group_theory.submonoid.inverses ⟷ Mathlib.GroupTheory.Submonoid.Inverses

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.GroupTheory.Submonoid.Pointwise
+import GroupTheory.Submonoid.Pointwise
 
 #align_import group_theory.submonoid.inverses from "leanprover-community/mathlib"@"0ebfdb71919ac6ca5d7fbc61a082fa2519556818"
 

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

@@ -40,7 +40,7 @@ noncomputable instance [Monoid M] : Group (IsUnit.submonoid M) :=
     show Monoid (IsUnit.submonoid M) by
       infer_instance with
     inv := fun x => ⟨_, x.Prop.Unit⁻¹.IsUnit⟩
-    mul_left_inv := fun x => Subtype.eq x.Prop.Unit.inv_val }
+    hMul_left_inv := fun x => Subtype.eq x.Prop.Unit.inv_val }
 
 @[to_additive]
 noncomputable instance [CommMonoid M] : CommGroup (IsUnit.submonoid M) :=
@@ -66,7 +66,7 @@ variable [Monoid M] (S : Submonoid M)
 def leftInv : Submonoid M where
   carrier := {x : M | ∃ y : S, x * y = 1}
   one_mem' := ⟨1, mul_one 1⟩
-  mul_mem' := fun a b ⟨a', ha⟩ ⟨b', hb⟩ =>
+  hMul_mem' := fun a b ⟨a', ha⟩ ⟨b', hb⟩ =>
     ⟨b' * a', by rw [coe_mul, ← mul_assoc, mul_assoc a, hb, mul_one, ha]⟩
 #align submonoid.left_inv Submonoid.leftInv
 #align add_submonoid.left_neg AddSubmonoid.leftNeg

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module group_theory.submonoid.inverses
-! leanprover-community/mathlib commit 0ebfdb71919ac6ca5d7fbc61a082fa2519556818
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.Submonoid.Pointwise
 
+#align_import group_theory.submonoid.inverses from "leanprover-community/mathlib"@"0ebfdb71919ac6ca5d7fbc61a082fa2519556818"
+
 /-!
 
 # Submonoid of inverses

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

@@ -49,12 +49,14 @@ noncomputable instance [Monoid M] : Group (IsUnit.submonoid M) :=
 noncomputable instance [CommMonoid M] : CommGroup (IsUnit.submonoid M) :=
   { show Group (IsUnit.submonoid M) by infer_instance with mul_comm := fun a b => mul_comm a b }
 
+#print Submonoid.IsUnit.Submonoid.coe_inv /-
 @[to_additive]
 theorem IsUnit.Submonoid.coe_inv [Monoid M] (x : IsUnit.submonoid M) :
     ↑x⁻¹ = (↑x.Prop.Unit⁻¹ : M) :=
   rfl
 #align submonoid.is_unit.submonoid.coe_inv Submonoid.IsUnit.Submonoid.coe_inv
 #align add_submonoid.is_unit.submonoid.coe_neg AddSubmonoid.IsUnit.Submonoid.coe_neg
+-/
 
 section Monoid
 
@@ -73,6 +75,7 @@ def leftInv : Submonoid M where
 #align add_submonoid.left_neg AddSubmonoid.leftNeg
 -/
 
+#print Submonoid.leftInv_leftInv_le /-
 @[to_additive]
 theorem leftInv_leftInv_le : S.left_inv.left_inv ≤ S :=
   by
@@ -81,13 +84,17 @@ theorem leftInv_leftInv_le : S.left_inv.left_inv ≤ S :=
   rw [← mul_one x, ← h₁, ← mul_assoc, h₂, one_mul]
 #align submonoid.left_inv_left_inv_le Submonoid.leftInv_leftInv_le
 #align add_submonoid.left_neg_left_neg_le AddSubmonoid.leftNeg_leftNeg_le
+-/
 
+#print Submonoid.unit_mem_leftInv /-
 @[to_additive]
 theorem unit_mem_leftInv (x : Mˣ) (hx : (x : M) ∈ S) : ((x⁻¹ : _) : M) ∈ S.left_inv :=
   ⟨⟨x, hx⟩, x.inv_val⟩
 #align submonoid.unit_mem_left_inv Submonoid.unit_mem_leftInv
 #align add_submonoid.add_unit_mem_left_neg AddSubmonoid.addUnit_mem_leftNeg
+-/
 
+#print Submonoid.leftInv_leftInv_eq /-
 @[to_additive]
 theorem leftInv_leftInv_eq (hS : S ≤ IsUnit.submonoid M) : S.left_inv.left_inv = S :=
   by
@@ -98,7 +105,9 @@ theorem leftInv_leftInv_eq (hS : S ≤ IsUnit.submonoid M) : S.left_inv.left_inv
   exact S.left_inv.unit_mem_left_inv _ (S.unit_mem_left_inv _ hx)
 #align submonoid.left_inv_left_inv_eq Submonoid.leftInv_leftInv_eq
 #align add_submonoid.left_neg_left_neg_eq AddSubmonoid.leftNeg_leftNeg_eq
+-/
 
+#print Submonoid.fromLeftInv /-
 /-- The function from `S.left_inv` to `S` sending an element to its right inverse in `S`.
 This is a `monoid_hom` when `M` is commutative. -/
 @[to_additive
@@ -106,18 +115,23 @@ This is a `monoid_hom` when `M` is commutative. -/
 noncomputable def fromLeftInv : S.left_inv → S := fun x => x.Prop.some
 #align submonoid.from_left_inv Submonoid.fromLeftInv
 #align add_submonoid.from_left_neg AddSubmonoid.fromLeftNeg
+-/
 
+#print Submonoid.mul_fromLeftInv /-
 @[simp, to_additive]
 theorem mul_fromLeftInv (x : S.left_inv) : (x : M) * S.fromLeftInv x = 1 :=
   x.Prop.choose_spec
 #align submonoid.mul_from_left_inv Submonoid.mul_fromLeftInv
 #align add_submonoid.add_from_left_neg AddSubmonoid.add_fromLeftNeg
+-/
 
+#print Submonoid.fromLeftInv_one /-
 @[simp, to_additive]
 theorem fromLeftInv_one : S.fromLeftInv 1 = 1 :=
   (one_mul _).symm.trans (Subtype.eq <| S.mul_fromLeftInv 1)
 #align submonoid.from_left_inv_one Submonoid.fromLeftInv_one
 #align add_submonoid.from_left_neg_zero AddSubmonoid.fromLeftNeg_zero
+-/
 
 end Monoid
 
@@ -125,24 +139,31 @@ section CommMonoid
 
 variable [CommMonoid M] (S : Submonoid M)
 
+#print Submonoid.fromLeftInv_mul /-
 @[simp, to_additive]
 theorem fromLeftInv_mul (x : S.left_inv) : (S.fromLeftInv x : M) * x = 1 := by
   rw [mul_comm, mul_from_left_inv]
 #align submonoid.from_left_inv_mul Submonoid.fromLeftInv_mul
 #align add_submonoid.from_left_neg_add AddSubmonoid.fromLeftNeg_add
+-/
 
