apply {N S : Type _} [MulOneClass N] [SetLike S M] [SubmonoidClass S M]
@@ -1828,7 +1828,7 @@ theorem restrict_mrange (f : M →* N) : (f.restrict S).mrange = S.map f := by
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {S : Type.{u3}} [_inst_4 : SetLike.{u3, u2} S N] [_inst_5 : SubmonoidClass.{u3, u2} S N _inst_2 _inst_4] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (s : S), (forall (x : M), Membership.Mem.{u2, u3} N S (SetLike.hasMem.{u3, u2} S N _inst_4) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f x) s) -> (MonoidHom.{u1, u2} M (coeSort.{succ u3, succ (succ u2)} S Type.{u2} (SetLike.hasCoeToSort.{u3, u2} S N _inst_4) s) _inst_1 (SubmonoidClass.toMulOneClass.{u2, u3} N _inst_2 S _inst_4 _inst_5 s))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {S : Type.{u3}} [_inst_4 : SetLike.{u3, u2} S N] [_inst_5 : SubmonoidClass.{u3, u2} S N _inst_2 _inst_4] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (s : S), (forall (x : M), Membership.mem.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) x) S (SetLike.instMembership.{u3, u2} S N _inst_4) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f x) s) -> (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u3} N S (SetLike.instMembership.{u3, u2} S N _inst_4) x s)) _inst_1 (SubmonoidClass.toMulOneClass.{u2, u3} N _inst_2 S _inst_4 _inst_5 s))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {S : Type.{u3}} [_inst_4 : SetLike.{u3, u2} S N] [_inst_5 : SubmonoidClass.{u3, u2} S N _inst_2 _inst_4] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (s : S), (forall (x : M), Membership.mem.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) S (SetLike.instMembership.{u3, u2} S N _inst_4) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f x) s) -> (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u3} N S (SetLike.instMembership.{u3, u2} S N _inst_4) x s)) _inst_1 (SubmonoidClass.toMulOneClass.{u2, u3} N _inst_2 S _inst_4 _inst_5 s))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.cod_restrict MonoidHom.codRestrictₓ'. -/
 /-- Restriction of a monoid hom to a submonoid of the codomain. -/
 @[to_additive "Restriction of an `add_monoid` hom to an `add_submonoid` of the codomain.",
@@ -1858,7 +1858,7 @@ def mrangeRestrict {N} [MulOneClass N] (f : M →* N) : M →* f.mrange :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} [_inst_4 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (x : M), Eq.{succ u2} N ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) N (coeSubtype.{succ u2} N (fun (x : N) => Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)))))) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (fun (_x : MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) => M -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHom.hasCoeToFun.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.setLike.{u2} N _inst_4)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_4 f) x)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_4) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_4) f x)
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} [_inst_4 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (x : M), Eq.{succ u2} N (Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4) (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) (MonoidHom.monoidHomClass.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_4 f) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4))) f x)
+  forall {M : Type.{u1}} [_inst_1 : MulOneClass.{u1} M] {N : Type.{u2}} [_inst_4 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_4) (x : M), Eq.{succ u2} N (Subtype.val.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Set.{u2} N) (Set.instMembershipSet.{u2} N) x (SetLike.coe.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4) (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f)) (MonoidHom.monoidHomClass.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_4) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_4) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_4)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_4 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_4 (MonoidHom.{u1, u2} M N _inst_1 _inst_4) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4) f))))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_4 f) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_4) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_4) M N _inst_1 _inst_4 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_4))) f x)
 Case conversion may be inaccurate. Consider using '#align monoid_hom.coe_mrange_restrict MonoidHom.coe_mrangeRestrictₓ'. -/
 @[simp, to_additive]
 theorem coe_mrangeRestrict {N} [MulOneClass N] (f : M →* N) (x : M) :
@@ -1871,7 +1871,7 @@ theorem coe_mrangeRestrict {N} [MulOneClass N] (f : M →* N) (x : M) :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2), Function.Surjective.{succ u1, succ u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (fun (_x : MonoidHom.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) => M -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MonoidHom.hasCoeToFun.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) _inst_1 (Submonoid.toMulOneClass.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MonoidHom.mrangeRestrict.{u1, u2} M _inst_1 N _inst_2 f))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2), Function.Surjective.{succ u2, succ u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f)) (MonoidHom.monoidHomClass.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))))) (MonoidHom.mrangeRestrict.{u2, u1} M _inst_1 N _inst_2 f))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2), Function.Surjective.{succ u2, succ u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f)) (MonoidHom.monoidHomClass.{u2, u1} M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))) _inst_1 (Submonoid.toMulOneClass.{u1} N _inst_2 (MonoidHom.mrange.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f))))) (MonoidHom.mrangeRestrict.{u2, u1} M _inst_1 N _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mrange_restrict_surjective MonoidHom.mrangeRestrict_surjectiveₓ'. -/
 @[to_additive]
 theorem mrangeRestrict_surjective (f : M →* N) : Function.Surjective f.mrangeRestrict :=
@@ -1896,7 +1896,7 @@ def mker (f : F) : Submonoid M :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F) {x : M}, Iff (Membership.Mem.{u1, u1} M (Submonoid.{u1} M _inst_1) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) x (MonoidHom.mker.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Eq.{succ u2} N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f x) (OfNat.ofNat.{u2} N 1 (OfNat.mk.{u2} N 1 (One.one.{u2} N (MulOneClass.toHasOne.{u2} N _inst_2)))))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {x : M}, Iff (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) x) 1 (One.toOfNat1.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) x) (MulOneClass.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) x) _inst_2))))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F) {x : M}, Iff (Membership.mem.{u3, u3} M (Submonoid.{u3} M _inst_1) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1)) x (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) 1 (One.toOfNat1.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) (MulOneClass.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) x) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.mem_mker MonoidHom.mem_mkerₓ'. -/
 @[to_additive]
 theorem mem_mker (f : F) {x : M} : x ∈ mker f ↔ f x = 1 :=
@@ -1908,7 +1908,7 @@ theorem mem_mker (f : F) {x : M} : x ∈ mker f ↔ f x = 1 :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submonoid.{u1} M _inst_1) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} M _inst_1) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)))) (MonoidHom.mker.{u1, u2, u3} M N _inst_1 _inst_2 F mc f)) (Set.preimage.{u1, u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f) (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.hasSingleton.{u2} N) (OfNat.ofNat.{u2} N 1 (OfNat.mk.{u2} N 1 (One.one.{u2} N (MulOneClass.toHasOne.{u2} N _inst_2))))))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Set.preimage.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.instSingletonSet.{u2} N) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (MulOneClass.toOne.{u2} N _inst_2)))))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (f : F), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (Submonoid.{u3} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u3} M _inst_1) (MonoidHom.mker.{u3, u2, u1} M N _inst_1 _inst_2 F mc f)) (Set.preimage.{u3, u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f) (Singleton.singleton.{u2, u2} N (Set.{u2} N) (Set.instSingletonSet.{u2} N) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (MulOneClass.toOne.{u2} N _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.coe_mker MonoidHom.coe_mkerₓ'. -/
 @[to_additive]
 theorem coe_mker (f : F) : (mker f : Set M) = (f : M → N) ⁻¹' {1} :=
@@ -2090,7 +2090,7 @@ def submonoidMap (f : M →* N) (M' : Submonoid M) : M' →* M'.map f
