group_theory.subgroup.pointwise | Mathlib porting status

(last sync)

feat(algebra/group_power/lemmas): Induction principle for powers (#18668)

A property holds for all powers of g if it is holds for 1 and is preserved under multiplication and division by g.

Also rename subgroup.zpowers_subset/add_subgroup.zmultiples_subset to subgroup.zpowers_le_of_mem/add_subgroup.zmultiples_le_of_mem because there is no ⊆ in the statement.

The motivation is the Cauchy-Davenport theorem: https://github.com/leanprover-community/mathlib/blob/321b67021163ac504c6cfa35d5678a47b357869d/src/combinatorics/additive/cauchy_davenport.lean#L176-L181

Diff

@@ -55,15 +55,19 @@ begin
   { simp only [true_and, coe_to_submonoid, union_subset_iff, subset_closure, inv_subset_closure] }
 end
 
-@[to_additive] lemma closure_induction_left {p : G → Prop} {x : G}
-  (h : x ∈ closure s) (H1 : p 1) (Hmul : ∀ (x ∈ s) y, p y → p (x * y))
-  (Hinv : ∀ (x ∈ s) y, p y → p (x⁻¹ * y)) : p x :=
+/-- For subgroups generated by a single element, see the simpler `zpow_induction_left`. -/
+@[to_additive "For additive subgroups generated by a single element, see the simpler
+`zsmul_induction_left`."]
+lemma closure_induction_left {p : G → Prop} {x : G} (h : x ∈ closure s) (H1 : p 1)
+  (Hmul : ∀ (x ∈ s) y, p y → p (x * y)) (Hinv : ∀ (x ∈ s) y, p y → p (x⁻¹ * y)) : p x :=
 let key := (closure_to_submonoid s).le in submonoid.closure_induction_left (key h) H1 $
   λ x hx, hx.elim (Hmul x) $ λ hx y hy, (congr_arg _ $ inv_inv x).mp $ Hinv x⁻¹ hx y hy
 
-@[to_additive] lemma closure_induction_right {p : G → Prop} {x : G}
-  (h : x ∈ closure s) (H1 : p 1) (Hmul : ∀ x (y ∈ s), p x → p (x * y))
-  (Hinv : ∀ x (y ∈ s), p x → p (x * y⁻¹)) : p x :=
+/-- For subgroups generated by a single element, see the simpler `zpow_induction_right`. -/
+@[to_additive "For additive subgroups generated by a single element, see the simpler
+`zsmul_induction_right`."]
+lemma closure_induction_right {p : G → Prop} {x : G} (h : x ∈ closure s) (H1 : p 1)
+  (Hmul : ∀ x (y ∈ s), p x → p (x * y)) (Hinv : ∀ x (y ∈ s), p x → p (x * y⁻¹)) : p x :=
 let key := (closure_to_submonoid s).le in submonoid.closure_induction_right (key h) H1 $
   λ x y hy, hy.elim (Hmul x y) $ λ hy hx, (congr_arg _ $ inv_inv y).mp $ Hinv x y⁻¹ hy hx

refactor(topology/algebra/field): drop topological_space_units (#18536)

See Zulip chat

Also generalize TC assumptions in inv_mem_iff.

Diff

@@ -30,11 +30,14 @@ Where possible, try to keep them in sync.
 open set
 open_locale pointwise
 
-variables {α G A S : Type*} [group G] [add_group A] {s : set G}
+variables {α G A S : Type*}
 
 @[simp, to_additive]
-lemma inv_coe_set [set_like S G] [subgroup_class S G] {H : S} : (H : set G)⁻¹ = H :=
-by { ext, simp }
+lemma inv_coe_set [has_involutive_inv G] [set_like S G] [inv_mem_class S G] {H : S} :
+  (H : set G)⁻¹ = H :=
+set.ext $ λ _, inv_mem_iff
+
+variables [group G] [add_group A] {s : set G}
 
 namespace subgroup

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -129,7 +129,7 @@ then it holds for all elements of the supremum of `S`. -/
 theorem iSup_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
     (hp : ∀ (i), ∀ x ∈ S i, C x) (h1 : C 1) (hmul : ∀ x y, C x → C y → C (x * y)) : C x :=
   by
-  rw [supr_eq_closure] at hx 
+  rw [supr_eq_closure] at hx
   refine' closure_induction'' hx (fun x hx => _) (fun x hx => _) h1 hmul
   · obtain ⟨i, hi⟩ := set.mem_Union.mp hx
     exact hp _ _ hi
@@ -267,7 +267,7 @@ theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
 #print Subgroup.sup_normal /-
 instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔ K).Normal
     where conj_mem n hmem g := by
-    change n ∈ ↑(H ⊔ K) at hmem 
+    change n ∈ ↑(H ⊔ K) at hmem
     change g * n * g⁻¹ ∈ ↑(H ⊔ K)
     rw [normal_mul, Set.mem_mul] at *
     rcases hmem with ⟨h, k, hh, hk, rfl⟩
@@ -481,13 +481,13 @@ theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (
   constructor
   · intro h
     have := hH.conj_mem (g⁻¹ • x) _ (ConjAct.ofConjAct g)
-    rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem] at h 
+    rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem] at h
     dsimp at *
     rw [ConjAct.smul_def] at *
     simp only [ConjAct.ofConjAct_inv, ConjAct.ofConjAct_toConjAct, inv_inv] at *
     convert this
     simp only [← mul_assoc, mul_right_inv, one_mul, mul_inv_cancel_right]
-    rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem] at h 
+    rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem] at h
     exact h
   · intro h
     rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem, ConjAct.smul_def]

bump to nightly-2023-10-05-06

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

e028a08c

Diff

@@ -168,15 +168,15 @@ theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure
 #align add_subgroup.closure_add_le AddSubgroup.closure_add_le
 -/
 
-#print Subgroup.sup_eq_closure /-
+#print Subgroup.sup_eq_closure_mul /-
 @[to_additive]
-theorem sup_eq_closure (H K : Subgroup G) : H ⊔ K = closure (H * K) :=
+theorem sup_eq_closure_mul (H K : Subgroup G) : H ⊔ K = closure (H * K) :=
   le_antisymm
     (sup_le (fun h hh => subset_closure ⟨h, 1, hh, K.one_mem, mul_one h⟩) fun k hk =>
       subset_closure ⟨1, k, H.one_mem, hk, one_mul k⟩)
     (by conv_rhs => rw [← closure_eq H, ← closure_eq K] <;> apply closure_mul_le)
-#align subgroup.sup_eq_closure Subgroup.sup_eq_closure
-#align add_subgroup.sup_eq_closure AddSubgroup.sup_eq_closure
+#align subgroup.sup_eq_closure Subgroup.sup_eq_closure_mul
+#align add_subgroup.sup_eq_closure AddSubgroup.sup_eq_closure_add
 -/
 
 @[to_additive]
@@ -198,7 +198,7 @@ private def mul_normal_aux (H N : Subgroup G) [hN : N.Normal] : Subgroup G
 theorem mul_normal (H N : Subgroup G) [N.Normal] : (↑(H ⊔ N) : Set G) = H * N :=
   Set.Subset.antisymm
     (show H ⊔ N ≤ mulNormalAux H N by rw [sup_eq_closure]; apply sInf_le _; dsimp; rfl)
-    ((sup_eq_closure H N).symm ▸ subset_closure)
+    ((sup_eq_closure_mul H N).symm ▸ subset_closure)
 #align subgroup.mul_normal Subgroup.mul_normal
 #align add_subgroup.add_normal AddSubgroup.add_normal
 -/
@@ -222,7 +222,7 @@ private def normal_mul_aux (N H : Subgroup G) [hN : N.Normal] : Subgroup G
 theorem normal_mul (N H : Subgroup G) [N.Normal] : (↑(N ⊔ H) : Set G) = N * H :=
   Set.Subset.antisymm
     (show N ⊔ H ≤ normalMulAux N H by rw [sup_eq_closure]; apply sInf_le _; dsimp; rfl)
-    ((sup_eq_closure N H).symm ▸ subset_closure)
+    ((sup_eq_closure_mul N H).symm ▸ subset_closure)
 #align subgroup.normal_mul Subgroup.normal_mul
 #align add_subgroup.normal_add AddSubgroup.normal_add
 -/

bump to nightly-2023-09-30-06

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

0742bc05

Diff

@@ -278,7 +278,7 @@ instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔
 
 #print Subgroup.smul_opposite_image_mul_preimage /-
 @[to_additive]
-theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.opposite) (s : Set G) :
+theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.opEquiv) (s : Set G) :
     (fun y => h • y) '' (Mul.mul g ⁻¹' s) = Mul.mul g ⁻¹' ((fun y => h • y) '' s) := by ext x;
   cases h; simp [(· • ·), mul_assoc]
 #align subgroup.smul_opposite_image_mul_preimage Subgroup.smul_opposite_image_mul_preimage

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.GroupTheory.Subgroup.MulOpposite
-import Mathbin.GroupTheory.Submonoid.Pointwise
-import Mathbin.GroupTheory.GroupAction.ConjAct
+import GroupTheory.Subgroup.MulOpposite
+import GroupTheory.Submonoid.Pointwise
+import GroupTheory.GroupAction.ConjAct
 
 #align_import group_theory.subgroup.pointwise from "leanprover-community/mathlib"@"e655e4ea5c6d02854696f97494997ba4c31be802"