+#print Submonoid.leftInv_le_isUnit /-
 @[to_additive]
 theorem leftInv_le_isUnit : S.left_inv ≤ IsUnit.submonoid M := fun x ⟨y, hx⟩ =>
   ⟨⟨x, y, hx, mul_comm x y ▸ hx⟩, rfl⟩
 #align submonoid.left_inv_le_is_unit Submonoid.leftInv_le_isUnit
 #align add_submonoid.left_neg_le_is_add_unit AddSubmonoid.leftNeg_le_isAddUnit
+-/
 
+#print Submonoid.fromLeftInv_eq_iff /-
 @[to_additive]
 theorem fromLeftInv_eq_iff (a : S.left_inv) (b : M) : (S.fromLeftInv a : M) = b ↔ (a : M) * b = 1 :=
   by rw [← IsUnit.mul_right_inj (left_inv_le_is_unit _ a.prop), S.mul_from_left_inv, eq_comm]
 #align submonoid.from_left_inv_eq_iff Submonoid.fromLeftInv_eq_iff
 #align add_submonoid.from_left_neg_eq_iff AddSubmonoid.fromLeftNeg_eq_iff
+-/
 
+#print Submonoid.fromCommLeftInv /-
 /-- The `monoid_hom` from `S.left_inv` to `S` sending an element to its right inverse in `S`. -/
 @[to_additive
       "The `add_monoid_hom` from `S.left_neg` to `S` sending an element to its\nright additive inverse in `S`.",
@@ -157,11 +178,11 @@ noncomputable def fromCommLeftInv : S.left_inv →* S
         mul_assoc (x : M), mul_from_left_inv, one_mul, mul_from_left_inv]
 #align submonoid.from_comm_left_inv Submonoid.fromCommLeftInv
 #align add_submonoid.from_comm_left_neg AddSubmonoid.fromCommLeftNeg
+-/
 
 variable (hS : S ≤ IsUnit.submonoid M)
 
-include hS
-
+#print Submonoid.leftInvEquiv /-
 /-- The submonoid of pointwise inverse of `S` is `mul_equiv` to `S`. -/
 @[to_additive "The additive submonoid of pointwise additive inverse of `S` is\n`add_equiv` to `S`.",
   simps apply]
@@ -178,41 +199,54 @@ noncomputable def leftInvEquiv : S.left_inv ≃* S :=
       exact (hS x.prop).choose_spec.symm }
 #align submonoid.left_inv_equiv Submonoid.leftInvEquiv
 #align add_submonoid.left_neg_equiv AddSubmonoid.leftNegEquiv
+-/
 
+#print Submonoid.fromLeftInv_leftInvEquiv_symm /-
 @[simp, to_additive]
 theorem fromLeftInv_leftInvEquiv_symm (x : S) : S.fromLeftInv ((S.leftInvEquiv hS).symm x) = x :=
   (S.leftInvEquiv hS).right_inv x
 #align submonoid.from_left_inv_left_inv_equiv_symm Submonoid.fromLeftInv_leftInvEquiv_symm
 #align add_submonoid.from_left_neg_left_neg_equiv_symm AddSubmonoid.fromLeftNeg_leftNegEquiv_symm
+-/
 
+#print Submonoid.leftInvEquiv_symm_fromLeftInv /-
 @[simp, to_additive]
 theorem leftInvEquiv_symm_fromLeftInv (x : S.left_inv) :
     (S.leftInvEquiv hS).symm (S.fromLeftInv x) = x :=
   (S.leftInvEquiv hS).left_inv x
 #align submonoid.left_inv_equiv_symm_from_left_inv Submonoid.leftInvEquiv_symm_fromLeftInv
 #align add_submonoid.left_neg_equiv_symm_from_left_neg AddSubmonoid.leftNegEquiv_symm_fromLeftNeg
+-/
 
+#print Submonoid.leftInvEquiv_mul /-
 @[to_additive]
 theorem leftInvEquiv_mul (x : S.left_inv) : (S.leftInvEquiv hS x : M) * x = 1 := by simp
 #align submonoid.left_inv_equiv_mul Submonoid.leftInvEquiv_mul
 #align add_submonoid.left_neg_equiv_add AddSubmonoid.leftNegEquiv_add
+-/
 
+#print Submonoid.mul_leftInvEquiv /-
 @[to_additive]
 theorem mul_leftInvEquiv (x : S.left_inv) : (x : M) * S.leftInvEquiv hS x = 1 := by simp
 #align submonoid.mul_left_inv_equiv Submonoid.mul_leftInvEquiv
 #align add_submonoid.add_left_neg_equiv AddSubmonoid.add_leftNegEquiv
+-/
 
+#print Submonoid.leftInvEquiv_symm_mul /-
 @[simp, to_additive]
 theorem leftInvEquiv_symm_mul (x : S) : ((S.leftInvEquiv hS).symm x : M) * x = 1 := by
   convert S.mul_left_inv_equiv hS ((S.left_inv_equiv hS).symm x); simp
 #align submonoid.left_inv_equiv_symm_mul Submonoid.leftInvEquiv_symm_mul
 #align add_submonoid.left_neg_equiv_symm_add AddSubmonoid.leftNegEquiv_symm_add
+-/
 
+#print Submonoid.mul_leftInvEquiv_symm /-
 @[simp, to_additive]
 theorem mul_leftInvEquiv_symm (x : S) : (x : M) * (S.leftInvEquiv hS).symm x = 1 := by
   convert S.left_inv_equiv_mul hS ((S.left_inv_equiv hS).symm x); simp
 #align submonoid.mul_left_inv_equiv_symm Submonoid.mul_leftInvEquiv_symm
 #align add_submonoid.add_left_neg_equiv_symm AddSubmonoid.add_leftNegEquiv_symm
+-/
 
 end CommMonoid
 
@@ -232,11 +266,13 @@ theorem leftInv_eq_inv : S.left_inv = S⁻¹ :=
 #align add_submonoid.left_neg_eq_neg AddSubmonoid.leftNeg_eq_neg
 -/
 
+#print Submonoid.fromLeftInv_eq_inv /-
 @[simp, to_additive]
 theorem fromLeftInv_eq_inv (x : S.left_inv) : (S.fromLeftInv x : M) = x⁻¹ := by
   rw [← mul_right_inj (x : M), mul_right_inv, mul_from_left_inv]
 #align submonoid.from_left_inv_eq_inv Submonoid.fromLeftInv_eq_inv
 #align add_submonoid.from_left_neg_eq_neg AddSubmonoid.fromLeftNeg_eq_neg
+-/
 
 end Group
 
@@ -244,11 +280,13 @@ section CommGroup
 
 variable [CommGroup M] (S : Submonoid M) (hS : S ≤ IsUnit.submonoid M)
 