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) (M' : Submonoid.{u1} M _inst_1), Function.Surjective.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (Submonoid.toMulOneClass.{u1} M _inst_1 M') (Submonoid.toMulOneClass.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) (fun (_x : MonoidHom.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (Submonoid.toMulOneClass.{u1} M _inst_1 M') (Submonoid.toMulOneClass.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) (MonoidHom.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) M') (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M')) (Submonoid.toMulOneClass.{u1} M _inst_1 M') (Submonoid.toMulOneClass.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f M'))) (MonoidHom.submonoidMap.{u1, u2} M N _inst_1 _inst_2 f M'))
 but is expected to have type
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_inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M')) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))))) (MonoidHom.submonoidMap.{u2, u1} M N _inst_1 _inst_2 f M'))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (f : MonoidHom.{u2, u1} M N _inst_1 _inst_2) (M' : Submonoid.{u2} M _inst_1), Function.Surjective.{succ u2, succ u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Submonoid.toMulOneClass.{u2} M _inst_1 M')) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M')) (MonoidHom.monoidHomClass.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x M')) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))) (Submonoid.toMulOneClass.{u2} M _inst_1 M') (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) f M'))))) (MonoidHom.submonoidMap.{u2, u1} M N _inst_1 _inst_2 f M'))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.submonoid_map_surjective MonoidHom.submonoidMap_surjectiveₓ'. -/
 @[to_additive]
 theorem submonoidMap_surjective (f : M →* N) (M' : Submonoid M) :
@@ -2331,7 +2331,7 @@ def submonoidCongr (h : S = T) : S ≃* T :=
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) {g : N -> M}, (Function.LeftInverse.{succ u1, succ u2} M N g (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (fun (_x : MonoidHom.{u1, u2} M N _inst_1 _inst_2) => M -> N) (MonoidHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_2) f)) -> (MulEquiv.{u1, u2} M (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)) (MulOneClass.toHasMul.{u1} M _inst_1) (Submonoid.mul.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)))
 but is expected to have type
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) {g : N -> M}, (Function.LeftInverse.{succ u1, succ u2} M N g (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u1} M _inst_1) (Submonoid.mul.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (f : MonoidHom.{u1, u2} M N _inst_1 _inst_2) {g : N -> M}, (Function.LeftInverse.{succ u1, succ u2} M N g (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N (MulOneClass.toMul.{u1} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} M N _inst_1 _inst_2) M N _inst_1 _inst_2 (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2))) f)) -> (MulEquiv.{u1, u2} M (Subtype.{succ u2} N (fun (x : N) => Membership.mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u2} N _inst_2)) x (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f))) (MulOneClass.toMul.{u1} M _inst_1) (Submonoid.mul.{u2} N _inst_2 (MonoidHom.mrange.{u1, u2, max u1 u2} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) f)))
 Case conversion may be inaccurate. Consider using '#align mul_equiv.of_left_inverse' MulEquiv.ofLeftInverse'ₓ'. -/
 -- this name is primed so that the version to `f.range` instead of `f.mrange` can be unprimed.
 /-- A monoid homomorphism `f : M →* N` with a left-inverse `g : N → M` defines a multiplicative
@@ -2373,7 +2373,7 @@ def submonoidMap (e : M ≃* N) (S : Submonoid M) : S ≃* S.map e.toMonoidHom :
 lean 3 declaration is
   forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (e : MulEquiv.{u1, u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2)) (S : Submonoid.{u1} M _inst_1) (g : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S), Eq.{succ u2} N ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) N (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) N (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) N (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)) N (coeSubtype.{succ u2} N (fun (x : N) => Membership.Mem.{u2, u2} N (Submonoid.{u2} N _inst_2) (SetLike.hasMem.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) x (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MulEquiv.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 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 but is expected to have type
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_inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)))))) (MulEquiv.submonoidMap.{u2, u1} M N _inst_1 _inst_2 e S) g)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))))) e (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) g))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (e : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) (S : Submonoid.{u2} M _inst_1) (g : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (MulOneClass.toMul.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u2} M _inst_1 S)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)))))) (MulEquiv.submonoidMap.{u2, u1} M N _inst_1 _inst_2 e S) g)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))))) e (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) g))
 Case conversion may be inaccurate. Consider using '#align mul_equiv.coe_submonoid_map_apply MulEquiv.coe_submonoidMap_applyₓ'. -/
 @[simp, to_additive]
 theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
@@ -2386,7 +2386,7 @@ theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
 lean 3 declaration is
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 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (e : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) (S : Submonoid.{u2} M _inst_1) (g : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) g) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (Submonoid.mul.{u2} M _inst_1 S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (fun (_x : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (Submonoid.mul.{u2} M _inst_1 S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) 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(Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (MulEquivClass.instMonoidHomClass.{max u2 u1, u1, u2} (MulEquiv.{u1, u2} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (Submonoid.mul.{u2} M _inst_1 S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Submonoid.toMulOneClass.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (Submonoid.toMulOneClass.{u2} M _inst_1 S) (MulEquiv.instMulEquivClassMulEquiv.{u1, u2} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) 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(Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S)) (MulEquiv.submonoidMap.{u2, u1} M N _inst_1 _inst_2 e S)) g) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun 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(Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Iff.mp (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} N M (MulOneClass.toMul.{u1} N _inst_2) (MulOneClass.toMul.{u2} M _inst_1)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => M) _x) 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_inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g) (Set.image.{u2, u1} M N (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} M N) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : M) => N) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} M N) (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e)) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S))) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : N) => M) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Set.{u2} M) 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(MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S)) (Set.mem_image_equiv.{u1, u2} M N (SetLike.coe.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1) S) (MulEquiv.toEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) e) (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) g)) (Subtype.property.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S)) g))))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (e : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) (S : Submonoid.{u2} M _inst_1) (g : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) g) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u1, u2} (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N 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(MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S)) g))))
 Case conversion may be inaccurate. Consider using '#align mul_equiv.submonoid_map_symm_apply MulEquiv.submonoidMap_symm_applyₓ'. -/
 @[simp, to_additive AddEquiv.add_submonoid_map_symm_apply]
 theorem submonoidMap_symm_apply (e : M ≃* N) (S : Submonoid M) (g : S.map (e : M →* N)) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25