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -144,7 +144,7 @@ theorem iSup_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x
 @[elab_as_elim, to_additive "A dependent version of `add_subgroup.supr_induction`. "]
 theorem iSup_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
     (hp : ∀ (i), ∀ x ∈ S i, C x (mem_iSup_of_mem i ‹_›)) (h1 : C 1 (one_mem _))
-    (hmul : ∀ x y hx hy, C x hx → C y hy → C (x * y) (mul_mem ‹_› ‹_›)) {x : G}
+    (hmul : ∀ x y hx hy, C x hx → C y hy → C (x * y) (hMul_mem ‹_› ‹_›)) {x : G}
     (hx : x ∈ ⨆ i, S i) : C x hx :=
   by
   refine' Exists.elim _ fun (hx : x ∈ ⨆ i, S i) (hc : C x hx) => hc
@@ -162,7 +162,7 @@ theorem iSup_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈
 theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure T :=
   sInf_le fun x ⟨s, t, hs, ht, hx⟩ =>
     hx ▸
-      (closure S ⊔ closure T).mul_mem (SetLike.le_def.mp le_sup_left <| subset_closure hs)
+      (closure S ⊔ closure T).hMul_mem (SetLike.le_def.mp le_sup_left <| subset_closure hs)
         (SetLike.le_def.mp le_sup_right <| subset_closure ht)
 #align subgroup.closure_mul_le Subgroup.closure_mul_le
 #align add_subgroup.closure_add_le AddSubgroup.closure_add_le
@@ -184,9 +184,9 @@ private def mul_normal_aux (H N : Subgroup G) [hN : N.Normal] : Subgroup G
     where
   carrier := (H : Set G) * N
   one_mem' := ⟨1, 1, H.one_mem, N.one_mem, by rw [mul_one]⟩
-  mul_mem' := fun a b ⟨h, n, hh, hn, ha⟩ ⟨h', n', hh', hn', hb⟩ =>
-    ⟨h * h', h'⁻¹ * n * h' * n', H.mul_mem hh hh',
-      N.mul_mem (by simpa using hN.conj_mem _ hn h'⁻¹) hn', by simp [← ha, ← hb, mul_assoc]⟩
+  hMul_mem' := fun a b ⟨h, n, hh, hn, ha⟩ ⟨h', n', hh', hn', hb⟩ =>
+    ⟨h * h', h'⁻¹ * n * h' * n', H.hMul_mem hh hh',
+      N.hMul_mem (by simpa using hN.conj_mem _ hn h'⁻¹) hn', by simp [← ha, ← hb, mul_assoc]⟩
   inv_mem' := fun x ⟨h, n, hh, hn, hx⟩ =>
     ⟨h⁻¹, h * n⁻¹ * h⁻¹, H.inv_mem hh, hN.conj_mem _ (N.inv_mem hn) h, by
       rw [mul_assoc h, inv_mul_cancel_left, ← hx, mul_inv_rev]⟩
@@ -208,8 +208,8 @@ private def normal_mul_aux (N H : Subgroup G) [hN : N.Normal] : Subgroup G
     where
   carrier := (N : Set G) * H
   one_mem' := ⟨1, 1, N.one_mem, H.one_mem, by rw [mul_one]⟩
-  mul_mem' := fun a b ⟨n, h, hn, hh, ha⟩ ⟨n', h', hn', hh', hb⟩ =>
-    ⟨n * (h * n' * h⁻¹), h * h', N.mul_mem hn (hN.conj_mem _ hn' _), H.mul_mem hh hh', by
+  hMul_mem' := fun a b ⟨n, h, hn, hh, ha⟩ ⟨n', h', hn', hh', hb⟩ =>
+    ⟨n * (h * n' * h⁻¹), h * h', N.hMul_mem hn (hN.conj_mem _ hn' _), H.hMul_mem hh hh', by
       simp [← ha, ← hb, mul_assoc]⟩
   inv_mem' := fun x ⟨n, h, hn, hh, hx⟩ =>
     ⟨h⁻¹ * n⁻¹ * h, h⁻¹, by simpa using hN.conj_mem _ (N.inv_mem hn) h⁻¹, H.inv_mem hh, by
@@ -300,7 +300,7 @@ protected def pointwiseMulAction : MulAction α (Subgroup G)
     where
   smul a S := S.map (MulDistribMulAction.toMonoidEnd _ _ a)
   one_smul S := (congr_arg (fun f => S.map f) (MonoidHom.map_one _)).trans S.map_id
-  mul_smul a₁ a₂ S :=
+  hMul_smul a₁ a₂ S :=
     (congr_arg (fun f => S.map f) (MonoidHom.map_mul _ _ _)).trans (S.map_map _ _).symm
 #align subgroup.pointwise_mul_action Subgroup.pointwiseMulAction
 -/
@@ -571,7 +571,7 @@ protected def pointwiseMulAction : MulAction α (AddSubgroup A)
     where
   smul a S := S.map (DistribMulAction.toAddMonoidEnd _ _ a)
   one_smul S := (congr_arg (fun f => S.map f) (MonoidHom.map_one _)).trans S.map_id
-  mul_smul a₁ a₂ S :=
+  hMul_smul a₁ a₂ S :=
     (congr_arg (fun f => S.map f) (MonoidHom.map_mul _ _ _)).trans (S.map_map _ _).symm
 #align add_subgroup.pointwise_mul_action AddSubgroup.pointwiseMulAction
 -/

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module group_theory.subgroup.pointwise
-! leanprover-community/mathlib commit e655e4ea5c6d02854696f97494997ba4c31be802
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.Subgroup.MulOpposite
 import Mathbin.GroupTheory.Submonoid.Pointwise
 import Mathbin.GroupTheory.GroupAction.ConjAct
 
+#align_import group_theory.subgroup.pointwise from "leanprover-community/mathlib"@"e655e4ea5c6d02854696f97494997ba4c31be802"
+
 /-! # Pointwise instances on `subgroup` and `add_subgroup`s
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -39,22 +39,27 @@ open scoped Pointwise
 
 variable {α G A S : Type _}
 
+#print inv_coe_set /-
 @[simp, to_additive]
 theorem inv_coe_set [InvolutiveInv G] [SetLike S G] [InvMemClass S G] {H : S} : (H : Set G)⁻¹ = H :=
   Set.ext fun _ => inv_mem_iff
 #align inv_coe_set inv_coe_set
 #align neg_coe_set neg_coe_set
+-/
 
 variable [Group G] [AddGroup A] {s : Set G}
 
 namespace Subgroup
 
+#print Subgroup.inv_subset_closure /-
 @[simp, to_additive]
 theorem inv_subset_closure (S : Set G) : S⁻¹ ⊆ closure S := fun s hs => by
   rw [SetLike.mem_coe, ← Subgroup.inv_mem_iff]; exact subset_closure (mem_inv.mp hs)
 #align subgroup.inv_subset_closure Subgroup.inv_subset_closure
 #align add_subgroup.neg_subset_closure AddSubgroup.neg_subset_closure
+-/
 
+#print Subgroup.closure_toSubmonoid /-
 @[to_additive]
 theorem closure_toSubmonoid (S : Set G) : (closure S).toSubmonoid = Submonoid.closure (S ∪ S⁻¹) :=
   by
@@ -67,7 +72,9 @@ theorem closure_toSubmonoid (S : Set G) : (closure S).toSubmonoid = Submonoid.cl
   · simp only [true_and_iff, coe_to_submonoid, union_subset_iff, subset_closure, inv_subset_closure]
 #align subgroup.closure_to_submonoid Subgroup.closure_toSubmonoid
 #align add_subgroup.closure_to_add_submonoid AddSubgroup.closure_toAddSubmonoid
+-/
 
+#print Subgroup.closure_induction_left /-
 /-- For subgroups generated by a single element, see the simpler `zpow_induction_left`. -/
 @[to_additive
       "For additive subgroups generated by a single element, see the simpler\n`zsmul_induction_left`."]
@@ -78,7 +85,9 @@ theorem closure_induction_left {p : G → Prop} {x : G} (h : x ∈ closure s) (H
     hx.elim (Hmul x) fun hx y hy => (congr_arg _ <| inv_inv x).mp <| Hinv x⁻¹ hx y hy
 #align subgroup.closure_induction_left Subgroup.closure_induction_left
 #align add_subgroup.closure_induction_left AddSubgroup.closure_induction_left
+-/
 
+#print Subgroup.closure_induction_right /-
 /-- For subgroups generated by a single element, see the simpler `zpow_induction_right`. -/
 @[to_additive
       "For additive subgroups generated by a single element, see the simpler\n`zsmul_induction_right`."]
@@ -89,13 +98,17 @@ theorem closure_induction_right {p : G → Prop} {x : G} (h : x ∈ closure s) (
     hy.elim (Hmul x y) fun hy hx => (congr_arg _ <| inv_inv y).mp <| Hinv x y⁻¹ hy hx
 #align subgroup.closure_induction_right Subgroup.closure_induction_right
 #align add_subgroup.closure_induction_right AddSubgroup.closure_induction_right
+-/
 
+#print Subgroup.closure_inv /-
 @[simp, to_additive]
 theorem closure_inv (s : Set G) : closure s⁻¹ = closure s := by
   simp only [← to_submonoid_eq, closure_to_submonoid, inv_inv, union_comm]
 #align subgroup.closure_inv Subgroup.closure_inv
 #align add_subgroup.closure_neg AddSubgroup.closure_neg
+-/
 