+#print Submonoid.leftInvEquiv_symm_eq_inv /-
 @[simp, to_additive]
 theorem leftInvEquiv_symm_eq_inv (x : S) : ((S.leftInvEquiv hS).symm x : M) = x⁻¹ := by
   rw [← mul_right_inj (x : M), mul_right_inv, mul_left_inv_equiv_symm]
 #align submonoid.left_inv_equiv_symm_eq_inv Submonoid.leftInvEquiv_symm_eq_inv
 #align add_submonoid.left_neg_equiv_symm_eq_neg AddSubmonoid.leftNegEquiv_symm_eq_neg
+-/
 
 end CommGroup
 

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

@@ -65,7 +65,7 @@ variable [Monoid M] (S : Submonoid M)
 @[to_additive
       "`S.left_neg` is the additive submonoid containing all the left additive inverses\nof `S`."]
 def leftInv : Submonoid M where
-  carrier := { x : M | ∃ y : S, x * y = 1 }
+  carrier := {x : M | ∃ y : S, x * y = 1}
   one_mem' := ⟨1, mul_one 1⟩
   mul_mem' := fun a b ⟨a', ha⟩ ⟨b', hb⟩ =>
     ⟨b' * a', by rw [coe_mul, ← mul_assoc, mul_assoc a, hb, mul_one, ha]⟩
@@ -174,7 +174,7 @@ noncomputable def leftInvEquiv : S.left_inv ≃* S :=
         dsimp; generalize_proofs h; rw [← h.some.mul_left_inj]
         exact h.some.inv_val.trans ((S.mul_from_left_inv x).symm.trans (by rw [h.some_spec]))
     right_inv := fun x => by
-      dsimp; ext; rw [from_left_inv_eq_iff]; convert(hS x.prop).some.inv_val
+      dsimp; ext; rw [from_left_inv_eq_iff]; convert (hS x.prop).some.inv_val
       exact (hS x.prop).choose_spec.symm }
 #align submonoid.left_inv_equiv Submonoid.leftInvEquiv
 #align add_submonoid.left_neg_equiv AddSubmonoid.leftNegEquiv

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

@@ -220,7 +220,7 @@ section Group
 
 variable [Group M] (S : Submonoid M)
 
-open Pointwise
+open scoped Pointwise
 
 #print Submonoid.leftInv_eq_inv /-
 @[to_additive]

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

@@ -49,12 +49,6 @@ noncomputable instance [Monoid M] : Group (IsUnit.submonoid M) :=
 noncomputable instance [CommMonoid M] : CommGroup (IsUnit.submonoid M) :=
   { show Group (IsUnit.submonoid M) by infer_instance with mul_comm := fun a b => mul_comm a b }
 
-/- warning: submonoid.is_unit.submonoid.coe_inv -> Submonoid.IsUnit.Submonoid.coe_inv is a dubious translation:
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 @[to_additive]
 theorem IsUnit.Submonoid.coe_inv [Monoid M] (x : IsUnit.submonoid M) :
     ↑x⁻¹ = (↑x.Prop.Unit⁻¹ : M) :=
@@ -79,12 +73,6 @@ def leftInv : Submonoid M where
 #align add_submonoid.left_neg AddSubmonoid.leftNeg
 -/
 
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 @[to_additive]
 theorem leftInv_leftInv_le : S.left_inv.left_inv ≤ S :=
   by
@@ -94,24 +82,12 @@ theorem leftInv_leftInv_le : S.left_inv.left_inv ≤ S :=
 #align submonoid.left_inv_left_inv_le Submonoid.leftInv_leftInv_le
 #align add_submonoid.left_neg_left_neg_le AddSubmonoid.leftNeg_leftNeg_le
 
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 @[to_additive]
 theorem unit_mem_leftInv (x : Mˣ) (hx : (x : M) ∈ S) : ((x⁻¹ : _) : M) ∈ S.left_inv :=
   ⟨⟨x, hx⟩, x.inv_val⟩
 #align submonoid.unit_mem_left_inv Submonoid.unit_mem_leftInv
 #align add_submonoid.add_unit_mem_left_neg AddSubmonoid.addUnit_mem_leftNeg
 
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 @[to_additive]
 theorem leftInv_leftInv_eq (hS : S ≤ IsUnit.submonoid M) : S.left_inv.left_inv = S :=
   by
@@ -123,12 +99,6 @@ theorem leftInv_leftInv_eq (hS : S ≤ IsUnit.submonoid M) : S.left_inv.left_inv
 #align submonoid.left_inv_left_inv_eq Submonoid.leftInv_leftInv_eq
 #align add_submonoid.left_neg_left_neg_eq AddSubmonoid.leftNeg_leftNeg_eq
 
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 /-- The function from `S.left_inv` to `S` sending an element to its right inverse in `S`.
 This is a `monoid_hom` when `M` is commutative. -/
 @[to_additive
@@ -137,24 +107,12 @@ noncomputable def fromLeftInv : S.left_inv → S := fun x => x.Prop.some
 #align submonoid.from_left_inv Submonoid.fromLeftInv
 #align add_submonoid.from_left_neg AddSubmonoid.fromLeftNeg
 
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 @[simp, to_additive]
 theorem mul_fromLeftInv (x : S.left_inv) : (x : M) * S.fromLeftInv x = 1 :=
   x.Prop.choose_spec
 #align submonoid.mul_from_left_inv Submonoid.mul_fromLeftInv
 #align add_submonoid.add_from_left_neg AddSubmonoid.add_fromLeftNeg
 
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 @[simp, to_additive]
 theorem fromLeftInv_one : S.fromLeftInv 1 = 1 :=
   (one_mul _).symm.trans (Subtype.eq <| S.mul_fromLeftInv 1)
@@ -167,48 +125,24 @@ section CommMonoid
 
 variable [CommMonoid M] (S : Submonoid M)
 
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 @[simp, to_additive]
 theorem fromLeftInv_mul (x : S.left_inv) : (S.fromLeftInv x : M) * x = 1 := by
   rw [mul_comm, mul_from_left_inv]
 #align submonoid.from_left_inv_mul Submonoid.fromLeftInv_mul
 #align add_submonoid.from_left_neg_add AddSubmonoid.fromLeftNeg_add
 
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 @[to_additive]
 theorem leftInv_le_isUnit : S.left_inv ≤ IsUnit.submonoid M := fun x ⟨y, hx⟩ =>
   ⟨⟨x, y, hx, mul_comm x y ▸ hx⟩, rfl⟩
 #align submonoid.left_inv_le_is_unit Submonoid.leftInv_le_isUnit
 #align add_submonoid.left_neg_le_is_add_unit AddSubmonoid.leftNeg_le_isAddUnit
 
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 @[to_additive]
 theorem fromLeftInv_eq_iff (a : S.left_inv) (b : M) : (S.fromLeftInv a : M) = b ↔ (a : M) * b = 1 :=
   by rw [← IsUnit.mul_right_inj (left_inv_le_is_unit _ a.prop), S.mul_from_left_inv, eq_comm]
 #align submonoid.from_left_inv_eq_iff Submonoid.fromLeftInv_eq_iff
 #align add_submonoid.from_left_neg_eq_iff AddSubmonoid.fromLeftNeg_eq_iff
 
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 /-- The `monoid_hom` from `S.left_inv` to `S` sending an element to its right inverse in `S`. -/
 @[to_additive
       "The `add_monoid_hom` from `S.left_neg` to `S` sending an element to its\nright additive inverse in `S`.",
@@ -228,12 +162,6 @@ variable (hS : S ≤ IsUnit.submonoid M)
 
 include hS
 
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 /-- The submonoid of pointwise inverse of `S` is `mul_equiv` to `S`. -/
 @[to_additive "The additive submonoid of pointwise additive inverse of `S` is\n`add_equiv` to `S`.",
   simps apply]
@@ -251,18 +179,12 @@ noncomputable def leftInvEquiv : S.left_inv ≃* S :=
 #align submonoid.left_inv_equiv Submonoid.leftInvEquiv
 #align add_submonoid.left_neg_equiv AddSubmonoid.leftNegEquiv
 