@@ -2369,13 +2369,25 @@ def submonoidMap (e : M ≃* N) (S : Submonoid M) : S ≃* S.map e.toMonoidHom :
 #align mul_equiv.submonoid_map MulEquiv.submonoidMap
 #align add_equiv.add_submonoid_map AddEquiv.addSubmonoidMap
 
+/- warning: mul_equiv.coe_submonoid_map_apply -> MulEquiv.coe_submonoidMap_apply is a dubious translation:
+lean 3 declaration is
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_inst_2 e) S)) (Submonoid.mul.{u1} M _inst_1 S) (Submonoid.mul.{u2} N _inst_2 (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S))) => (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M _inst_1) M (Submonoid.setLike.{u1} M _inst_1)) S) -> (coeSort.{succ u2, succ (succ u2)} (Submonoid.{u2} N _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submonoid.{u2} N _inst_2) N (Submonoid.setLike.{u2} N _inst_2)) (Submonoid.map.{u1, u2, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u1, u2} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u1, u2} M N _inst_1 _inst_2 e) S))) (MulEquiv.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M 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+but is expected to have type
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (e : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) (S : Submonoid.{u2} M _inst_1) (g : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2) (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MulEquiv.toMonoidHom.{u2, u1} M N _inst_1 _inst_2 e) S))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => 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+Case conversion may be inaccurate. Consider using '#align mul_equiv.coe_submonoid_map_apply MulEquiv.coe_submonoidMap_applyₓ'. -/
 @[simp, to_additive]
 theorem coe_submonoidMap_apply (e : M ≃* N) (S : Submonoid M) (g : S) :
     ((submonoidMap e S g : S.map (e : M →* N)) : N) = e g :=
   rfl
 #align mul_equiv.coe_submonoid_map_apply MulEquiv.coe_submonoidMap_apply
-#align add_equiv.coe_add_submonoid_map_apply AddEquiv.coe_add_submonoid_map_apply
+#align add_equiv.coe_add_submonoid_map_apply AddEquiv.coe_addSubmonoidMap_apply
 
+/- warning: mul_equiv.submonoid_map_symm_apply -> MulEquiv.submonoidMap_symm_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mul_equiv.submonoid_map_symm_apply MulEquiv.submonoidMap_symm_applyₓ'. -/
 @[simp, to_additive AddEquiv.add_submonoid_map_symm_apply]
 theorem submonoidMap_symm_apply (e : M ≃* N) (S : Submonoid M) (g : S.map (e : M →* N)) :
     (e.submonoidMap S).symm g = ⟨e.symm g, SetLike.mem_coe.1 <| Set.mem_image_equiv.1 g.2⟩ :=
@@ -2385,6 +2397,12 @@ theorem submonoidMap_symm_apply (e : M ≃* N) (S : Submonoid M) (g : S.map (e :
 
 end MulEquiv
 
+/- warning: submonoid.equiv_map_of_injective_coe_mul_equiv -> Submonoid.equivMapOfInjective_coe_mulEquiv is a dubious translation:
+lean 3 declaration is
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u2} M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2))) e)) (MulEquiv.submonoidMap.{u1, u2} M N _inst_1 _inst_2 e S)
+but is expected to have type
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (S : Submonoid.{u2} M _inst_1) (e : MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)), Eq.{max (succ u2) (succ u1)} (MulEquiv.{u2, u1} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submonoid.{u2} M _inst_1) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} M _inst_1) M (Submonoid.instSetLikeSubmonoid.{u2} M _inst_1)) x S)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Submonoid.{u1} N _inst_2) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} N _inst_2) N (Submonoid.instSetLikeSubmonoid.{u1} N _inst_2)) x (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) (Submonoid.mul.{u2} M _inst_1 S) (Submonoid.mul.{u1} N _inst_2 (Submonoid.map.{u2, u1, max u2 u1} M N _inst_1 _inst_2 (MonoidHom.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.monoidHomClass.{u2, u1} M N _inst_1 _inst_2) (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) S))) (Submonoid.equivMapOfInjective.{u2, u1} M N _inst_1 _inst_2 S (MonoidHomClass.toMonoidHom.{u2, u1, max u2 u1} M N (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) _inst_1 _inst_2 (MulEquivClass.instMonoidHomClass.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N _inst_1 _inst_2 (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e) (EquivLike.injective.{max (succ u2) (succ u1), succ u1, succ u2} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N (MulEquivClass.toEquivLike.{max u2 u1, u2, u1} (MulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2)) M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2) (MulEquiv.instMulEquivClassMulEquiv.{u2, u1} M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u1} N _inst_2))) e)) (MulEquiv.submonoidMap.{u2, u1} M N _inst_1 _inst_2 e S)
+Case conversion may be inaccurate. Consider using '#align submonoid.equiv_map_of_injective_coe_mul_equiv Submonoid.equivMapOfInjective_coe_mulEquivₓ'. -/
 @[simp, to_additive]
 theorem Submonoid.equivMapOfInjective_coe_mulEquiv (e : M ≃* N) :
     S.equivMapOfInjective (e : M →* N) (EquivLike.injective e) = e.submonoidMap S :=
@@ -2392,7 +2410,7 @@ theorem Submonoid.equivMapOfInjective_coe_mulEquiv (e : M ≃* N) :
   ext
   rfl
 #align submonoid.equiv_map_of_injective_coe_mul_equiv Submonoid.equivMapOfInjective_coe_mulEquiv
-#align add_submonoid.equiv_map_of_injective_coe_add_equiv AddSubmonoid.equiv_map_of_injective_coe_add_equiv
+#align add_submonoid.equiv_map_of_injective_coe_add_equiv AddSubmonoid.equivMapOfInjective_coe_addEquiv
 
 section Actions
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -496,9 +496,9 @@ theorem comap_map_comap {S : Submonoid N} {f : F} : ((S.comap f).map f).comap f
 
 /- warning: submonoid.map_sup -> Submonoid.map_sup is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1) (f : F), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (HasSup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) S T)) (HasSup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1) (f : F), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Sup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) S T)) (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1) (f : F), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (HasSup.sup.{u3} (Submonoid.{u3} M _inst_1) (SemilatticeSup.toHasSup.{u3} (Submonoid.{u3} M _inst_1) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) S T)) (HasSup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1) (f : F), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u3} (Submonoid.{u3} M _inst_1) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} M _inst_1) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) S T)) (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_sup Submonoid.map_supₓ'. -/
 @[to_additive]
 theorem map_sup (S T : Submonoid M) (f : F) : (S ⊔ T).map f = S.map f ⊔ T.map f :=
@@ -520,9 +520,9 @@ theorem map_supᵢ {ι : Sort _} (f : F) (s : ι → Submonoid M) : (supᵢ s).m
 
 /- warning: submonoid.comap_inf -> Submonoid.comap_inf is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2) (f : F), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (HasInf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) S T)) (HasInf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2) (f : F), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) S T)) (Inf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2) (f : F), Eq.{succ u2} (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (HasInf.inf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instHasInfSubmonoid.{u3} N _inst_2) S T)) (HasInf.inf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instHasInfSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2) (f : F), Eq.{succ u2} (Submonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSubmonoid.{u3} N _inst_2) S T)) (Inf.inf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instInfSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_inf Submonoid.comap_infₓ'. -/
 @[to_additive]
 theorem comap_inf (S T : Submonoid N) (f : F) : (S ⊓ T).comap f = S.comap f ⊓ T.comap f :=
@@ -634,9 +634,9 @@ theorem map_injective_of_injective : Function.Injective (map f) :=
 