+#print Subgroup.closure_induction'' /-
 /-- An induction principle for closure membership. If `p` holds for `1` and all elements of
 `k` and their inverse, and is preserved under multiplication, then `p` holds for all elements of
 the closure of `k`. -/
@@ -107,7 +120,9 @@ theorem closure_induction'' {p : G → Prop} {x} (h : x ∈ closure s) (Hk : ∀
     Hmul x⁻¹ y <| Hk_inv x hx
 #align subgroup.closure_induction'' Subgroup.closure_induction''
 #align add_subgroup.closure_induction'' AddSubgroup.closure_induction''
+-/
 
+#print Subgroup.iSup_induction /-
 /-- An induction principle for elements of `⨆ i, S i`.
 If `C` holds for `1` and all elements of `S i` for all `i`, and is preserved under multiplication,
 then it holds for all elements of the supremum of `S`. -/
@@ -125,7 +140,9 @@ theorem iSup_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x
     exact hp _ _ (inv_mem hi)
 #align subgroup.supr_induction Subgroup.iSup_induction
 #align add_subgroup.supr_induction AddSubgroup.iSup_induction
+-/
 
+#print Subgroup.iSup_induction' /-
 /-- A dependent version of `subgroup.supr_induction`. -/
 @[elab_as_elim, to_additive "A dependent version of `add_subgroup.supr_induction`. "]
 theorem iSup_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
@@ -141,7 +158,9 @@ theorem iSup_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈
     refine' ⟨_, hmul _ _ _ _ Cx Cy⟩
 #align subgroup.supr_induction' Subgroup.iSup_induction'
 #align add_subgroup.supr_induction' AddSubgroup.iSup_induction'
+-/
 
+#print Subgroup.closure_mul_le /-
 @[to_additive]
 theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure T :=
   sInf_le fun x ⟨s, t, hs, ht, hx⟩ =>
@@ -150,7 +169,9 @@ theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure
         (SetLike.le_def.mp le_sup_right <| subset_closure ht)
 #align subgroup.closure_mul_le Subgroup.closure_mul_le
 #align add_subgroup.closure_add_le AddSubgroup.closure_add_le
+-/
 
+#print Subgroup.sup_eq_closure /-
 @[to_additive]
 theorem sup_eq_closure (H K : Subgroup G) : H ⊔ K = closure (H * K) :=
   le_antisymm
@@ -159,6 +180,7 @@ theorem sup_eq_closure (H K : Subgroup G) : H ⊔ K = closure (H * K) :=
     (by conv_rhs => rw [← closure_eq H, ← closure_eq K] <;> apply closure_mul_le)
 #align subgroup.sup_eq_closure Subgroup.sup_eq_closure
 #align add_subgroup.sup_eq_closure AddSubgroup.sup_eq_closure
+-/
 
 @[to_additive]
 private def mul_normal_aux (H N : Subgroup G) [hN : N.Normal] : Subgroup G
@@ -172,6 +194,7 @@ private def mul_normal_aux (H N : Subgroup G) [hN : N.Normal] : Subgroup G
     ⟨h⁻¹, h * n⁻¹ * h⁻¹, H.inv_mem hh, hN.conj_mem _ (N.inv_mem hn) h, by
       rw [mul_assoc h, inv_mul_cancel_left, ← hx, mul_inv_rev]⟩
 
+#print Subgroup.mul_normal /-
 /-- The carrier of `H ⊔ N` is just `↑H * ↑N` (pointwise set product) when `N` is normal. -/
 @[to_additive
       "The carrier of `H ⊔ N` is just `↑H + ↑N` (pointwise set addition)\nwhen `N` is normal."]
@@ -181,6 +204,7 @@ theorem mul_normal (H N : Subgroup G) [N.Normal] : (↑(H ⊔ N) : Set G) = H *
     ((sup_eq_closure H N).symm ▸ subset_closure)
 #align subgroup.mul_normal Subgroup.mul_normal
 #align add_subgroup.add_normal AddSubgroup.add_normal
+-/
 
 @[to_additive]
 private def normal_mul_aux (N H : Subgroup G) [hN : N.Normal] : Subgroup G
@@ -194,6 +218,7 @@ private def normal_mul_aux (N H : Subgroup G) [hN : N.Normal] : Subgroup G
     ⟨h⁻¹ * n⁻¹ * h, h⁻¹, by simpa using hN.conj_mem _ (N.inv_mem hn) h⁻¹, H.inv_mem hh, by
       rw [mul_inv_cancel_right, ← mul_inv_rev, hx]⟩
 
+#print Subgroup.normal_mul /-
 /-- The carrier of `N ⊔ H` is just `↑N * ↑H` (pointwise set product) when `N` is normal. -/
 @[to_additive
       "The carrier of `N ⊔ H` is just `↑N + ↑H` (pointwise set addition)\nwhen `N` is normal."]
@@ -203,7 +228,9 @@ theorem normal_mul (N H : Subgroup G) [N.Normal] : (↑(N ⊔ H) : Set G) = N *
     ((sup_eq_closure N H).symm ▸ subset_closure)
 #align subgroup.normal_mul Subgroup.normal_mul
 #align add_subgroup.normal_add AddSubgroup.normal_add
+-/
 
+#print Subgroup.mul_inf_assoc /-
 @[to_additive]
 theorem mul_inf_assoc (A B C : Subgroup G) (h : A ≤ C) : (A : Set G) * ↑(B ⊓ C) = A * B ⊓ C :=
   by
@@ -219,7 +246,9 @@ theorem mul_inf_assoc (A B C : Subgroup G) (h : A ≤ C) : (A : Set G) * ↑(B 
   exact mul_mem (inv_mem (h hy)) hyz
 #align subgroup.mul_inf_assoc Subgroup.mul_inf_assoc
 #align add_subgroup.add_inf_assoc AddSubgroup.add_inf_assoc
+-/
 
+#print Subgroup.inf_mul_assoc /-
 @[to_additive]
 theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
     ((A ⊓ B : Subgroup G) : Set G) * C = A ⊓ B * C :=
@@ -236,7 +265,9 @@ theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
   exact mul_mem hyz (inv_mem (h hz))
 #align subgroup.inf_mul_assoc Subgroup.inf_mul_assoc
 #align add_subgroup.inf_add_assoc AddSubgroup.inf_add_assoc
+-/
 
+#print Subgroup.sup_normal /-
 instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔ K).Normal
     where conj_mem n hmem g := by
     change n ∈ ↑(H ⊔ K) at hmem 
@@ -246,13 +277,16 @@ instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔
     refine' ⟨g * h * g⁻¹, g * k * g⁻¹, hH.conj_mem h hh g, hK.conj_mem k hk g, _⟩
     simp
 #align subgroup.sup_normal Subgroup.sup_normal
+-/
 
+#print Subgroup.smul_opposite_image_mul_preimage /-
 @[to_additive]
 theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.opposite) (s : Set G) :
     (fun y => h • y) '' (Mul.mul g ⁻¹' s) = Mul.mul g ⁻¹' ((fun y => h • y) '' s) := by ext x;
   cases h; simp [(· • ·), mul_assoc]
 #align subgroup.smul_opposite_image_mul_preimage Subgroup.smul_opposite_image_mul_preimage
 #align add_subgroup.vadd_opposite_image_add_preimage AddSubgroup.vadd_opposite_image_add_preimage
+-/
 
 /-! ### Pointwise action -/
 
@@ -278,15 +312,19 @@ scoped[Pointwise] attribute [instance] Subgroup.pointwiseMulAction
 
 open scoped Pointwise
 
+#print Subgroup.pointwise_smul_def /-
 theorem pointwise_smul_def {a : α} (S : Subgroup G) :
     a • S = S.map (MulDistribMulAction.toMonoidEnd _ _ a) :=
   rfl
 #align subgroup.pointwise_smul_def Subgroup.pointwise_smul_def
+-/
 
+#print Subgroup.coe_pointwise_smul /-
 @[simp]
 theorem coe_pointwise_smul (a : α) (S : Subgroup G) : ↑(a • S) = a • (S : Set G) :=
   rfl
 #align subgroup.coe_pointwise_smul Subgroup.coe_pointwise_smul
+-/
 
 #print Subgroup.pointwise_smul_toSubmonoid /-
 @[simp]
@@ -296,23 +334,31 @@ theorem pointwise_smul_toSubmonoid (a : α) (S : Subgroup G) :
 #align subgroup.pointwise_smul_to_submonoid Subgroup.pointwise_smul_toSubmonoid
 -/
 
+#print Subgroup.smul_mem_pointwise_smul /-
 theorem smul_mem_pointwise_smul (m : G) (a : α) (S : Subgroup G) : m ∈ S → a • m ∈ a • S :=
   (Set.smul_mem_smul_set : _ → _ ∈ a • (S : Set G))
 #align subgroup.smul_mem_pointwise_smul Subgroup.smul_mem_pointwise_smul
+-/
 
+#print Subgroup.mem_smul_pointwise_iff_exists /-
 theorem mem_smul_pointwise_iff_exists (m : G) (a : α) (S : Subgroup G) :
     m ∈ a • S ↔ ∃ s : G, s ∈ S ∧ a • s = m :=
   (Set.mem_smul_set : m ∈ a • (S : Set G) ↔ _)
 #align subgroup.mem_smul_pointwise_iff_exists Subgroup.mem_smul_pointwise_iff_exists
+-/
 