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 @[simp, to_additive]
 theorem fromLeftInv_leftInvEquiv_symm (x : S) : S.fromLeftInv ((S.leftInvEquiv hS).symm x) = x :=
   (S.leftInvEquiv hS).right_inv x
 #align submonoid.from_left_inv_left_inv_equiv_symm Submonoid.fromLeftInv_leftInvEquiv_symm
 #align add_submonoid.from_left_neg_left_neg_equiv_symm AddSubmonoid.fromLeftNeg_leftNegEquiv_symm
 
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 @[simp, to_additive]
 theorem leftInvEquiv_symm_fromLeftInv (x : S.left_inv) :
     (S.leftInvEquiv hS).symm (S.fromLeftInv x) = x :=
@@ -270,34 +192,22 @@ theorem leftInvEquiv_symm_fromLeftInv (x : S.left_inv) :
 #align submonoid.left_inv_equiv_symm_from_left_inv Submonoid.leftInvEquiv_symm_fromLeftInv
 #align add_submonoid.left_neg_equiv_symm_from_left_neg AddSubmonoid.leftNegEquiv_symm_fromLeftNeg
 
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 @[to_additive]
 theorem leftInvEquiv_mul (x : S.left_inv) : (S.leftInvEquiv hS x : M) * x = 1 := by simp
 #align submonoid.left_inv_equiv_mul Submonoid.leftInvEquiv_mul
 #align add_submonoid.left_neg_equiv_add AddSubmonoid.leftNegEquiv_add
 
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 @[to_additive]
 theorem mul_leftInvEquiv (x : S.left_inv) : (x : M) * S.leftInvEquiv hS x = 1 := by simp
 #align submonoid.mul_left_inv_equiv Submonoid.mul_leftInvEquiv
 #align add_submonoid.add_left_neg_equiv AddSubmonoid.add_leftNegEquiv
 
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 @[simp, to_additive]
 theorem leftInvEquiv_symm_mul (x : S) : ((S.leftInvEquiv hS).symm x : M) * x = 1 := by
   convert S.mul_left_inv_equiv hS ((S.left_inv_equiv hS).symm x); simp
 #align submonoid.left_inv_equiv_symm_mul Submonoid.leftInvEquiv_symm_mul
 #align add_submonoid.left_neg_equiv_symm_add AddSubmonoid.leftNegEquiv_symm_add
 
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 @[simp, to_additive]
 theorem mul_leftInvEquiv_symm (x : S) : (x : M) * (S.leftInvEquiv hS).symm x = 1 := by
   convert S.left_inv_equiv_mul hS ((S.left_inv_equiv hS).symm x); simp
@@ -322,12 +232,6 @@ theorem leftInv_eq_inv : S.left_inv = S⁻¹ :=
 #align add_submonoid.left_neg_eq_neg AddSubmonoid.leftNeg_eq_neg
 -/
 
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 @[simp, to_additive]
 theorem fromLeftInv_eq_inv (x : S.left_inv) : (S.fromLeftInv x : M) = x⁻¹ := by
   rw [← mul_right_inj (x : M), mul_right_inv, mul_from_left_inv]
@@ -340,9 +244,6 @@ section CommGroup
 
 variable [CommGroup M] (S : Submonoid M) (hS : S ≤ IsUnit.submonoid M)
 
-/- warning: submonoid.left_inv_equiv_symm_eq_inv -> Submonoid.leftInvEquiv_symm_eq_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv_symm_eq_inv Submonoid.leftInvEquiv_symm_eq_invₓ'. -/
 @[simp, to_additive]
 theorem leftInvEquiv_symm_eq_inv (x : S) : ((S.leftInvEquiv hS).symm x : M) = x⁻¹ := by
   rw [← mul_right_inj (x : M), mul_right_inv, mul_left_inv_equiv_symm]

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

@@ -117,10 +117,7 @@ theorem leftInv_leftInv_eq (hS : S ≤ IsUnit.submonoid M) : S.left_inv.left_inv
   by
   refine' le_antisymm S.left_inv_left_inv_le _
   intro x hx
-  have : x = ((hS hx).Unit⁻¹⁻¹ : Mˣ) :=
-    by
-    rw [inv_inv (hS hx).Unit]
-    rfl
+  have : x = ((hS hx).Unit⁻¹⁻¹ : Mˣ) := by rw [inv_inv (hS hx).Unit]; rfl
   rw [this]
   exact S.left_inv.unit_mem_left_inv _ (S.unit_mem_left_inv _ hx)
 #align submonoid.left_inv_left_inv_eq Submonoid.leftInv_leftInv_eq
@@ -243,18 +240,13 @@ Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equ
 noncomputable def leftInvEquiv : S.left_inv ≃* S :=
   {
     S.fromCommLeftInv with
-    invFun := fun x => by
-      choose x' hx using hS x.prop
-      exact ⟨x'.inv, x, hx ▸ x'.inv_val⟩
+    invFun := fun x => by choose x' hx using hS x.prop; exact ⟨x'.inv, x, hx ▸ x'.inv_val⟩
     left_inv := fun x =>
       Subtype.eq <| by
         dsimp; generalize_proofs h; rw [← h.some.mul_left_inj]
         exact h.some.inv_val.trans ((S.mul_from_left_inv x).symm.trans (by rw [h.some_spec]))
     right_inv := fun x => by
-      dsimp
-      ext
-      rw [from_left_inv_eq_iff]
-      convert(hS x.prop).some.inv_val
+      dsimp; ext; rw [from_left_inv_eq_iff]; convert(hS x.prop).some.inv_val
       exact (hS x.prop).choose_spec.symm }
 #align submonoid.left_inv_equiv Submonoid.leftInvEquiv
 #align add_submonoid.left_neg_equiv AddSubmonoid.leftNegEquiv
@@ -298,10 +290,8 @@ theorem mul_leftInvEquiv (x : S.left_inv) : (x : M) * S.leftInvEquiv hS x = 1 :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv_symm_mul Submonoid.leftInvEquiv_symm_mulₓ'. -/
 @[simp, to_additive]
-theorem leftInvEquiv_symm_mul (x : S) : ((S.leftInvEquiv hS).symm x : M) * x = 1 :=
-  by
-  convert S.mul_left_inv_equiv hS ((S.left_inv_equiv hS).symm x)
-  simp
+theorem leftInvEquiv_symm_mul (x : S) : ((S.leftInvEquiv hS).symm x : M) * x = 1 := by
+  convert S.mul_left_inv_equiv hS ((S.left_inv_equiv hS).symm x); simp
 #align submonoid.left_inv_equiv_symm_mul Submonoid.leftInvEquiv_symm_mul
 #align add_submonoid.left_neg_equiv_symm_add AddSubmonoid.leftNegEquiv_symm_add
 