 /- warning: submonoid.comap_inf_map_of_injective -> Submonoid.comap_inf_map_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (HasInf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (HasInf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) S T))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (HasInf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instHasInfSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (HasInf.inf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instHasInfSubmonoid.{u3} M _inst_1) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instInfSubmonoid.{u2} N _inst_2) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instInfSubmonoid.{u3} M _inst_1) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_inf_map_of_injective Submonoid.comap_inf_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_inf_map_of_injective (S T : Submonoid M) : (S.map f ⊓ T.map f).comap f = S ⊓ T :=
@@ -658,9 +658,9 @@ theorem comap_infᵢ_map_of_injective (S : ι → Submonoid M) : (⨅ i, (S i).m
 
 /- warning: submonoid.comap_sup_map_of_injective -> Submonoid.comap_sup_map_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (HasSup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (HasSup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) S T))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u1} M _inst_1) (T : Submonoid.{u1} M _inst_1), Eq.{succ u1} (Submonoid.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) S T))
 but is expected to have type
-  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (HasSup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (HasSup.sup.{u3} (Submonoid.{u3} M _inst_1) (SemilatticeSup.toHasSup.{u3} (Submonoid.{u3} M _inst_1) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) S T))
+  forall {M : Type.{u3}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u3} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u3, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Injective.{succ u3, succ u2} M N (FunLike.coe.{succ u1, succ u3, succ u2} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u3, u2} F M N (MulOneClass.toMul.{u3} M _inst_1) (MulOneClass.toMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u3, u2} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} M _inst_1) (T : Submonoid.{u3} M _inst_1), Eq.{succ u3} (Submonoid.{u3} M _inst_1) (Submonoid.comap.{u3, u2, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u2} N _inst_2)))) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.map.{u3, u2, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} M _inst_1) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} M _inst_1) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} M _inst_1) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u3} M _inst_1)))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.comap_sup_map_of_injective Submonoid.comap_sup_map_of_injectiveₓ'. -/
 @[to_additive]
 theorem comap_sup_map_of_injective (S T : Submonoid M) : (S.map f ⊔ T.map f).comap f = S ⊔ T :=
@@ -765,9 +765,9 @@ theorem comap_injective_of_surjective : Function.Injective (comap f) :=
 
 /- warning: submonoid.map_inf_comap_of_surjective -> Submonoid.map_inf_comap_of_surjective is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (HasInf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (HasInf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) S T))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Inf.inf.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasInf.{u1} M _inst_1) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasInf.{u2} N _inst_2) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (HasInf.inf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instHasInfSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (HasInf.inf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instHasInfSubmonoid.{u3} N _inst_2) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Inf.inf.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instInfSubmonoid.{u2} M _inst_1) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Inf.inf.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instInfSubmonoid.{u3} N _inst_2) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_inf_comap_of_surjective Submonoid.map_inf_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_inf_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊓ T.comap f).map f = S ⊓ T :=
@@ -789,9 +789,9 @@ theorem map_infᵢ_comap_of_surjective (S : ι → Submonoid N) : (⨅ i, (S i).
 
 /- warning: submonoid.map_sup_comap_of_surjective -> Submonoid.map_sup_comap_of_surjective is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (HasSup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (HasSup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) S T))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] {F : Type.{u3}} [mc : MonoidHomClass.{u3, u1, u2} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u1, succ u2} M N (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => M -> N) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F M (fun (_x : M) => N) (MulHomClass.toFunLike.{u3, u1, u2} F M N (MulOneClass.toHasMul.{u1} M _inst_1) (MulOneClass.toHasMul.{u2} N _inst_2) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F M N _inst_1 _inst_2 mc))) f)) -> (forall (S : Submonoid.{u2} N _inst_2) (T : Submonoid.{u2} N _inst_2), Eq.{succ u2} (Submonoid.{u2} N _inst_2) (Submonoid.map.{u1, u2, u3} M N _inst_1 _inst_2 F mc f (Sup.sup.{u1} (Submonoid.{u1} M _inst_1) (SemilatticeSup.toHasSup.{u1} (Submonoid.{u1} M _inst_1) (Lattice.toSemilatticeSup.{u1} (Submonoid.{u1} M _inst_1) (CompleteLattice.toLattice.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.completeLattice.{u1} M _inst_1)))) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u1, u2, u3} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u2} (Submonoid.{u2} N _inst_2) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} N _inst_2) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} N _inst_2) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.completeLattice.{u2} N _inst_2)))) S T))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (HasSup.sup.{u2} (Submonoid.{u2} M _inst_1) (SemilatticeSup.toHasSup.{u2} (Submonoid.{u2} M _inst_1) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (HasSup.sup.{u3} (Submonoid.{u3} N _inst_2) (SemilatticeSup.toHasSup.{u3} (Submonoid.{u3} N _inst_2) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) S T))
+  forall {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u3} N] {F : Type.{u1}} [mc : MonoidHomClass.{u1, u2, u3} F M N _inst_1 _inst_2] {f : F}, (Function.Surjective.{succ u2, succ u3} M N (FunLike.coe.{succ u1, succ u2, succ u3} F M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : M) => N) _x) (MulHomClass.toFunLike.{u1, u2, u3} F M N (MulOneClass.toMul.{u2} M _inst_1) (MulOneClass.toMul.{u3} N _inst_2) (MonoidHomClass.toMulHomClass.{u1, u2, u3} F M N _inst_1 _inst_2 mc)) f)) -> (forall (S : Submonoid.{u3} N _inst_2) (T : Submonoid.{u3} N _inst_2), Eq.{succ u3} (Submonoid.{u3} N _inst_2) (Submonoid.map.{u2, u3, u1} M N _inst_1 _inst_2 F mc f (Sup.sup.{u2} (Submonoid.{u2} M _inst_1) (SemilatticeSup.toSup.{u2} (Submonoid.{u2} M _inst_1) (Lattice.toSemilatticeSup.{u2} (Submonoid.{u2} M _inst_1) (CompleteLattice.toLattice.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instCompleteLatticeSubmonoid.{u2} M _inst_1)))) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f S) (Submonoid.comap.{u2, u3, u1} M N _inst_1 _inst_2 F mc f T))) (Sup.sup.{u3} (Submonoid.{u3} N _inst_2) (SemilatticeSup.toSup.{u3} (Submonoid.{u3} N _inst_2) (Lattice.toSemilatticeSup.{u3} (Submonoid.{u3} N _inst_2) (CompleteLattice.toLattice.{u3} (Submonoid.{u3} N _inst_2) (Submonoid.instCompleteLatticeSubmonoid.{u3} N _inst_2)))) S T))
 Case conversion may be inaccurate. Consider using '#align submonoid.map_sup_comap_of_surjective Submonoid.map_sup_comap_of_surjectiveₓ'. -/
 @[to_additive]
 theorem map_sup_comap_of_surjective (S T : Submonoid N) : (S.comap f ⊔ T.comap f).map f = S ⊔ T :=
@@ -1510,9 +1510,9 @@ theorem map_inr (s : Submonoid N) : s.map (inr M N) = prod ⊥ s :=
 