+#print Subgroup.smul_bot /-
 @[simp]
 theorem smul_bot (a : α) : a • (⊥ : Subgroup G) = ⊥ :=
   map_bot _
 #align subgroup.smul_bot Subgroup.smul_bot
+-/
 
+#print Subgroup.smul_sup /-
 theorem smul_sup (a : α) (S T : Subgroup G) : a • (S ⊔ T) = a • S ⊔ a • T :=
   map_sup _ _ _
 #align subgroup.smul_sup Subgroup.smul_sup
+-/
 
 #print Subgroup.smul_closure /-
 theorem smul_closure (a : α) (s : Set G) : a • closure s = closure (a • s) :=
@@ -327,12 +373,15 @@ instance pointwise_isCentralScalar [MulDistribMulAction αᵐᵒᵖ G] [IsCentra
 #align subgroup.pointwise_central_scalar Subgroup.pointwise_isCentralScalar
 -/
 
+#print Subgroup.conj_smul_le_of_le /-
 theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.conj (h : G) • P ≤ H :=
   by
   rintro - ⟨g, hg, rfl⟩
   exact H.mul_mem (H.mul_mem h.2 (hP hg)) (H.inv_mem h.2)
 #align subgroup.conj_smul_le_of_le Subgroup.conj_smul_le_of_le
+-/
 
+#print Subgroup.conj_smul_subgroupOf /-
 theorem conj_smul_subgroupOf {P H : Subgroup G} (hP : P ≤ H) (h : H) :
     MulAut.conj h • P.subgroupOf H = (MulAut.conj (h : G) • P).subgroupOf H :=
   by
@@ -342,6 +391,7 @@ theorem conj_smul_subgroupOf {P H : Subgroup G} (hP : P ≤ H) (h : H) :
   · rintro p ⟨g, hg, hp⟩
     exact ⟨⟨g, hP hg⟩, hg, Subtype.ext hp⟩
 #align subgroup.conj_smul_subgroup_of Subgroup.conj_smul_subgroupOf
+-/
 
 end Monoid
 
@@ -351,44 +401,61 @@ variable [Group α] [MulDistribMulAction α G]
 
 open scoped Pointwise
 
+#print Subgroup.smul_mem_pointwise_smul_iff /-
 @[simp]
 theorem smul_mem_pointwise_smul_iff {a : α} {S : Subgroup G} {x : G} : a • x ∈ a • S ↔ x ∈ S :=
   smul_mem_smul_set_iff
 #align subgroup.smul_mem_pointwise_smul_iff Subgroup.smul_mem_pointwise_smul_iff
+-/
 
+#print Subgroup.mem_pointwise_smul_iff_inv_smul_mem /-
 theorem mem_pointwise_smul_iff_inv_smul_mem {a : α} {S : Subgroup G} {x : G} :
     x ∈ a • S ↔ a⁻¹ • x ∈ S :=
   mem_smul_set_iff_inv_smul_mem
 #align subgroup.mem_pointwise_smul_iff_inv_smul_mem Subgroup.mem_pointwise_smul_iff_inv_smul_mem
+-/
 
+#print Subgroup.mem_inv_pointwise_smul_iff /-
 theorem mem_inv_pointwise_smul_iff {a : α} {S : Subgroup G} {x : G} : x ∈ a⁻¹ • S ↔ a • x ∈ S :=
   mem_inv_smul_set_iff
 #align subgroup.mem_inv_pointwise_smul_iff Subgroup.mem_inv_pointwise_smul_iff
+-/
 
+#print Subgroup.pointwise_smul_le_pointwise_smul_iff /-
 @[simp]
 theorem pointwise_smul_le_pointwise_smul_iff {a : α} {S T : Subgroup G} : a • S ≤ a • T ↔ S ≤ T :=
   set_smul_subset_set_smul_iff
 #align subgroup.pointwise_smul_le_pointwise_smul_iff Subgroup.pointwise_smul_le_pointwise_smul_iff
+-/
 
+#print Subgroup.pointwise_smul_subset_iff /-
 theorem pointwise_smul_subset_iff {a : α} {S T : Subgroup G} : a • S ≤ T ↔ S ≤ a⁻¹ • T :=
   set_smul_subset_iff
 #align subgroup.pointwise_smul_subset_iff Subgroup.pointwise_smul_subset_iff
+-/
 
+#print Subgroup.subset_pointwise_smul_iff /-
 theorem subset_pointwise_smul_iff {a : α} {S T : Subgroup G} : S ≤ a • T ↔ a⁻¹ • S ≤ T :=
   subset_set_smul_iff
 #align subgroup.subset_pointwise_smul_iff Subgroup.subset_pointwise_smul_iff
+-/
 
+#print Subgroup.smul_inf /-
 @[simp]
 theorem smul_inf (a : α) (S T : Subgroup G) : a • (S ⊓ T) = a • S ⊓ a • T := by
   simp [SetLike.ext_iff, mem_pointwise_smul_iff_inv_smul_mem]
 #align subgroup.smul_inf Subgroup.smul_inf
+-/
 
+#print Subgroup.equivSMul /-
 /-- Applying a `mul_distrib_mul_action` results in an isomorphic subgroup -/
 @[simps]
 def equivSMul (a : α) (H : Subgroup G) : H ≃* (a • H : Subgroup G) :=
   (MulDistribMulAction.toMulEquiv G a).subgroupMap H
 #align subgroup.equiv_smul Subgroup.equivSMul
+-/
 
+#print Subgroup.subgroup_mul_singleton /-
 theorem subgroup_mul_singleton {H : Subgroup G} {h : G} (hh : h ∈ H) : (H : Set G) * {h} = H :=
   by
   refine'
@@ -397,7 +464,9 @@ theorem subgroup_mul_singleton {H : Subgroup G} {h : G} (hh : h ∈ H) : (H : Se
   rintro _ ⟨h', h, hh', rfl : _ = _, rfl⟩
   exact H.mul_mem hh' hh
 #align subgroup.subgroup_mul_singleton Subgroup.subgroup_mul_singleton
+-/
 
+#print Subgroup.singleton_mul_subgroup /-
 theorem singleton_mul_subgroup {H : Subgroup G} {h : G} (hh : h ∈ H) : {h} * (H : Set G) = H :=
   by
   refine'
@@ -406,7 +475,9 @@ theorem singleton_mul_subgroup {H : Subgroup G} {h : G} (hh : h ∈ H) : {h} * (
   rintro _ ⟨h, h', rfl : _ = _, hh', rfl⟩
   exact H.mul_mem hh hh'
 #align subgroup.singleton_mul_subgroup Subgroup.singleton_mul_subgroup
+-/
 
+#print Subgroup.Normal.conjAct /-
 theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (g : ConjAct G) :
     g • H = H := by
   ext
@@ -426,11 +497,14 @@ theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (
     apply hH.conj_mem
     exact h
 #align subgroup.normal.conj_act Subgroup.Normal.conjAct
+-/
 
+#print Subgroup.smul_normal /-
 @[simp]
 theorem smul_normal (g : G) (H : Subgroup G) [h : Normal H] : MulAut.conj g • H = H :=
   h.ConjAct g
 #align subgroup.smul_normal Subgroup.smul_normal
+-/
 
 end Group
 
@@ -440,35 +514,47 @@ variable [GroupWithZero α] [MulDistribMulAction α G]
 
 open scoped Pointwise
 
+#print Subgroup.smul_mem_pointwise_smul_iff₀ /-
 @[simp]
 theorem smul_mem_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : Subgroup G) (x : G) :
     a • x ∈ a • S ↔ x ∈ S :=
   smul_mem_smul_set_iff₀ ha (S : Set G) x
 #align subgroup.smul_mem_pointwise_smul_iff₀ Subgroup.smul_mem_pointwise_smul_iff₀
+-/
 
+#print Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀ /-
 theorem mem_pointwise_smul_iff_inv_smul_mem₀ {a : α} (ha : a ≠ 0) (S : Subgroup G) (x : G) :
     x ∈ a • S ↔ a⁻¹ • x ∈ S :=
   mem_smul_set_iff_inv_smul_mem₀ ha (S : Set G) x
 #align subgroup.mem_pointwise_smul_iff_inv_smul_mem₀ Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀
+-/
 
+#print Subgroup.mem_inv_pointwise_smul_iff₀ /-
 theorem mem_inv_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : Subgroup G) (x : G) :
     x ∈ a⁻¹ • S ↔ a • x ∈ S :=
   mem_inv_smul_set_iff₀ ha (S : Set G) x
 #align subgroup.mem_inv_pointwise_smul_iff₀ Subgroup.mem_inv_pointwise_smul_iff₀
+-/
 
+#print Subgroup.pointwise_smul_le_pointwise_smul_iff₀ /-
 @[simp]
 theorem pointwise_smul_le_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) {S T : Subgroup G} :
     a • S ≤ a • T ↔ S ≤ T :=
   set_smul_subset_set_smul_iff₀ ha
 #align subgroup.pointwise_smul_le_pointwise_smul_iff₀ Subgroup.pointwise_smul_le_pointwise_smul_iff₀
+-/
 
+#print Subgroup.pointwise_smul_le_iff₀ /-
 theorem pointwise_smul_le_iff₀ {a : α} (ha : a ≠ 0) {S T : Subgroup G} : a • S ≤ T ↔ S ≤ a⁻¹ • T :=
   set_smul_subset_iff₀ ha
 #align subgroup.pointwise_smul_le_iff₀ Subgroup.pointwise_smul_le_iff₀
+-/
 