@@ -309,10 +299,8 @@ theorem leftInvEquiv_symm_mul (x : S) : ((S.leftInvEquiv hS).symm x : M) * x = 1
 <too large>
 Case conversion may be inaccurate. Consider using '#align submonoid.mul_left_inv_equiv_symm Submonoid.mul_leftInvEquiv_symmₓ'. -/
 @[simp, to_additive]
-theorem mul_leftInvEquiv_symm (x : S) : (x : M) * (S.leftInvEquiv hS).symm x = 1 :=
-  by
-  convert S.left_inv_equiv_mul hS ((S.left_inv_equiv hS).symm x)
-  simp
+theorem mul_leftInvEquiv_symm (x : S) : (x : M) * (S.leftInvEquiv hS).symm x = 1 := by
+  convert S.left_inv_equiv_mul hS ((S.left_inv_equiv hS).symm x); simp
 #align submonoid.mul_left_inv_equiv_symm Submonoid.mul_leftInvEquiv_symm
 #align add_submonoid.add_left_neg_equiv_symm AddSubmonoid.add_leftNegEquiv_symm
 

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

@@ -260,10 +260,7 @@ noncomputable def leftInvEquiv : S.left_inv ≃* S :=
 #align add_submonoid.left_neg_equiv AddSubmonoid.leftNegEquiv
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submonoid.from_left_inv_left_inv_equiv_symm Submonoid.fromLeftInv_leftInvEquiv_symmₓ'. -/
 @[simp, to_additive]
 theorem fromLeftInv_leftInvEquiv_symm (x : S) : S.fromLeftInv ((S.leftInvEquiv hS).symm x) = x :=
@@ -272,10 +269,7 @@ theorem fromLeftInv_leftInvEquiv_symm (x : S) : S.fromLeftInv ((S.leftInvEquiv h
 #align add_submonoid.from_left_neg_left_neg_equiv_symm AddSubmonoid.fromLeftNeg_leftNegEquiv_symm
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv_symm_from_left_inv Submonoid.leftInvEquiv_symm_fromLeftInvₓ'. -/
 @[simp, to_additive]
 theorem leftInvEquiv_symm_fromLeftInv (x : S.left_inv) :
@@ -285,10 +279,7 @@ theorem leftInvEquiv_symm_fromLeftInv (x : S.left_inv) :
 #align add_submonoid.left_neg_equiv_symm_from_left_neg AddSubmonoid.leftNegEquiv_symm_fromLeftNeg
 
 /- warning: submonoid.left_inv_equiv_mul -> Submonoid.leftInvEquiv_mul is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv_mul Submonoid.leftInvEquiv_mulₓ'. -/
 @[to_additive]
 theorem leftInvEquiv_mul (x : S.left_inv) : (S.leftInvEquiv hS x : M) * x = 1 := by simp
@@ -296,10 +287,7 @@ theorem leftInvEquiv_mul (x : S.left_inv) : (S.leftInvEquiv hS x : M) * x = 1 :=
 #align add_submonoid.left_neg_equiv_add AddSubmonoid.leftNegEquiv_add
 
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 Case conversion may be inaccurate. Consider using '#align submonoid.mul_left_inv_equiv Submonoid.mul_leftInvEquivₓ'. -/
 @[to_additive]
 theorem mul_leftInvEquiv (x : S.left_inv) : (x : M) * S.leftInvEquiv hS x = 1 := by simp
@@ -307,10 +295,7 @@ theorem mul_leftInvEquiv (x : S.left_inv) : (x : M) * S.leftInvEquiv hS x = 1 :=
 #align add_submonoid.add_left_neg_equiv AddSubmonoid.add_leftNegEquiv
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv_symm_mul Submonoid.leftInvEquiv_symm_mulₓ'. -/
 @[simp, to_additive]
 theorem leftInvEquiv_symm_mul (x : S) : ((S.leftInvEquiv hS).symm x : M) * x = 1 :=
@@ -321,10 +306,7 @@ theorem leftInvEquiv_symm_mul (x : S) : ((S.leftInvEquiv hS).symm x : M) * x = 1
 #align add_submonoid.left_neg_equiv_symm_add AddSubmonoid.leftNegEquiv_symm_add
 
 /- warning: submonoid.mul_left_inv_equiv_symm -> Submonoid.mul_leftInvEquiv_symm is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submonoid.mul_left_inv_equiv_symm Submonoid.mul_leftInvEquiv_symmₓ'. -/
 @[simp, to_additive]
 theorem mul_leftInvEquiv_symm (x : S) : (x : M) * (S.leftInvEquiv hS).symm x = 1 :=
@@ -371,10 +353,7 @@ section CommGroup
 variable [CommGroup M] (S : Submonoid M) (hS : S ≤ IsUnit.submonoid M)
 
 /- warning: submonoid.left_inv_equiv_symm_eq_inv -> Submonoid.leftInvEquiv_symm_eq_inv is a dubious translation:
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(CommGroup.toCommMonoid.{u1} M _inst_1) S hS)) x)) (Inv.inv.{u1} M (InvOneClass.toInv.{u1} M (DivInvOneMonoid.toInvOneClass.{u1} M (DivisionMonoid.toDivInvOneMonoid.{u1} M (DivisionCommMonoid.toDivisionMonoid.{u1} M (CommGroup.toDivisionCommMonoid.{u1} M _inst_1))))) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) S)) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv_symm_eq_inv Submonoid.leftInvEquiv_symm_eq_invₓ'. -/
 @[simp, to_additive]
 theorem leftInvEquiv_symm_eq_inv (x : S) : ((S.leftInvEquiv hS).symm x : M) = x⁻¹ := by

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

@@ -81,7 +81,7 @@ def leftInv : Submonoid M where
 
 /- warning: submonoid.left_inv_left_inv_le -> Submonoid.leftInv_leftInv_le is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)), LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))))) (Submonoid.leftInv.{u1} M _inst_1 (Submonoid.leftInv.{u1} M _inst_1 S)) S
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)), LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))))) (Submonoid.leftInv.{u1} M _inst_1 (Submonoid.leftInv.{u1} M _inst_1 S)) S
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)), LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Submonoid.instCompleteLatticeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)))))) (Submonoid.leftInv.{u1} M _inst_1 (Submonoid.leftInv.{u1} M _inst_1 S)) S
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_left_inv_le Submonoid.leftInv_leftInv_leₓ'. -/
@@ -108,7 +108,7 @@ theorem unit_mem_leftInv (x : Mˣ) (hx : (x : M) ∈ S) : ((x⁻¹ : _) : M) ∈
 
 /- warning: submonoid.left_inv_left_inv_eq -> Submonoid.leftInv_leftInv_eq is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)), (LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))))) S (IsUnit.submonoid.{u1} M _inst_1)) -> (Eq.{succ u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M _inst_1 (Submonoid.leftInv.{u1} M _inst_1 S)) S)
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)), (LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))))) S (IsUnit.submonoid.{u1} M _inst_1)) -> (Eq.{succ u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M _inst_1 (Submonoid.leftInv.{u1} M _inst_1 S)) S)
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)), (LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Submonoid.instCompleteLatticeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)))))) S (IsUnit.submonoid.{u1} M _inst_1)) -> (Eq.{succ u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M _inst_1 (Submonoid.leftInv.{u1} M _inst_1 S)) S)
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_left_inv_eq Submonoid.leftInv_leftInv_eqₓ'. -/
@@ -184,7 +184,7 @@ theorem fromLeftInv_mul (x : S.left_inv) : (S.fromLeftInv x : M) * x = 1 := by
 