 /- warning: submonoid.prod_bot_sup_bot_prod -> Submonoid.prod_bot_sup_bot_prod is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (s : Submonoid.{u1} M _inst_1) (t : Submonoid.{u2} N _inst_2), Eq.{succ (max u1 u2)} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (HasSup.sup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SemilatticeSup.toHasSup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Lattice.toSemilatticeSup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (CompleteLattice.toLattice.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Submonoid.completeLattice.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s (Bot.bot.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasBot.{u2} N _inst_2))) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 (Bot.bot.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasBot.{u1} M _inst_1)) t)) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s t)
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N] (s : Submonoid.{u1} M _inst_1) (t : Submonoid.{u2} N _inst_2), Eq.{succ (max u1 u2)} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Sup.sup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SemilatticeSup.toHasSup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Lattice.toSemilatticeSup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (CompleteLattice.toLattice.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Submonoid.completeLattice.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s (Bot.bot.{u2} (Submonoid.{u2} N _inst_2) (Submonoid.hasBot.{u2} N _inst_2))) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 (Bot.bot.{u1} (Submonoid.{u1} M _inst_1) (Submonoid.hasBot.{u1} M _inst_1)) t)) (Submonoid.prod.{u1, u2} M N _inst_1 _inst_2 s t)
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (s : Submonoid.{u2} M _inst_1) (t : Submonoid.{u1} N _inst_2), Eq.{max (succ u2) (succ u1)} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (HasSup.sup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (SemilatticeSup.toHasSup.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Lattice.toSemilatticeSup.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteLattice.toLattice.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instCompleteLatticeSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2))))) (Submonoid.prod.{u2, u1} M N _inst_1 _inst_2 s (Bot.bot.{u1} (Submonoid.{u1} N _inst_2) (Submonoid.instBotSubmonoid.{u1} N _inst_2))) (Submonoid.prod.{u2, u1} M N _inst_1 _inst_2 (Bot.bot.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instBotSubmonoid.{u2} M _inst_1)) t)) (Submonoid.prod.{u2, u1} M N _inst_1 _inst_2 s t)
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N] (s : Submonoid.{u2} M _inst_1) (t : Submonoid.{u1} N _inst_2), Eq.{max (succ u2) (succ u1)} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Sup.sup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (SemilatticeSup.toSup.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Lattice.toSemilatticeSup.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteLattice.toLattice.{max u2 u1} (Submonoid.{max u1 u2} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instCompleteLatticeSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2))))) (Submonoid.prod.{u2, u1} M N _inst_1 _inst_2 s (Bot.bot.{u1} (Submonoid.{u1} N _inst_2) (Submonoid.instBotSubmonoid.{u1} N _inst_2))) (Submonoid.prod.{u2, u1} M N _inst_1 _inst_2 (Bot.bot.{u2} (Submonoid.{u2} M _inst_1) (Submonoid.instBotSubmonoid.{u2} M _inst_1)) t)) (Submonoid.prod.{u2, u1} M N _inst_1 _inst_2 s t)
 Case conversion may be inaccurate. Consider using '#align submonoid.prod_bot_sup_bot_prod Submonoid.prod_bot_sup_bot_prodₓ'. -/
 @[simp, to_additive prod_bot_sup_bot_prod]
 theorem prod_bot_sup_bot_prod (s : Submonoid M) (t : Submonoid N) :
@@ -2204,9 +2204,9 @@ theorem prod_eq_top_iff {s : Submonoid M} {t : Submonoid N} : s.Prod t = ⊤ ↔
 
 /- warning: submonoid.mrange_inl_sup_mrange_inr -> Submonoid.mrange_inl_sup_mrange_inr is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N], Eq.{succ (max u1 u2)} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (HasSup.sup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SemilatticeSup.toHasSup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Lattice.toSemilatticeSup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (CompleteLattice.toLattice.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Submonoid.completeLattice.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (MonoidHom.mrange.{u1, max u1 u2, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.{u1, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u1, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.inl.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.mrange.{u2, max u1 u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.{u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.inr.{u1, u2} M N _inst_1 _inst_2))) (Top.top.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Submonoid.hasTop.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)))
+  forall {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : MulOneClass.{u1} M] [_inst_2 : MulOneClass.{u2} N], Eq.{succ (max u1 u2)} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Sup.sup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (SemilatticeSup.toHasSup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Lattice.toSemilatticeSup.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (CompleteLattice.toLattice.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Submonoid.completeLattice.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2))))) (MonoidHom.mrange.{u1, max u1 u2, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.{u1, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u1, max u1 u2} M (Prod.{u1, u2} M N) _inst_1 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.inl.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.mrange.{u2, max u1 u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2) (MonoidHom.{u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (Prod.{u1, u2} M N) _inst_2 (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (MonoidHom.inr.{u1, u2} M N _inst_1 _inst_2))) (Top.top.{max u1 u2} (Submonoid.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)) (Submonoid.hasTop.{max u1 u2} (Prod.{u1, u2} M N) (Prod.mulOneClass.{u1, u2} M N _inst_1 _inst_2)))
 but is expected to have type
-  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N], Eq.{max (succ u2) (succ u1)} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (HasSup.sup.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (SemilatticeSup.toHasSup.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Lattice.toSemilatticeSup.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteLattice.toLattice.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instCompleteLatticeSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2))))) (MonoidHom.mrange.{u2, max u2 u1, max u2 u1} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.{u2, max u1 u2} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u2, max u2 u1} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.inl.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.mrange.{u1, max u2 u1, max u2 u1} N (Prod.{u2, u1} M N) _inst_2 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.{u1, max u1 u2} N (Prod.{u2, u1} M N) _inst_2 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (Prod.{u2, u1} M N) _inst_2 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.inr.{u2, u1} M N _inst_1 _inst_2))) (Top.top.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instTopSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)))
+  forall {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : MulOneClass.{u2} M] [_inst_2 : MulOneClass.{u1} N], Eq.{max (succ u2) (succ u1)} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Sup.sup.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (SemilatticeSup.toSup.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Lattice.toSemilatticeSup.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (CompleteLattice.toLattice.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instCompleteLatticeSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2))))) (MonoidHom.mrange.{u2, max u2 u1, max u2 u1} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.{u2, max u1 u2} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u2, max u2 u1} M (Prod.{u2, u1} M N) _inst_1 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.inl.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.mrange.{u1, max u2 u1, max u2 u1} N (Prod.{u2, u1} M N) _inst_2 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2) (MonoidHom.{u1, max u1 u2} N (Prod.{u2, u1} M N) _inst_2 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (Prod.{u2, u1} M N) _inst_2 (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (MonoidHom.inr.{u2, u1} M N _inst_1 _inst_2))) (Top.top.{max u2 u1} (Submonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)) (Submonoid.instTopSubmonoid.{max u2 u1} (Prod.{u2, u1} M N) (Prod.instMulOneClassProd.{u2, u1} M N _inst_1 _inst_2)))
 Case conversion may be inaccurate. Consider using '#align submonoid.mrange_inl_sup_mrange_inr Submonoid.mrange_inl_sup_mrange_inrₓ'. -/
 @[simp, to_additive]
 theorem mrange_inl_sup_mrange_inr : (inl M N).mrange ⊔ (inr M N).mrange = ⊤ := by

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

• Add CoprodI.lift_comp_of, CoprodI.lift_comp_of', CoprodI.lift_of', CoprodI.iSup_mrange_of, CoprodI.mclosure_iUnion_range_of, CoprodI.induction_left
• Add MonoidHom.mrange_id, MonoidHom.mclosure_range, as well as additive versions.