+#print Subgroup.le_pointwise_smul_iff₀ /-
 theorem le_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) {S T : Subgroup G} : S ≤ a • T ↔ a⁻¹ • S ≤ T :=
   subset_set_smul_iff₀ ha
 #align subgroup.le_pointwise_smul_iff₀ Subgroup.le_pointwise_smul_iff₀
+-/
 
 end GroupWithZero
 
@@ -497,10 +583,12 @@ scoped[Pointwise] attribute [instance] AddSubgroup.pointwiseMulAction
 
 open scoped Pointwise
 
+#print AddSubgroup.coe_pointwise_smul /-
 @[simp]
 theorem coe_pointwise_smul (a : α) (S : AddSubgroup A) : ↑(a • S) = a • (S : Set A) :=
   rfl
 #align add_subgroup.coe_pointwise_smul AddSubgroup.coe_pointwise_smul
+-/
 
 #print AddSubgroup.pointwise_smul_toAddSubmonoid /-
 @[simp]
@@ -510,19 +598,25 @@ theorem pointwise_smul_toAddSubmonoid (a : α) (S : AddSubgroup A) :
 #align add_subgroup.pointwise_smul_to_add_submonoid AddSubgroup.pointwise_smul_toAddSubmonoid
 -/
 
+#print AddSubgroup.smul_mem_pointwise_smul /-
 theorem smul_mem_pointwise_smul (m : A) (a : α) (S : AddSubgroup A) : m ∈ S → a • m ∈ a • S :=
   (Set.smul_mem_smul_set : _ → _ ∈ a • (S : Set A))
 #align add_subgroup.smul_mem_pointwise_smul AddSubgroup.smul_mem_pointwise_smul
+-/
 
+#print AddSubgroup.mem_smul_pointwise_iff_exists /-
 theorem mem_smul_pointwise_iff_exists (m : A) (a : α) (S : AddSubgroup A) :
     m ∈ a • S ↔ ∃ s : A, s ∈ S ∧ a • s = m :=
   (Set.mem_smul_set : m ∈ a • (S : Set A) ↔ _)
 #align add_subgroup.mem_smul_pointwise_iff_exists AddSubgroup.mem_smul_pointwise_iff_exists
+-/
 
+#print AddSubgroup.pointwise_isCentralScalar /-
 instance pointwise_isCentralScalar [DistribMulAction αᵐᵒᵖ A] [IsCentralScalar α A] :
     IsCentralScalar α (AddSubgroup A) :=
   ⟨fun a S => (congr_arg fun f => S.map f) <| AddMonoidHom.ext <| op_smul_eq_smul _⟩
 #align add_subgroup.pointwise_central_scalar AddSubgroup.pointwise_isCentralScalar
+-/
 
 end Monoid
 
@@ -532,33 +626,45 @@ variable [Group α] [DistribMulAction α A]
 
 open scoped Pointwise
 
+#print AddSubgroup.smul_mem_pointwise_smul_iff /-
 @[simp]
 theorem smul_mem_pointwise_smul_iff {a : α} {S : AddSubgroup A} {x : A} : a • x ∈ a • S ↔ x ∈ S :=
   smul_mem_smul_set_iff
 #align add_subgroup.smul_mem_pointwise_smul_iff AddSubgroup.smul_mem_pointwise_smul_iff
+-/
 
+#print AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem /-
 theorem mem_pointwise_smul_iff_inv_smul_mem {a : α} {S : AddSubgroup A} {x : A} :
     x ∈ a • S ↔ a⁻¹ • x ∈ S :=
   mem_smul_set_iff_inv_smul_mem
 #align add_subgroup.mem_pointwise_smul_iff_inv_smul_mem AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem
+-/
 
+#print AddSubgroup.mem_inv_pointwise_smul_iff /-
 theorem mem_inv_pointwise_smul_iff {a : α} {S : AddSubgroup A} {x : A} : x ∈ a⁻¹ • S ↔ a • x ∈ S :=
   mem_inv_smul_set_iff
 #align add_subgroup.mem_inv_pointwise_smul_iff AddSubgroup.mem_inv_pointwise_smul_iff
+-/
 
+#print AddSubgroup.pointwise_smul_le_pointwise_smul_iff /-
 @[simp]
 theorem pointwise_smul_le_pointwise_smul_iff {a : α} {S T : AddSubgroup A} :
     a • S ≤ a • T ↔ S ≤ T :=
   set_smul_subset_set_smul_iff
 #align add_subgroup.pointwise_smul_le_pointwise_smul_iff AddSubgroup.pointwise_smul_le_pointwise_smul_iff
+-/
 
+#print AddSubgroup.pointwise_smul_le_iff /-
 theorem pointwise_smul_le_iff {a : α} {S T : AddSubgroup A} : a • S ≤ T ↔ S ≤ a⁻¹ • T :=
   set_smul_subset_iff
 #align add_subgroup.pointwise_smul_le_iff AddSubgroup.pointwise_smul_le_iff
+-/
 
+#print AddSubgroup.le_pointwise_smul_iff /-
 theorem le_pointwise_smul_iff {a : α} {S T : AddSubgroup A} : S ≤ a • T ↔ a⁻¹ • S ≤ T :=
   subset_set_smul_iff
 #align add_subgroup.le_pointwise_smul_iff AddSubgroup.le_pointwise_smul_iff
+-/
 
 end Group
 
@@ -568,37 +674,49 @@ variable [GroupWithZero α] [DistribMulAction α A]
 
 open scoped Pointwise
 
+#print AddSubgroup.smul_mem_pointwise_smul_iff₀ /-
 @[simp]
 theorem smul_mem_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : AddSubgroup A) (x : A) :
     a • x ∈ a • S ↔ x ∈ S :=
   smul_mem_smul_set_iff₀ ha (S : Set A) x
 #align add_subgroup.smul_mem_pointwise_smul_iff₀ AddSubgroup.smul_mem_pointwise_smul_iff₀
+-/
 
+#print AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀ /-
 theorem mem_pointwise_smul_iff_inv_smul_mem₀ {a : α} (ha : a ≠ 0) (S : AddSubgroup A) (x : A) :
     x ∈ a • S ↔ a⁻¹ • x ∈ S :=
   mem_smul_set_iff_inv_smul_mem₀ ha (S : Set A) x
 #align add_subgroup.mem_pointwise_smul_iff_inv_smul_mem₀ AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀
+-/
 
+#print AddSubgroup.mem_inv_pointwise_smul_iff₀ /-
 theorem mem_inv_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : AddSubgroup A) (x : A) :
     x ∈ a⁻¹ • S ↔ a • x ∈ S :=
   mem_inv_smul_set_iff₀ ha (S : Set A) x
 #align add_subgroup.mem_inv_pointwise_smul_iff₀ AddSubgroup.mem_inv_pointwise_smul_iff₀
+-/
 
+#print AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀ /-
 @[simp]
 theorem pointwise_smul_le_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) {S T : AddSubgroup A} :
     a • S ≤ a • T ↔ S ≤ T :=
   set_smul_subset_set_smul_iff₀ ha
 #align add_subgroup.pointwise_smul_le_pointwise_smul_iff₀ AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀
+-/
 
+#print AddSubgroup.pointwise_smul_le_iff₀ /-
 theorem pointwise_smul_le_iff₀ {a : α} (ha : a ≠ 0) {S T : AddSubgroup A} :
     a • S ≤ T ↔ S ≤ a⁻¹ • T :=
   set_smul_subset_iff₀ ha
 #align add_subgroup.pointwise_smul_le_iff₀ AddSubgroup.pointwise_smul_le_iff₀
+-/
 
+#print AddSubgroup.le_pointwise_smul_iff₀ /-
 theorem le_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) {S T : AddSubgroup A} :
     S ≤ a • T ↔ a⁻¹ • S ≤ T :=
   subset_set_smul_iff₀ ha
 #align add_subgroup.le_pointwise_smul_iff₀ AddSubgroup.le_pointwise_smul_iff₀
+-/
 
 end GroupWithZero

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -117,7 +117,7 @@ then it holds for all elements of the supremum of `S`. -/
 theorem iSup_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
     (hp : ∀ (i), ∀ x ∈ S i, C x) (h1 : C 1) (hmul : ∀ x y, C x → C y → C (x * y)) : C x :=
   by
-  rw [supr_eq_closure] at hx
+  rw [supr_eq_closure] at hx 
   refine' closure_induction'' hx (fun x hx => _) (fun x hx => _) h1 hmul
   · obtain ⟨i, hi⟩ := set.mem_Union.mp hx
     exact hp _ _ hi
@@ -239,7 +239,7 @@ theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
 
 instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔ K).Normal
     where conj_mem n hmem g := by
-    change n ∈ ↑(H ⊔ K) at hmem
+    change n ∈ ↑(H ⊔ K) at hmem 
     change g * n * g⁻¹ ∈ ↑(H ⊔ K)
     rw [normal_mul, Set.mem_mul] at *
     rcases hmem with ⟨h, k, hh, hk, rfl⟩
@@ -413,13 +413,13 @@ theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (
   constructor
   · intro h
     have := hH.conj_mem (g⁻¹ • x) _ (ConjAct.ofConjAct g)
-    rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem] at h
+    rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem] at h 
     dsimp at *
     rw [ConjAct.smul_def] at *
     simp only [ConjAct.ofConjAct_inv, ConjAct.ofConjAct_toConjAct, inv_inv] at *
     convert this
     simp only [← mul_assoc, mul_right_inv, one_mul, mul_inv_cancel_right]
-    rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem] at h
+    rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem] at h 
     exact h
   · intro h
     rw [Subgroup.mem_pointwise_smul_iff_inv_smul_mem, ConjAct.smul_def]