 /- warning: submonoid.left_inv_le_is_unit -> Submonoid.leftInv_le_isUnit is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : CommMonoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))), LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))))) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S) (IsUnit.submonoid.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))
+  forall {M : Type.{u1}} [_inst_1 : CommMonoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))), LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Preorder.toHasLe.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))))) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S) (IsUnit.submonoid.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : CommMonoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))), LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Submonoid.instCompleteLatticeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))))))) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S) (IsUnit.submonoid.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_le_is_unit Submonoid.leftInv_le_isUnitₓ'. -/
@@ -233,7 +233,7 @@ include hS
 
 /- warning: submonoid.left_inv_equiv -> Submonoid.leftInvEquiv is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : CommMonoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))), (LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))))) S (IsUnit.submonoid.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) -> (MulEquiv.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S))
+  forall {M : Type.{u1}} [_inst_1 : CommMonoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))), (LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Preorder.toHasLe.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))))) S (IsUnit.submonoid.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) -> (MulEquiv.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : CommMonoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))), (LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Submonoid.instCompleteLatticeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))))))) S (IsUnit.submonoid.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) -> (MulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S))
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv Submonoid.leftInvEquivₓ'. -/
@@ -261,7 +261,7 @@ noncomputable def leftInvEquiv : S.left_inv ≃* S :=
 
 /- warning: submonoid.from_left_inv_left_inv_equiv_symm -> Submonoid.fromLeftInv_leftInvEquiv_symm is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : CommMonoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (hS : LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))))) S (IsUnit.submonoid.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (x : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M 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 but is expected to have type
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(Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M 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(Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.leftInvEquiv.{u1} M _inst_1 S hS)) x)) x
 Case conversion may be inaccurate. Consider using '#align submonoid.from_left_inv_left_inv_equiv_symm Submonoid.fromLeftInv_leftInvEquiv_symmₓ'. -/
@@ -273,7 +273,7 @@ theorem fromLeftInv_leftInvEquiv_symm (x : S) : S.fromLeftInv ((S.leftInvEquiv h
 
 /- warning: submonoid.left_inv_equiv_symm_from_left_inv -> Submonoid.leftInvEquiv_symm_fromLeftInv is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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_inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M 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_inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (MulEquivClass.toEquivLike.{u1, u1, u1} (MulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (MulEquiv.instMulEquivClassMulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)))))) (MulEquiv.symm.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.leftInvEquiv.{u1} M _inst_1 S hS)) (Submonoid.fromLeftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S x)) x
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv_symm_from_left_inv Submonoid.leftInvEquiv_symm_fromLeftInvₓ'. -/
@@ -286,7 +286,7 @@ theorem leftInvEquiv_symm_fromLeftInv (x : S.left_inv) :
 
 /- warning: submonoid.left_inv_equiv_mul -> Submonoid.leftInvEquiv_mul is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv_mul Submonoid.leftInvEquiv_mulₓ'. -/
@@ -297,7 +297,7 @@ theorem leftInvEquiv_mul (x : S.left_inv) : (S.leftInvEquiv hS x : M) * x = 1 :=
 
 /- warning: submonoid.mul_left_inv_equiv -> Submonoid.mul_leftInvEquiv is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align submonoid.mul_left_inv_equiv Submonoid.mul_leftInvEquivₓ'. -/
@@ -308,7 +308,7 @@ theorem mul_leftInvEquiv (x : S.left_inv) : (x : M) * S.leftInvEquiv hS x = 1 :=
 
 /- warning: submonoid.left_inv_equiv_symm_mul -> Submonoid.leftInvEquiv_symm_mul is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : CommMonoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (hS : LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Submonoid.instCompleteLatticeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))))))) S (IsUnit.submonoid.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)), Eq.{succ u1} M (HMul.hMul.{u1, u1, u1} M M M (instHMul.{u1} M (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (FunLike.coe.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (MulEquivClass.toEquivLike.{u1, u1, u1} (MulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (MulEquiv.instMulEquivClassMulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)))))) (MulEquiv.symm.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.leftInvEquiv.{u1} M _inst_1 S hS)) x)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) S)) x)) (OfNat.ofNat.{u1} M 1 (One.toOfNat1.{u1} M (Monoid.toOne.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))))
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv_symm_mul Submonoid.leftInvEquiv_symm_mulₓ'. -/
@@ -322,7 +322,7 @@ theorem leftInvEquiv_symm_mul (x : S) : ((S.leftInvEquiv hS).symm x : M) * x = 1
 
 /- warning: submonoid.mul_left_inv_equiv_symm -> Submonoid.mul_leftInvEquiv_symm is a dubious translation:
 lean 3 declaration is
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(CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (MulEquivClass.toEquivLike.{u1, u1, u1} (MulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (MulEquiv.instMulEquivClassMulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)))))) (MulEquiv.symm.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)))) x S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1) S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1)) S) (Submonoid.leftInvEquiv.{u1} M _inst_1 S hS)) x))) (OfNat.ofNat.{u1} M 1 (One.toOfNat1.{u1} M (Monoid.toOne.{u1} M (CommMonoid.toMonoid.{u1} M _inst_1))))
 Case conversion may be inaccurate. Consider using '#align submonoid.mul_left_inv_equiv_symm Submonoid.mul_leftInvEquiv_symmₓ'. -/
@@ -372,7 +372,7 @@ variable [CommGroup M] (S : Submonoid M) (hS : S ≤ IsUnit.submonoid M)
 
 /- warning: submonoid.left_inv_equiv_symm_eq_inv -> Submonoid.leftInvEquiv_symm_eq_inv is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : CommGroup.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) (hS : LE.le.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) (Preorder.toLE.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) (Submonoid.instCompleteLatticeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))))))) S (IsUnit.submonoid.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1)))))) x S)), Eq.{succ u1} M (Subtype.val.{succ 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_inst_1))))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} 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Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))))) x S)) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)) S))) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))))) x S)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) M (Submonoid.instSetLikeSubmonoid.{u1} M 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(CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)) S))) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))) S) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)) S)))))) (MulEquiv.symm.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))))) x (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)) S))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))))) x S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))) (Submonoid.leftInv.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1)) S)) (Submonoid.mul.{u1} M (Monoid.toMulOneClass.{u1} M (CommMonoid.toMonoid.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1))) S) (Submonoid.leftInvEquiv.{u1} M (CommGroup.toCommMonoid.{u1} M _inst_1) S hS)) x)) (Inv.inv.{u1} M (InvOneClass.toInv.{u1} M (DivInvOneMonoid.toInvOneClass.{u1} M (DivisionMonoid.toDivInvOneMonoid.{u1} M (DivisionCommMonoid.toDivisionMonoid.{u1} M (CommGroup.toDivisionCommMonoid.{u1} M _inst_1))))) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M (DivInvMonoid.toMonoid.{u1} M (Group.toDivInvMonoid.{u1} M (CommGroup.toGroup.{u1} M _inst_1))))) S)) x))
 Case conversion may be inaccurate. Consider using '#align submonoid.left_inv_equiv_symm_eq_inv Submonoid.leftInvEquiv_symm_eq_invₓ'. -/