@@ -979,6 +979,10 @@ theorem mrange_eq_map (f : F) : mrange f = (⊤ : Submonoid M).map f :=
 #align monoid_hom.mrange_eq_map MonoidHom.mrange_eq_map
 #align add_monoid_hom.mrange_eq_map AddMonoidHom.mrange_eq_map
 
+@[to_additive (attr := simp)]
+theorem mrange_id : mrange (MonoidHom.id M) = ⊤ := by
+  simp [mrange_eq_map]
+
 @[to_additive]
 theorem map_mrange (g : N →* P) (f : M →* N) : f.mrange.map g = mrange (comp g f) := by
   simpa only [mrange_eq_map] using (⊤ : Submonoid M).map_map g f
@@ -1019,6 +1023,10 @@ theorem map_mclosure (f : F) (s : Set M) : (closure s).map f = closure (f '' s)
 #align monoid_hom.map_mclosure MonoidHom.map_mclosure
 #align add_monoid_hom.map_mclosure AddMonoidHom.map_mclosure
 
+@[to_additive (attr := simp)]
+theorem mclosure_range (f : F) : closure (Set.range f) = mrange f := by
+  rw [← Set.image_univ, ← map_mclosure, mrange_eq_map, closure_univ]
+
 /-- Restriction of a monoid hom to a submonoid of the domain. -/
 @[to_additive "Restriction of an `AddMonoid` hom to an `AddSubmonoid` of the domain."]
 def restrict {N S : Type*} [MulOneClass N] [SetLike S M] [SubmonoidClass S M] (f : M →* N)

@@ -1493,8 +1493,7 @@ namespace Submonoid
 elements of `M`. -/
 @[to_additive (attr := simps!) " The additive equivalence between the type of additive units of `M`
   and the additive submonoid whose elements are the additive units of `M`. "]
-noncomputable def unitsTypeEquivIsUnitSubmonoid [Monoid M] :
-  Mˣ ≃* IsUnit.submonoid M where
+noncomputable def unitsTypeEquivIsUnitSubmonoid [Monoid M] : Mˣ ≃* IsUnit.submonoid M where
   toFun x := ⟨x, Units.isUnit x⟩
   invFun x := x.prop.unit
   left_inv x := IsUnit.unit_of_val_units _

This is a far from a complete success at the PR title, but it makes a fair bit of progress, and then guards this with appropriate assert_not_exists Ring statements.

It also breaks apart the Mathlib.GroupTheory.Subsemigroup.[Center|Centralizer] files, to pull the Set.center and Set.centralizer declarations into their own files not depending on Subsemigroup.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
 Amelia Livingston, Yury Kudryashov
 -/
-import Mathlib.Algebra.Ring.Nat
+import Mathlib.Algebra.Group.Nat
 import Mathlib.GroupTheory.GroupAction.Defs
 import Mathlib.GroupTheory.Submonoid.Basic
 import Mathlib.GroupTheory.Subsemigroup.Operations

Follow-up to #10816.

Remaining places containing such lemmas are

• Option.bex_ne_none and Option.ball_ne_none: defined in Lean core
• Nat.decidableBallLT and Nat.decidableBallLE: defined in Lean core
• bef_def is still used in a number of places and could be renamed
• BAll.imp_{left,right}, BEx.imp_{left,right}, BEx.intro and BEx.elim

I only audited the first ~150 lemmas mentioning "ball"; too many lemmas named after Metric.ball/openBall/closedBall.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -231,9 +231,7 @@ theorem coe_map (f : F) (S : Submonoid M) : (S.map f : Set N) = f '' S :=
 #align add_submonoid.coe_map AddSubmonoid.coe_map
 
 @[to_additive (attr := simp)]
-theorem mem_map {f : F} {S : Submonoid M} {y : N} : y ∈ S.map f ↔ ∃ x ∈ S, f x = y := by
-  rw [← bex_def]
-  exact mem_image_iff_bex
+theorem mem_map {f : F} {S : Submonoid M} {y : N} : y ∈ S.map f ↔ ∃ x ∈ S, f x = y := Iff.rfl
 #align submonoid.mem_map Submonoid.mem_map
 #align add_submonoid.mem_map AddSubmonoid.mem_map
 

Scatter the content of Data.Nat.Basic across:

• Data.Nat.Defs for the lemmas having no dependencies
• Algebra.Group.Nat for the monoid instances and the few miscellaneous lemmas needing them.
• Algebra.Ring.Nat for the semiring instance and the few miscellaneous lemmas following it.

Similarly, scatter

• Data.Int.Basic across Data.Int.Defs, Algebra.Group.Int, Algebra.Ring.Int
• Data.Nat.Order.Basic across Data.Nat.Defs, Algebra.Order.Group.Nat, Algebra.Order.Ring.Nat
• Data.Int.Order.Basic across Data.Int.Defs, Algebra.Order.Group.Int, Algebra.Order.Ring.Int

Also move a few lemmas from Data.Nat.Order.Lemmas to Data.Nat.Defs.

Before

After

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
 Amelia Livingston, Yury Kudryashov
 -/
-import Mathlib.Data.Nat.Basic
+import Mathlib.Algebra.Ring.Nat
 import Mathlib.GroupTheory.GroupAction.Defs
 import Mathlib.GroupTheory.Submonoid.Basic
 import Mathlib.GroupTheory.Subsemigroup.Operations

@@ -1305,7 +1305,7 @@ theorem nontrivial_iff_exists_ne_one (S : Submonoid M) : Nontrivial S ↔ ∃ x
   calc
     Nontrivial S ↔ ∃ x : S, x ≠ 1 := nontrivial_iff_exists_ne 1
     _ ↔ ∃ (x : _) (hx : x ∈ S), (⟨x, hx⟩ : S) ≠ ⟨1, S.one_mem⟩ := Subtype.exists
-    _ ↔ ∃ x ∈ S, x ≠ (1 : M) := by simp [Ne.def]
+    _ ↔ ∃ x ∈ S, x ≠ (1 : M) := by simp [Ne]
 #align submonoid.nontrivial_iff_exists_ne_one Submonoid.nontrivial_iff_exists_ne_one
 #align add_submonoid.nontrivial_iff_exists_ne_zero AddSubmonoid.nontrivial_iff_exists_ne_zero
 

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".

@@ -680,7 +680,7 @@ protected theorem pow_mem {M : Type*} [Monoid M] (S : Submonoid M) {x : M} (hx :
 #align submonoid.pow_mem Submonoid.pow_mem
 #align add_submonoid.nsmul_mem AddSubmonoid.nsmul_mem
 
--- porting note: coe_pow removed, syntactic tautology
+-- Porting note: coe_pow removed, syntactic tautology
 #noalign submonoid.coe_pow
 #noalign add_submonoid.coe_smul
 

Also golf the existing instance for ℚ and rename Rat.num_nonneg_iff_zero_le to Rat.num_nonneg, Rat.num_pos_iff_pos to Rat.num_pos.