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -35,7 +35,7 @@ Where possible, try to keep them in sync.
 
 open Set
 
-open Pointwise
+open scoped Pointwise
 
 variable {α G A S : Type _}
 
@@ -276,7 +276,7 @@ protected def pointwiseMulAction : MulAction α (Subgroup G)
 
 scoped[Pointwise] attribute [instance] Subgroup.pointwiseMulAction
 
-open Pointwise
+open scoped Pointwise
 
 theorem pointwise_smul_def {a : α} (S : Subgroup G) :
     a • S = S.map (MulDistribMulAction.toMonoidEnd _ _ a) :=
@@ -349,7 +349,7 @@ section Group
 
 variable [Group α] [MulDistribMulAction α G]
 
-open Pointwise
+open scoped Pointwise
 
 @[simp]
 theorem smul_mem_pointwise_smul_iff {a : α} {S : Subgroup G} {x : G} : a • x ∈ a • S ↔ x ∈ S :=
@@ -438,7 +438,7 @@ section GroupWithZero
 
 variable [GroupWithZero α] [MulDistribMulAction α G]
 
-open Pointwise
+open scoped Pointwise
 
 @[simp]
 theorem smul_mem_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : Subgroup G) (x : G) :
@@ -495,7 +495,7 @@ protected def pointwiseMulAction : MulAction α (AddSubgroup A)
 
 scoped[Pointwise] attribute [instance] AddSubgroup.pointwiseMulAction
 
-open Pointwise
+open scoped Pointwise
 
 @[simp]
 theorem coe_pointwise_smul (a : α) (S : AddSubgroup A) : ↑(a • S) = a • (S : Set A) :=
@@ -530,7 +530,7 @@ section Group
 
 variable [Group α] [DistribMulAction α A]
 
-open Pointwise
+open scoped Pointwise
 
 @[simp]
 theorem smul_mem_pointwise_smul_iff {a : α} {S : AddSubgroup A} {x : A} : a • x ∈ a • S ↔ x ∈ S :=
@@ -566,7 +566,7 @@ section GroupWithZero
 
 variable [GroupWithZero α] [DistribMulAction α A]
 
-open Pointwise
+open scoped Pointwise
 
 @[simp]
 theorem smul_mem_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : AddSubgroup A) (x : A) :

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -39,12 +39,6 @@ open Pointwise
 
 variable {α G A S : Type _}
 
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-Case conversion may be inaccurate. Consider using '#align inv_coe_set inv_coe_setₓ'. -/
 @[simp, to_additive]
 theorem inv_coe_set [InvolutiveInv G] [SetLike S G] [InvMemClass S G] {H : S} : (H : Set G)⁻¹ = H :=
   Set.ext fun _ => inv_mem_iff
@@ -55,24 +49,12 @@ variable [Group G] [AddGroup A] {s : Set G}
 
 namespace Subgroup
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.inv_subset_closure Subgroup.inv_subset_closureₓ'. -/
 @[simp, to_additive]
 theorem inv_subset_closure (S : Set G) : S⁻¹ ⊆ closure S := fun s hs => by
   rw [SetLike.mem_coe, ← Subgroup.inv_mem_iff]; exact subset_closure (mem_inv.mp hs)
 #align subgroup.inv_subset_closure Subgroup.inv_subset_closure
 #align add_subgroup.neg_subset_closure AddSubgroup.neg_subset_closure
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.closure_to_submonoid Subgroup.closure_toSubmonoidₓ'. -/
 @[to_additive]
 theorem closure_toSubmonoid (S : Set G) : (closure S).toSubmonoid = Submonoid.closure (S ∪ S⁻¹) :=
   by
@@ -86,12 +68,6 @@ theorem closure_toSubmonoid (S : Set G) : (closure S).toSubmonoid = Submonoid.cl
 #align subgroup.closure_to_submonoid Subgroup.closure_toSubmonoid
 #align add_subgroup.closure_to_add_submonoid AddSubgroup.closure_toAddSubmonoid
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.closure_induction_left Subgroup.closure_induction_leftₓ'. -/
 /-- For subgroups generated by a single element, see the simpler `zpow_induction_left`. -/
 @[to_additive
       "For additive subgroups generated by a single element, see the simpler\n`zsmul_induction_left`."]
@@ -103,12 +79,6 @@ theorem closure_induction_left {p : G → Prop} {x : G} (h : x ∈ closure s) (H
 #align subgroup.closure_induction_left Subgroup.closure_induction_left
 #align add_subgroup.closure_induction_left AddSubgroup.closure_induction_left
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.closure_induction_right Subgroup.closure_induction_rightₓ'. -/
 /-- For subgroups generated by a single element, see the simpler `zpow_induction_right`. -/
 @[to_additive
       "For additive subgroups generated by a single element, see the simpler\n`zsmul_induction_right`."]
@@ -120,24 +90,12 @@ theorem closure_induction_right {p : G → Prop} {x : G} (h : x ∈ closure s) (
 #align subgroup.closure_induction_right Subgroup.closure_induction_right
 #align add_subgroup.closure_induction_right AddSubgroup.closure_induction_right
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.closure_inv Subgroup.closure_invₓ'. -/
 @[simp, to_additive]
 theorem closure_inv (s : Set G) : closure s⁻¹ = closure s := by
   simp only [← to_submonoid_eq, closure_to_submonoid, inv_inv, union_comm]
 #align subgroup.closure_inv Subgroup.closure_inv
 #align add_subgroup.closure_neg AddSubgroup.closure_neg
 
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 /-- An induction principle for closure membership. If `p` holds for `1` and all elements of
 `k` and their inverse, and is preserved under multiplication, then `p` holds for all elements of
 the closure of `k`. -/
@@ -150,12 +108,6 @@ theorem closure_induction'' {p : G → Prop} {x} (h : x ∈ closure s) (Hk : ∀
 #align subgroup.closure_induction'' Subgroup.closure_induction''
 #align add_subgroup.closure_induction'' AddSubgroup.closure_induction''
 
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 /-- An induction principle for elements of `⨆ i, S i`.
 If `C` holds for `1` and all elements of `S i` for all `i`, and is preserved under multiplication,
 then it holds for all elements of the supremum of `S`. -/
@@ -174,12 +126,6 @@ theorem iSup_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x
 #align subgroup.supr_induction Subgroup.iSup_induction
 #align add_subgroup.supr_induction AddSubgroup.iSup_induction
 
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 /-- A dependent version of `subgroup.supr_induction`. -/
 @[elab_as_elim, to_additive "A dependent version of `add_subgroup.supr_induction`. "]
 theorem iSup_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
@@ -196,12 +142,6 @@ theorem iSup_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈
 #align subgroup.supr_induction' Subgroup.iSup_induction'
 #align add_subgroup.supr_induction' AddSubgroup.iSup_induction'
 
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 @[to_additive]
 theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure T :=
   sInf_le fun x ⟨s, t, hs, ht, hx⟩ =>
@@ -211,12 +151,6 @@ theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure
 #align subgroup.closure_mul_le Subgroup.closure_mul_le
 #align add_subgroup.closure_add_le AddSubgroup.closure_add_le
 
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 @[to_additive]
 theorem sup_eq_closure (H K : Subgroup G) : H ⊔ K = closure (H * K) :=
   le_antisymm
@@ -238,12 +172,6 @@ private def mul_normal_aux (H N : Subgroup G) [hN : N.Normal] : Subgroup G
     ⟨h⁻¹, h * n⁻¹ * h⁻¹, H.inv_mem hh, hN.conj_mem _ (N.inv_mem hn) h, by
       rw [mul_assoc h, inv_mul_cancel_left, ← hx, mul_inv_rev]⟩
 
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 /-- The carrier of `H ⊔ N` is just `↑H * ↑N` (pointwise set product) when `N` is normal. -/
 @[to_additive
       "The carrier of `H ⊔ N` is just `↑H + ↑N` (pointwise set addition)\nwhen `N` is normal."]
@@ -266,12 +194,6 @@ private def normal_mul_aux (N H : Subgroup G) [hN : N.Normal] : Subgroup G
     ⟨h⁻¹ * n⁻¹ * h, h⁻¹, by simpa using hN.conj_mem _ (N.inv_mem hn) h⁻¹, H.inv_mem hh, by
       rw [mul_inv_cancel_right, ← mul_inv_rev, hx]⟩
 
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 /-- The carrier of `N ⊔ H` is just `↑N * ↑H` (pointwise set product) when `N` is normal. -/
 @[to_additive
       "The carrier of `N ⊔ H` is just `↑N + ↑H` (pointwise set addition)\nwhen `N` is normal."]
@@ -282,12 +204,6 @@ theorem normal_mul (N H : Subgroup G) [N.Normal] : (↑(N ⊔ H) : Set G) = N *
 #align subgroup.normal_mul Subgroup.normal_mul
 #align add_subgroup.normal_add AddSubgroup.normal_add
 