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

@@ -53,7 +53,7 @@ noncomputable instance [CommMonoid M] : CommGroup (IsUnit.submonoid M) :=
 lean 3 declaration is
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(Monoid.toMulOneClass.{u1} M _inst_1))) (IsUnit.submonoid.{u1} M _inst_1)) M (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) (IsUnit.submonoid.{u1} M _inst_1)) M (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) (IsUnit.submonoid.{u1} M _inst_1)) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1)))))) (Inv.inv.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) (IsUnit.submonoid.{u1} M _inst_1)) (DivInvMonoid.toHasInv.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) (IsUnit.submonoid.{u1} M _inst_1)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) (IsUnit.submonoid.{u1} M _inst_1)) (Submonoid.IsUnit.Submonoid.group.{u1} M _inst_1))) x)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} M _inst_1) M (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} M _inst_1) M (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} M _inst_1) M (coeBase.{succ u1, succ u1} (Units.{u1} M _inst_1) M (Units.hasCoe.{u1} M _inst_1)))) (Inv.inv.{u1} (Units.{u1} M _inst_1) (Units.hasInv.{u1} M _inst_1) (IsUnit.unit.{u1} M _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) M (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) M (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) M (coeBase.{succ u1, succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) M (coeSubtype.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1)))))) x) (Subtype.prop.{succ u1} M (fun (x : M) => Membership.Mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1)) x))))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))), Eq.{succ u1} M (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (IsUnit.submonoid.{u1} M _inst_1))) (Inv.inv.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) (InvOneClass.toInv.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) (DivInvOneMonoid.toInvOneClass.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) (DivisionMonoid.toDivInvOneMonoid.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) (Group.toDivisionMonoid.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) (Submonoid.instGroupSubtypeMemSubmonoidToMulOneClassInstMembershipInstSetLikeSubmonoidSubmonoid.{u1} M _inst_1))))) x)) (Units.val.{u1} M _inst_1 (Inv.inv.{u1} (Units.{u1} M _inst_1) (Units.instInvUnits.{u1} M _inst_1) (IsUnit.unit.{u1} M _inst_1 (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1)) x) (Subtype.prop.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1)) x))))
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))), Eq.{succ u1} M (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (IsUnit.submonoid.{u1} M _inst_1))) (Inv.inv.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) (InvOneClass.toInv.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) (DivInvOneMonoid.toInvOneClass.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) (DivisionMonoid.toDivInvOneMonoid.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) (Group.toDivisionMonoid.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1))) (Submonoid.instGroupSubtypeMemSubmonoidToMulOneClassInstMembershipInstSetLikeSubmonoidSubmonoid.{u1} M _inst_1))))) x)) (Units.val.{u1} M _inst_1 (Inv.inv.{u1} (Units.{u1} M _inst_1) (Units.instInv.{u1} M _inst_1) (IsUnit.unit.{u1} M _inst_1 (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1)) x) (Subtype.prop.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) x (IsUnit.submonoid.{u1} M _inst_1)) x))))
 Case conversion may be inaccurate. Consider using '#align submonoid.is_unit.submonoid.coe_inv Submonoid.IsUnit.Submonoid.coe_invₓ'. -/
 @[to_additive]
 theorem IsUnit.Submonoid.coe_inv [Monoid M] (x : IsUnit.submonoid M) :
@@ -98,7 +98,7 @@ theorem leftInv_leftInv_le : S.left_inv.left_inv ≤ S :=
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (x : Units.{u1} M _inst_1), (Membership.Mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} M _inst_1) M (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} M _inst_1) M (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} M _inst_1) M (coeBase.{succ u1, succ u1} (Units.{u1} M _inst_1) M (Units.hasCoe.{u1} M _inst_1)))) x) S) -> (Membership.Mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.setLike.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} M _inst_1) M (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} M _inst_1) M (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} M _inst_1) M (coeBase.{succ u1, succ u1} (Units.{u1} M _inst_1) M (Units.hasCoe.{u1} M _inst_1)))) (Inv.inv.{u1} (Units.{u1} M _inst_1) (Units.hasInv.{u1} M _inst_1) x)) (Submonoid.leftInv.{u1} M _inst_1 S))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (x : Units.{u1} M _inst_1), (Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) (Units.val.{u1} M _inst_1 x) S) -> (Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) (Units.val.{u1} M _inst_1 (Inv.inv.{u1} (Units.{u1} M _inst_1) (Units.instInvUnits.{u1} M _inst_1) x)) (Submonoid.leftInv.{u1} M _inst_1 S))
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (S : Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (x : Units.{u1} M _inst_1), (Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) (Units.val.{u1} M _inst_1 x) S) -> (Membership.mem.{u1, u1} M (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) M (Submonoid.instSetLikeSubmonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1))) (Units.val.{u1} M _inst_1 (Inv.inv.{u1} (Units.{u1} M _inst_1) (Units.instInv.{u1} M _inst_1) x)) (Submonoid.leftInv.{u1} M _inst_1 S))
 Case conversion may be inaccurate. Consider using '#align submonoid.unit_mem_left_inv Submonoid.unit_mem_leftInvₓ'. -/
 @[to_additive]
 theorem unit_mem_leftInv (x : Mˣ) (hx : (x : M) ∈ S) : ((x⁻¹ : _) : M) ∈ S.left_inv :=

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

@@ -254,7 +254,7 @@ noncomputable def leftInvEquiv : S.left_inv ≃* S :=
       dsimp
       ext
       rw [from_left_inv_eq_iff]
-      convert (hS x.prop).some.inv_val
+      convert(hS x.prop).some.inv_val
       exact (hS x.prop).choose_spec.symm }
 #align submonoid.left_inv_equiv Submonoid.leftInvEquiv
 #align add_submonoid.left_neg_equiv AddSubmonoid.leftNegEquiv

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

@@ -17,10 +17,10 @@ since the inverses are unique. When `N ≤ IsUnit.Submonoid M`, this is precisel
 the pointwise inverse of `N`, and we may define `leftInvEquiv : S.leftInv ≃* S`.
 
 For the pointwise inverse of submonoids of groups, please refer to
-`GroupTheory.Submonoid.Pointwise`.
+`Mathlib.GroupTheory.Submonoid.Pointwise`.
 
-`N.leftInv` is distinct from `N.units`, which is the subgroup of `Mˣ` containing all units that
-are in `N`. See the implementation notes of `GroupTheory/Submonoid/Units` for more details on
+`N.leftInv` is distinct from `N.units`, which is the subgroup of `Mˣ` containing all units that are
+in `N`. See the implementation notes of `Mathlib.GroupTheory.Submonoid.Units` for more details on
 related constructions.
 
 ## TODO

The subgroup of the type of units added in this PR is something we have in other guises, which are somewhat less useful for some forms of working. The intention is to provide different options depending on how you want to think about the group of units in a submonoid.

Co-authored-by: lines <34025592+linesthatinterlace@users.noreply.github.com> Co-authored-by: Johan Commelin <johan@commelin.net>

@@ -19,6 +19,10 @@ the pointwise inverse of `N`, and we may define `leftInvEquiv : S.leftInv ≃* S
 For the pointwise inverse of submonoids of groups, please refer to
 `GroupTheory.Submonoid.Pointwise`.
 
+`N.leftInv` is distinct from `N.units`, which is the subgroup of `Mˣ` containing all units that
+are in `N`. See the implementation notes of `GroupTheory/Submonoid/Units` for more details on
+related constructions.
+
 ## TODO
 
 Define the submonoid of right inverses and two-sided inverses.