From LeanAPAP

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
 Amelia Livingston, Yury Kudryashov
 -/
+import Mathlib.Data.Nat.Basic
 import Mathlib.GroupTheory.GroupAction.Defs
 import Mathlib.GroupTheory.Submonoid.Basic
 import Mathlib.GroupTheory.Subsemigroup.Operations
@@ -642,6 +643,9 @@ theorem coe_one : ((1 : S) : M) = 1 :=
 #align submonoid.coe_one Submonoid.coe_one
 #align add_submonoid.coe_zero AddSubmonoid.coe_zero
 
+@[to_additive (attr := simp)]
+lemma mk_eq_one {a : M} {ha} : (⟨a, ha⟩ : S) = 1 ↔ a = 1 := by simp [← SetLike.coe_eq_coe]
+
 @[to_additive (attr := simp)]
 theorem mk_mul_mk (x y : M) (hx : x ∈ S) (hy : y ∈ S) :
     (⟨x, hx⟩ : S) * ⟨y, hy⟩ = ⟨x * y, S.mul_mem hx hy⟩ :=
@@ -1502,3 +1506,14 @@ noncomputable def unitsTypeEquivIsUnitSubmonoid [Monoid M] :
 end Submonoid
 
 end Units
+
+open AddSubmonoid Set
+
+namespace Nat
+
+@[simp] lemma addSubmonoid_closure_one : closure ({1} : Set ℕ) = ⊤ := by
+  refine (eq_top_iff' _).2 <| Nat.rec (zero_mem _) ?_
+  simp_rw [Nat.succ_eq_add_one]
+  exact fun n hn ↦ AddSubmonoid.add_mem _ hn <| subset_closure <| Set.mem_singleton _
+
+end Nat

Moving these to separate files should make typeclass synthesis less expensive. Additionally two of them are quite long and this shrinks them slightly.

This handles:

• Submonoid
• Subgroup
• Subsemiring
• Subring
• Subfield
• Submodule
• Subalgebra

This also moves Units.posSubgroup into its own file.

The copyright headers are from:

• https://github.com/leanprover-community/mathlib/pull/6489
• https://github.com/leanprover-community/mathlib/pull/8466

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

@@ -4,9 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
 Amelia Livingston, Yury Kudryashov
 -/
-import Mathlib.Algebra.Order.Monoid.Basic
-import Mathlib.Algebra.Order.Ring.Lemmas
-import Mathlib.Algebra.Order.ZeroLEOne
 import Mathlib.GroupTheory.GroupAction.Defs
 import Mathlib.GroupTheory.Submonoid.Basic
 import Mathlib.GroupTheory.Subsemigroup.Operations
@@ -602,49 +599,6 @@ instance (priority := 75) toCommMonoid {M} [CommMonoid M] {A : Type*} [SetLike A
 #align submonoid_class.to_comm_monoid SubmonoidClass.toCommMonoid
 #align add_submonoid_class.to_add_comm_monoid AddSubmonoidClass.toAddCommMonoid
 
--- Prefer subclasses of `Monoid` over subclasses of `SubmonoidClass`.
-/-- A submonoid of an `OrderedCommMonoid` is an `OrderedCommMonoid`. -/
-@[to_additive "An `AddSubmonoid` of an `OrderedAddCommMonoid` is an `OrderedAddCommMonoid`."]
-instance (priority := 75) toOrderedCommMonoid {M} [OrderedCommMonoid M] {A : Type*} [SetLike A M]
-    [SubmonoidClass A M] (S : A) : OrderedCommMonoid S :=
-  Subtype.coe_injective.orderedCommMonoid (↑) rfl (fun _ _ => rfl) fun _ _ => rfl
-#align submonoid_class.to_ordered_comm_monoid SubmonoidClass.toOrderedCommMonoid
-#align add_submonoid_class.to_ordered_add_comm_monoid AddSubmonoidClass.toOrderedAddCommMonoid
-
--- Prefer subclasses of `Monoid` over subclasses of `SubmonoidClass`.
-/-- A submonoid of a `LinearOrderedCommMonoid` is a `LinearOrderedCommMonoid`. -/
-@[to_additive
-      "An `AddSubmonoid` of a `LinearOrderedAddCommMonoid` is a `LinearOrderedAddCommMonoid`."]
-instance (priority := 75) toLinearOrderedCommMonoid {M} [LinearOrderedCommMonoid M] {A : Type*}
-    [SetLike A M] [SubmonoidClass A M] (S : A) : LinearOrderedCommMonoid S :=
-  Subtype.coe_injective.linearOrderedCommMonoid (↑) rfl (fun _ _ => rfl) (fun _ _ => rfl)
-    (fun _ _ => rfl) fun _ _ => rfl
-#align submonoid_class.to_linear_ordered_comm_monoid SubmonoidClass.toLinearOrderedCommMonoid
-#align add_submonoid_class.to_linear_ordered_add_comm_monoid AddSubmonoidClass.toLinearOrderedAddCommMonoid
-
--- Prefer subclasses of `Monoid` over subclasses of `SubmonoidClass`.
-/-- A submonoid of an `OrderedCancelCommMonoid` is an `OrderedCancelCommMonoid`. -/
-@[to_additive AddSubmonoidClass.toOrderedCancelAddCommMonoid
-      "An `AddSubmonoid` of an `OrderedCancelAddCommMonoid` is an `OrderedCancelAddCommMonoid`."]
-instance (priority := 75) toOrderedCancelCommMonoid {M} [OrderedCancelCommMonoid M] {A : Type*}
-    [SetLike A M] [SubmonoidClass A M] (S : A) : OrderedCancelCommMonoid S :=
-  Subtype.coe_injective.orderedCancelCommMonoid (↑) rfl (fun _ _ => rfl) fun _ _ => rfl
-#align submonoid_class.to_ordered_cancel_comm_monoid SubmonoidClass.toOrderedCancelCommMonoid
-#align add_submonoid_class.to_ordered_cancel_add_comm_monoid AddSubmonoidClass.toOrderedCancelAddCommMonoid
-
--- Prefer subclasses of `Monoid` over subclasses of `SubmonoidClass`.
-/-- A submonoid of a `LinearOrderedCancelCommMonoid` is a `LinearOrderedCancelCommMonoid`.
--/
-@[to_additive AddSubmonoidClass.toLinearOrderedCancelAddCommMonoid
-      "An `AddSubmonoid` of a `LinearOrderedCancelAddCommMonoid` is
-      a `LinearOrderedCancelAddCommMonoid`."]
-instance (priority := 75) toLinearOrderedCancelCommMonoid {M} [LinearOrderedCancelCommMonoid M]
-    {A : Type*} [SetLike A M] [SubmonoidClass A M] (S : A) : LinearOrderedCancelCommMonoid S :=
-  Subtype.coe_injective.linearOrderedCancelCommMonoid (↑) rfl (fun _ _ => rfl) (fun _ _ => rfl)
-    (fun _ _ => rfl) fun _ _ => rfl
-#align submonoid_class.to_linear_ordered_cancel_comm_monoid SubmonoidClass.toLinearOrderedCancelCommMonoid
-#align add_submonoid_class.to_linear_ordered_cancel_add_comm_monoid AddSubmonoidClass.toLinearOrderedCancelAddCommMonoid
-
 /-- The natural monoid hom from a submonoid of monoid `M` to `M`. -/
 @[to_additive "The natural monoid hom from an `AddSubmonoid` of `AddMonoid` `M` to `M`."]
 def subtype : S' →* M where
@@ -740,44 +694,6 @@ instance toCommMonoid {M} [CommMonoid M] (S : Submonoid M) : CommMonoid S :=
 #align submonoid.to_comm_monoid Submonoid.toCommMonoid
 #align add_submonoid.to_add_comm_monoid AddSubmonoid.toAddCommMonoid
 