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 @[to_additive]
 theorem mul_inf_assoc (A B C : Subgroup G) (h : A ≤ C) : (A : Set G) * ↑(B ⊓ C) = A * B ⊓ C :=
   by
@@ -304,12 +220,6 @@ theorem mul_inf_assoc (A B C : Subgroup G) (h : A ≤ C) : (A : Set G) * ↑(B 
 #align subgroup.mul_inf_assoc Subgroup.mul_inf_assoc
 #align add_subgroup.add_inf_assoc AddSubgroup.add_inf_assoc
 
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 @[to_additive]
 theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
     ((A ⊓ B : Subgroup G) : Set G) * C = A ⊓ B * C :=
@@ -327,12 +237,6 @@ theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
 #align subgroup.inf_mul_assoc Subgroup.inf_mul_assoc
 #align add_subgroup.inf_add_assoc AddSubgroup.inf_add_assoc
 
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 instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔ K).Normal
     where conj_mem n hmem g := by
     change n ∈ ↑(H ⊔ K) at hmem
@@ -343,9 +247,6 @@ instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔
     simp
 #align subgroup.sup_normal Subgroup.sup_normal
 
-/- warning: subgroup.smul_opposite_image_mul_preimage -> Subgroup.smul_opposite_image_mul_preimage is a dubious translation:
-<too large>
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 @[to_additive]
 theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.opposite) (s : Set G) :
     (fun y => h • y) '' (Mul.mul g ⁻¹' s) = Mul.mul g ⁻¹' ((fun y => h • y) '' s) := by ext x;
@@ -377,23 +278,11 @@ scoped[Pointwise] attribute [instance] Subgroup.pointwiseMulAction
 
 open Pointwise
 
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 theorem pointwise_smul_def {a : α} (S : Subgroup G) :
     a • S = S.map (MulDistribMulAction.toMonoidEnd _ _ a) :=
   rfl
 #align subgroup.pointwise_smul_def Subgroup.pointwise_smul_def
 
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 @[simp]
 theorem coe_pointwise_smul (a : α) (S : Subgroup G) : ↑(a • S) = a • (S : Set G) :=
   rfl
@@ -407,44 +296,20 @@ theorem pointwise_smul_toSubmonoid (a : α) (S : Subgroup G) :
 #align subgroup.pointwise_smul_to_submonoid Subgroup.pointwise_smul_toSubmonoid
 -/
 
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 theorem smul_mem_pointwise_smul (m : G) (a : α) (S : Subgroup G) : m ∈ S → a • m ∈ a • S :=
   (Set.smul_mem_smul_set : _ → _ ∈ a • (S : Set G))
 #align subgroup.smul_mem_pointwise_smul Subgroup.smul_mem_pointwise_smul
 
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 theorem mem_smul_pointwise_iff_exists (m : G) (a : α) (S : Subgroup G) :
     m ∈ a • S ↔ ∃ s : G, s ∈ S ∧ a • s = m :=
   (Set.mem_smul_set : m ∈ a • (S : Set G) ↔ _)
 #align subgroup.mem_smul_pointwise_iff_exists Subgroup.mem_smul_pointwise_iff_exists
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.smul_bot Subgroup.smul_botₓ'. -/
 @[simp]
 theorem smul_bot (a : α) : a • (⊥ : Subgroup G) = ⊥ :=
   map_bot _
 #align subgroup.smul_bot Subgroup.smul_bot
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.smul_sup Subgroup.smul_supₓ'. -/
 theorem smul_sup (a : α) (S T : Subgroup G) : a • (S ⊔ T) = a • S ⊔ a • T :=
   map_sup _ _ _
 #align subgroup.smul_sup Subgroup.smul_sup
@@ -462,18 +327,12 @@ instance pointwise_isCentralScalar [MulDistribMulAction αᵐᵒᵖ G] [IsCentra
 #align subgroup.pointwise_central_scalar Subgroup.pointwise_isCentralScalar
 -/
 
-/- warning: subgroup.conj_smul_le_of_le -> Subgroup.conj_smul_le_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_le_of_le Subgroup.conj_smul_le_of_leₓ'. -/
 theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.conj (h : G) • P ≤ H :=
   by
   rintro - ⟨g, hg, rfl⟩
   exact H.mul_mem (H.mul_mem h.2 (hP hg)) (H.inv_mem h.2)
 #align subgroup.conj_smul_le_of_le Subgroup.conj_smul_le_of_le
 
-/- warning: subgroup.conj_smul_subgroup_of -> Subgroup.conj_smul_subgroupOf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_subgroup_of Subgroup.conj_smul_subgroupOfₓ'. -/
 theorem conj_smul_subgroupOf {P H : Subgroup G} (hP : P ≤ H) (h : H) :
     MulAut.conj h • P.subgroupOf H = (MulAut.conj (h : G) • P).subgroupOf H :=
   by
@@ -492,98 +351,44 @@ variable [Group α] [MulDistribMulAction α G]
 
 open Pointwise
 
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 @[simp]
 theorem smul_mem_pointwise_smul_iff {a : α} {S : Subgroup G} {x : G} : a • x ∈ a • S ↔ x ∈ S :=
   smul_mem_smul_set_iff
 #align subgroup.smul_mem_pointwise_smul_iff Subgroup.smul_mem_pointwise_smul_iff
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.mem_pointwise_smul_iff_inv_smul_mem Subgroup.mem_pointwise_smul_iff_inv_smul_memₓ'. -/
 theorem mem_pointwise_smul_iff_inv_smul_mem {a : α} {S : Subgroup G} {x : G} :
     x ∈ a • S ↔ a⁻¹ • x ∈ S :=
   mem_smul_set_iff_inv_smul_mem
 #align subgroup.mem_pointwise_smul_iff_inv_smul_mem Subgroup.mem_pointwise_smul_iff_inv_smul_mem
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.mem_inv_pointwise_smul_iff Subgroup.mem_inv_pointwise_smul_iffₓ'. -/
 theorem mem_inv_pointwise_smul_iff {a : α} {S : Subgroup G} {x : G} : x ∈ a⁻¹ • S ↔ a • x ∈ S :=
   mem_inv_smul_set_iff
 #align subgroup.mem_inv_pointwise_smul_iff Subgroup.mem_inv_pointwise_smul_iff
 
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 @[simp]
 theorem pointwise_smul_le_pointwise_smul_iff {a : α} {S T : Subgroup G} : a • S ≤ a • T ↔ S ≤ T :=
   set_smul_subset_set_smul_iff
 #align subgroup.pointwise_smul_le_pointwise_smul_iff Subgroup.pointwise_smul_le_pointwise_smul_iff
 
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 theorem pointwise_smul_subset_iff {a : α} {S T : Subgroup G} : a • S ≤ T ↔ S ≤ a⁻¹ • T :=
   set_smul_subset_iff
 #align subgroup.pointwise_smul_subset_iff Subgroup.pointwise_smul_subset_iff
 
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 theorem subset_pointwise_smul_iff {a : α} {S T : Subgroup G} : S ≤ a • T ↔ a⁻¹ • S ≤ T :=
   subset_set_smul_iff
 #align subgroup.subset_pointwise_smul_iff Subgroup.subset_pointwise_smul_iff
 
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 @[simp]
 theorem smul_inf (a : α) (S T : Subgroup G) : a • (S ⊓ T) = a • S ⊓ a • T := by
   simp [SetLike.ext_iff, mem_pointwise_smul_iff_inv_smul_mem]
 #align subgroup.smul_inf Subgroup.smul_inf
 
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 /-- Applying a `mul_distrib_mul_action` results in an isomorphic subgroup -/
 @[simps]
 def equivSMul (a : α) (H : Subgroup G) : H ≃* (a • H : Subgroup G) :=
   (MulDistribMulAction.toMulEquiv G a).subgroupMap H
 #align subgroup.equiv_smul Subgroup.equivSMul
 
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 theorem subgroup_mul_singleton {H : Subgroup G} {h : G} (hh : h ∈ H) : (H : Set G) * {h} = H :=
   by
   refine'
@@ -593,12 +398,6 @@ theorem subgroup_mul_singleton {H : Subgroup G} {h : G} (hh : h ∈ H) : (H : Se
   exact H.mul_mem hh' hh
 #align subgroup.subgroup_mul_singleton Subgroup.subgroup_mul_singleton
 
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 theorem singleton_mul_subgroup {H : Subgroup G} {h : G} (hh : h ∈ H) : {h} * (H : Set G) = H :=
   by
   refine'
@@ -608,12 +407,6 @@ theorem singleton_mul_subgroup {H : Subgroup G} {h : G} (hh : h ∈ H) : {h} * (
   exact H.mul_mem hh hh'
 #align subgroup.singleton_mul_subgroup Subgroup.singleton_mul_subgroup
 
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 theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (g : ConjAct G) :
     g • H = H := by
   ext
@@ -634,9 +427,6 @@ theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (
     exact h
 #align subgroup.normal.conj_act Subgroup.Normal.conjAct
 
-/- warning: subgroup.smul_normal -> Subgroup.smul_normal is a dubious translation:
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 @[simp]
 theorem smul_normal (g : G) (H : Subgroup G) [h : Normal H] : MulAut.conj g • H = H :=
   h.ConjAct g
@@ -650,68 +440,32 @@ variable [GroupWithZero α] [MulDistribMulAction α G]
 
 open Pointwise
 
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 @[simp]
 theorem smul_mem_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : Subgroup G) (x : G) :
     a • x ∈ a • S ↔ x ∈ S :=
   smul_mem_smul_set_iff₀ ha (S : Set G) x
 #align subgroup.smul_mem_pointwise_smul_iff₀ Subgroup.smul_mem_pointwise_smul_iff₀
 