@@ -152,9 +152,6 @@ noncomputable def fromCommLeftInv : S.leftInv →* S where
 
 variable (hS : S ≤ IsUnit.submonoid M)
 
--- Porting note: commented out next line
- -- include hS
-
 /-- The submonoid of pointwise inverse of `S` is `MulEquiv` to `S`. -/
 @[to_additive (attr := simps apply) "The additive submonoid of pointwise additive inverse of `S` is
 `AddEquiv` to `S`."]

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

This has nice performance benefits.

@@ -27,7 +27,7 @@ See the comments of #10679 for a possible implementation.
 -/
 
 
-variable {M : Type _}
+variable {M : Type*}
 
 namespace Submonoid
 

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module group_theory.submonoid.inverses
-! leanprover-community/mathlib commit 59694bd07f0a39c5beccba34bd9f413a160782bf
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.Submonoid.Pointwise
 
+#align_import group_theory.submonoid.inverses from "leanprover-community/mathlib"@"59694bd07f0a39c5beccba34bd9f413a160782bf"
+
 /-!
 
 # Submonoid of inverses

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -169,7 +169,7 @@ noncomputable def leftInvEquiv : S.leftInv ≃* S :=
     left_inv := fun x ↦
       Subtype.eq <| by
         dsimp only; generalize_proofs h; rw [← h.choose.mul_left_inj]
-        conv => rhs ; rw [h.choose_spec]
+        conv => rhs; rw [h.choose_spec]
         exact h.choose.inv_val.trans (S.mul_fromLeftInv x).symm
     right_inv := fun x ↦ by
       dsimp only [fromCommLeftInv]

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

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

@@ -86,8 +86,7 @@ theorem unit_mem_leftInv (x : Mˣ) (hx : (x : M) ∈ S) : ((x⁻¹ : _) : M) ∈
 theorem leftInv_leftInv_eq (hS : S ≤ IsUnit.submonoid M) : S.leftInv.leftInv = S := by
   refine' le_antisymm S.leftInv_leftInv_le _
   intro x hx
-  have : x = ((hS hx).unit⁻¹⁻¹ : Mˣ) :=
-    by
+  have : x = ((hS hx).unit⁻¹⁻¹ : Mˣ) := by
     rw [inv_inv (hS hx).unit]
     rfl
   rw [this]

@@ -129,23 +129,22 @@ theorem fromLeftInv_mul (x : S.leftInv) : (S.fromLeftInv x : M) * x = 1 := by
 #align add_submonoid.from_left_neg_add AddSubmonoid.fromLeftNeg_add
 
 @[to_additive]
-theorem leftInv_le_is_unit : S.leftInv ≤ IsUnit.submonoid M := fun x ⟨y, hx⟩ ↦
+theorem leftInv_le_isUnit : S.leftInv ≤ IsUnit.submonoid M := fun x ⟨y, hx⟩ ↦
   ⟨⟨x, y, hx, mul_comm x y ▸ hx⟩, rfl⟩
-#align submonoid.left_inv_le_is_unit Submonoid.leftInv_le_is_unit
-#align add_submonoid.left_neg_le_is_add_unit AddSubmonoid.leftNeg_le_is_addUnit
+#align submonoid.left_inv_le_is_unit Submonoid.leftInv_le_isUnit
+#align add_submonoid.left_neg_le_is_add_unit AddSubmonoid.leftNeg_le_isAddUnit
 
 @[to_additive]
 theorem fromLeftInv_eq_iff (a : S.leftInv) (b : M) : (S.fromLeftInv a : M) = b ↔ (a : M) * b = 1 :=
-  by rw [← IsUnit.mul_right_inj (leftInv_le_is_unit _ a.prop), S.mul_fromLeftInv, eq_comm]
+  by rw [← IsUnit.mul_right_inj (leftInv_le_isUnit _ a.prop), S.mul_fromLeftInv, eq_comm]
 #align submonoid.from_left_inv_eq_iff Submonoid.fromLeftInv_eq_iff
 #align add_submonoid.from_left_neg_eq_iff AddSubmonoid.fromLeftNeg_eq_iff
 
 /-- The `MonoidHom` from `S.leftInv` to `S` sending an element to its right inverse in `S`. -/
 @[to_additive (attr := simps)
-    "The `add_monoid_hom` from `S.leftNeg` to `S` sending an element to its
+    "The `AddMonoidHom` from `S.leftNeg` to `S` sending an element to its
     right additive inverse in `S`."]
-noncomputable def fromCommLeftInv : S.leftInv →* S
-    where
+noncomputable def fromCommLeftInv : S.leftInv →* S where
   toFun := S.fromLeftInv
   map_one' := S.fromLeftInv_one
   map_mul' x y :=
@@ -198,7 +197,6 @@ theorem leftInvEquiv_symm_fromLeftInv (x : S.leftInv) :
 @[to_additive]
 theorem leftInvEquiv_mul (x : S.leftInv) : (S.leftInvEquiv hS x : M) * x = 1 := by
   simpa only [leftInvEquiv_apply, fromCommLeftInv] using fromLeftInv_mul S x
-
 #align submonoid.left_inv_equiv_mul Submonoid.leftInvEquiv_mul
 #align add_submonoid.left_neg_equiv_add AddSubmonoid.leftNegEquiv_add
 

@@ -36,11 +36,10 @@ namespace Submonoid
 
 @[to_additive]
 noncomputable instance [Monoid M] : Group (IsUnit.submonoid M) :=
-  { show Monoid (IsUnit.submonoid M) by
-      infer_instance with
-    inv := fun x ↦ ⟨_, x.prop.unit⁻¹.isUnit⟩
-    mul_left_inv := fun x ↦ by
-      exact Subtype.mk_eq_mk.2 ((Units.val_mul _ _).trans x.prop.unit.inv_val) }
+  { inferInstanceAs (Monoid (IsUnit.submonoid M)) with
+    inv := fun x ↦ ⟨x.prop.unit⁻¹.val, x.prop.unit⁻¹.isUnit⟩
+    mul_left_inv := fun x ↦
+      Subtype.ext ((Units.val_mul x.prop.unit⁻¹ _).trans x.prop.unit.inv_val) }
 
 @[to_additive]
 noncomputable instance [CommMonoid M] : CommGroup (IsUnit.submonoid M) :=

Drop

• by delta mydef; infer_instance. This generates id _ in the proof.

• show _, by infer_instance. This generates let in let; not sure if it's bad for defeq but a reducible inferInstanceAs should not be worse.

@@ -44,8 +44,8 @@ noncomputable instance [Monoid M] : Group (IsUnit.submonoid M) :=
 
 @[to_additive]
 noncomputable instance [CommMonoid M] : CommGroup (IsUnit.submonoid M) :=
-  { show Group (IsUnit.submonoid M) by infer_instance
-      with mul_comm := fun a b ↦ by convert mul_comm a b }
+  { inferInstanceAs (Group (IsUnit.submonoid M)) with
+    mul_comm := fun a b ↦ by convert mul_comm a b }
 
 @[to_additive]
 theorem IsUnit.Submonoid.coe_inv [Monoid M] (x : IsUnit.submonoid M) :

Co-authored-by: Johan Commelin <johan@commelin.net>