-/-- A submonoid of an `OrderedCommMonoid` is an `OrderedCommMonoid`. -/
-@[to_additive "An `AddSubmonoid` of an `OrderedAddCommMonoid` is an `OrderedAddCommMonoid`."]
-instance toOrderedCommMonoid {M} [OrderedCommMonoid M] (S : Submonoid M) : OrderedCommMonoid S :=
-  Subtype.coe_injective.orderedCommMonoid (↑) rfl (fun _ _ => rfl) fun _ _ => rfl
-#align submonoid.to_ordered_comm_monoid Submonoid.toOrderedCommMonoid
-#align add_submonoid.to_ordered_add_comm_monoid AddSubmonoid.toOrderedAddCommMonoid
-
-/-- A submonoid of a `LinearOrderedCommMonoid` is a `LinearOrderedCommMonoid`. -/
-@[to_additive
-      "An `AddSubmonoid` of a `LinearOrderedAddCommMonoid` is a `LinearOrderedAddCommMonoid`."]
-instance toLinearOrderedCommMonoid {M} [LinearOrderedCommMonoid M] (S : Submonoid M) :
-    LinearOrderedCommMonoid S :=
-  Subtype.coe_injective.linearOrderedCommMonoid (↑) rfl (fun _ _ => rfl) (fun _ _ => rfl)
-    (fun _ _ => rfl) fun _ _ => rfl
-#align submonoid.to_linear_ordered_comm_monoid Submonoid.toLinearOrderedCommMonoid
-#align add_submonoid.to_linear_ordered_add_comm_monoid AddSubmonoid.toLinearOrderedAddCommMonoid
-
-/-- A submonoid of an `OrderedCancelCommMonoid` is an `OrderedCancelCommMonoid`. -/
-@[to_additive AddSubmonoid.toOrderedCancelAddCommMonoid
-      "An `AddSubmonoid` of an `OrderedCancelAddCommMonoid` is an `OrderedCancelAddCommMonoid`."]
-instance toOrderedCancelCommMonoid {M} [OrderedCancelCommMonoid M] (S : Submonoid M) :
-    OrderedCancelCommMonoid S :=
-  Subtype.coe_injective.orderedCancelCommMonoid (↑) rfl (fun _ _ => rfl) fun _ _ => rfl
-#align submonoid.to_ordered_cancel_comm_monoid Submonoid.toOrderedCancelCommMonoid
-#align add_submonoid.to_ordered_cancel_add_comm_monoid AddSubmonoid.toOrderedCancelAddCommMonoid
-
-/-- A submonoid of a `LinearOrderedCancelCommMonoid` is a `LinearOrderedCancelCommMonoid`.
--/
-@[to_additive AddSubmonoid.toLinearOrderedCancelAddCommMonoid
-      "An `AddSubmonoid` of a `LinearOrderedCancelAddCommMonoid` is
-      a `LinearOrderedCancelAddCommMonoid`."]
-instance toLinearOrderedCancelCommMonoid {M} [LinearOrderedCancelCommMonoid M] (S : Submonoid M) :
-    LinearOrderedCancelCommMonoid S :=
-  Subtype.coe_injective.linearOrderedCancelCommMonoid (↑) rfl (fun _ _ => rfl) (fun _ _ => rfl)
-    (fun _ _ => rfl) fun _ _ => rfl
-#align submonoid.to_linear_ordered_cancel_comm_monoid Submonoid.toLinearOrderedCancelCommMonoid
-#align add_submonoid.to_linear_ordered_cancel_add_comm_monoid AddSubmonoid.toLinearOrderedCancelAddCommMonoid
-
 /-- The natural monoid hom from a submonoid of monoid `M` to `M`. -/
 @[to_additive "The natural monoid hom from an `AddSubmonoid` of `AddMonoid` `M` to `M`."]
 def subtype : S →* M where
@@ -1562,40 +1478,7 @@ instance mulDistribMulAction [Monoid α] [MulDistribMulAction M' α] (S : Submon
 
 example {S : Submonoid M'} : IsScalarTower S M' M' := by infer_instance
 
-section Preorder
-variable (M)
-variable [Preorder M] [CovariantClass M M (· * ·) (· ≤ ·)] {a : M}
-
-/-- The submonoid of elements greater than `1`. -/
-@[to_additive (attr := simps) nonneg "The submonoid of nonnegative elements."]
-def oneLE : Submonoid M where
-  carrier := Set.Ici 1
-  mul_mem' := one_le_mul
-  one_mem' := le_rfl
-
-variable {M}
-
-@[to_additive (attr := simp) mem_nonneg] lemma mem_oneLE : a ∈ oneLE M ↔ 1 ≤ a := Iff.rfl
-
-end Preorder
-
-section MulZeroClass
-variable (α) [MulZeroOneClass α] [PartialOrder α] [PosMulStrictMono α] [ZeroLEOneClass α]
-  [NeZero (1 : α)] {a : α}
-
-/-- The submonoid of positive elements. -/
-@[simps] def pos : Submonoid α where
-  carrier := Set.Ioi 0
-  one_mem' := zero_lt_one
-  mul_mem' := mul_pos
-#align pos_submonoid Submonoid.pos
-
-variable {α}
-
-@[simp] lemma mem_pos : a ∈ pos α ↔ 0 < a := Iff.rfl
-#align mem_pos_monoid Submonoid.mem_pos
 
-end MulZeroClass
 end Submonoid
 
 end Actions
@@ -1618,4 +1501,4 @@ noncomputable def unitsTypeEquivIsUnitSubmonoid [Monoid M] :
 
 end Submonoid
 
-end Units
\ No newline at end of file
+end Units

and other basic lemmas, including a version of Cauchy-Schwarz stated using Real.sqrt

From LeanAPAP

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

@@ -1575,7 +1575,7 @@ def oneLE : Submonoid M where
 
 variable {M}
 
-@[to_additive (attr := simp)] lemma mem_oneLE : a ∈ oneLE M ↔ 1 ≤ a := Iff.rfl
+@[to_additive (attr := simp) mem_nonneg] lemma mem_oneLE : a ∈ oneLE M ↔ 1 ≤ a := Iff.rfl
 
 end Preorder