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 theorem mem_pointwise_smul_iff_inv_smul_mem₀ {a : α} (ha : a ≠ 0) (S : Subgroup G) (x : G) :
     x ∈ a • S ↔ a⁻¹ • x ∈ S :=
   mem_smul_set_iff_inv_smul_mem₀ ha (S : Set G) x
 #align subgroup.mem_pointwise_smul_iff_inv_smul_mem₀ Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.mem_inv_pointwise_smul_iff₀ Subgroup.mem_inv_pointwise_smul_iff₀ₓ'. -/
 theorem mem_inv_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : Subgroup G) (x : G) :
     x ∈ a⁻¹ • S ↔ a • x ∈ S :=
   mem_inv_smul_set_iff₀ ha (S : Set G) x
 #align subgroup.mem_inv_pointwise_smul_iff₀ Subgroup.mem_inv_pointwise_smul_iff₀
 
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 @[simp]
 theorem pointwise_smul_le_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) {S T : Subgroup G} :
     a • S ≤ a • T ↔ S ≤ T :=
   set_smul_subset_set_smul_iff₀ ha
 #align subgroup.pointwise_smul_le_pointwise_smul_iff₀ Subgroup.pointwise_smul_le_pointwise_smul_iff₀
 
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 theorem pointwise_smul_le_iff₀ {a : α} (ha : a ≠ 0) {S T : Subgroup G} : a • S ≤ T ↔ S ≤ a⁻¹ • T :=
   set_smul_subset_iff₀ ha
 #align subgroup.pointwise_smul_le_iff₀ Subgroup.pointwise_smul_le_iff₀
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.le_pointwise_smul_iff₀ Subgroup.le_pointwise_smul_iff₀ₓ'. -/
 theorem le_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) {S T : Subgroup G} : S ≤ a • T ↔ a⁻¹ • S ≤ T :=
   subset_set_smul_iff₀ ha
 #align subgroup.le_pointwise_smul_iff₀ Subgroup.le_pointwise_smul_iff₀
@@ -743,12 +497,6 @@ scoped[Pointwise] attribute [instance] AddSubgroup.pointwiseMulAction
 
 open Pointwise
 
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 @[simp]
 theorem coe_pointwise_smul (a : α) (S : AddSubgroup A) : ↑(a • S) = a • (S : Set A) :=
   rfl
@@ -762,33 +510,15 @@ theorem pointwise_smul_toAddSubmonoid (a : α) (S : AddSubgroup A) :
 #align add_subgroup.pointwise_smul_to_add_submonoid AddSubgroup.pointwise_smul_toAddSubmonoid
 -/
 
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 theorem smul_mem_pointwise_smul (m : A) (a : α) (S : AddSubgroup A) : m ∈ S → a • m ∈ a • S :=
   (Set.smul_mem_smul_set : _ → _ ∈ a • (S : Set A))
 #align add_subgroup.smul_mem_pointwise_smul AddSubgroup.smul_mem_pointwise_smul
 
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.mem_smul_pointwise_iff_exists AddSubgroup.mem_smul_pointwise_iff_existsₓ'. -/
 theorem mem_smul_pointwise_iff_exists (m : A) (a : α) (S : AddSubgroup A) :
     m ∈ a • S ↔ ∃ s : A, s ∈ S ∧ a • s = m :=
   (Set.mem_smul_set : m ∈ a • (S : Set A) ↔ _)
 #align add_subgroup.mem_smul_pointwise_iff_exists AddSubgroup.mem_smul_pointwise_iff_exists
 
-/- warning: add_subgroup.pointwise_central_scalar -> AddSubgroup.pointwise_isCentralScalar is a dubious translation:
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-  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Monoid.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A _inst_3 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] [_inst_5 : DistribMulAction.{u1, u2} (MulOpposite.{u1} α) A (MulOpposite.monoid.{u1} α _inst_3) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] [_inst_6 : IsCentralScalar.{u1, u2} α A (SMulZeroClass.toHasSmul.{u1, u2} α A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} α A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} α A _inst_3 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)) _inst_4))) (SMulZeroClass.toHasSmul.{u1, u2} (MulOpposite.{u1} α) A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} (MulOpposite.{u1} α) A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} (MulOpposite.{u1} α) A (MulOpposite.monoid.{u1} α _inst_3) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)) _inst_5)))], IsCentralScalar.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) _inst_3 (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 _inst_3 _inst_4)) (MulAction.toHasSmul.{u1, u2} (MulOpposite.{u1} α) (AddSubgroup.{u2} A _inst_2) (MulOpposite.monoid.{u1} α _inst_3) (AddSubgroup.pointwiseMulAction.{u1, u2} (MulOpposite.{u1} α) A _inst_2 (MulOpposite.monoid.{u1} α _inst_3) _inst_5))
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.pointwise_central_scalar AddSubgroup.pointwise_isCentralScalarₓ'. -/
 instance pointwise_isCentralScalar [DistribMulAction αᵐᵒᵖ A] [IsCentralScalar α A] :
     IsCentralScalar α (AddSubgroup A) :=
   ⟨fun a S => (congr_arg fun f => S.map f) <| AddMonoidHom.ext <| op_smul_eq_smul _⟩
@@ -802,66 +532,30 @@ variable [Group α] [DistribMulAction α A]
 
 open Pointwise
 
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.smul_mem_pointwise_smul_iff AddSubgroup.smul_mem_pointwise_smul_iffₓ'. -/
 @[simp]
 theorem smul_mem_pointwise_smul_iff {a : α} {S : AddSubgroup A} {x : A} : a • x ∈ a • S ↔ x ∈ S :=
   smul_mem_smul_set_iff
 #align add_subgroup.smul_mem_pointwise_smul_iff AddSubgroup.smul_mem_pointwise_smul_iff
 
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.mem_pointwise_smul_iff_inv_smul_mem AddSubgroup.mem_pointwise_smul_iff_inv_smul_memₓ'. -/
 theorem mem_pointwise_smul_iff_inv_smul_mem {a : α} {S : AddSubgroup A} {x : A} :
     x ∈ a • S ↔ a⁻¹ • x ∈ S :=
   mem_smul_set_iff_inv_smul_mem
 #align add_subgroup.mem_pointwise_smul_iff_inv_smul_mem AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem
 
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.mem_inv_pointwise_smul_iff AddSubgroup.mem_inv_pointwise_smul_iffₓ'. -/
 theorem mem_inv_pointwise_smul_iff {a : α} {S : AddSubgroup A} {x : A} : x ∈ a⁻¹ • S ↔ a • x ∈ S :=
   mem_inv_smul_set_iff
 #align add_subgroup.mem_inv_pointwise_smul_iff AddSubgroup.mem_inv_pointwise_smul_iff
 
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-lean 3 declaration is
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 @[simp]
 theorem pointwise_smul_le_pointwise_smul_iff {a : α} {S T : AddSubgroup A} :
     a • S ≤ a • T ↔ S ≤ T :=
   set_smul_subset_set_smul_iff
 #align add_subgroup.pointwise_smul_le_pointwise_smul_iff AddSubgroup.pointwise_smul_le_pointwise_smul_iff
 
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 theorem pointwise_smul_le_iff {a : α} {S T : AddSubgroup A} : a • S ≤ T ↔ S ≤ a⁻¹ • T :=
   set_smul_subset_iff
 #align add_subgroup.pointwise_smul_le_iff AddSubgroup.pointwise_smul_le_iff
 
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.le_pointwise_smul_iff AddSubgroup.le_pointwise_smul_iffₓ'. -/
 theorem le_pointwise_smul_iff {a : α} {S T : AddSubgroup A} : S ≤ a • T ↔ a⁻¹ • S ≤ T :=
   subset_set_smul_iff
 #align add_subgroup.le_pointwise_smul_iff AddSubgroup.le_pointwise_smul_iff
@@ -874,69 +568,33 @@ variable [GroupWithZero α] [DistribMulAction α A]
 
 open Pointwise
 
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 @[simp]
 theorem smul_mem_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : AddSubgroup A) (x : A) :
     a • x ∈ a • S ↔ x ∈ S :=
   smul_mem_smul_set_iff₀ ha (S : Set A) x
 #align add_subgroup.smul_mem_pointwise_smul_iff₀ AddSubgroup.smul_mem_pointwise_smul_iff₀
 
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 theorem mem_pointwise_smul_iff_inv_smul_mem₀ {a : α} (ha : a ≠ 0) (S : AddSubgroup A) (x : A) :
     x ∈ a • S ↔ a⁻¹ • x ∈ S :=
   mem_smul_set_iff_inv_smul_mem₀ ha (S : Set A) x
 #align add_subgroup.mem_pointwise_smul_iff_inv_smul_mem₀ AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀
 
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.mem_inv_pointwise_smul_iff₀ AddSubgroup.mem_inv_pointwise_smul_iff₀ₓ'. -/
 theorem mem_inv_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : AddSubgroup A) (x : A) :
     x ∈ a⁻¹ • S ↔ a • x ∈ S :=
   mem_inv_smul_set_iff₀ ha (S : Set A) x
 #align add_subgroup.mem_inv_pointwise_smul_iff₀ AddSubgroup.mem_inv_pointwise_smul_iff₀
 
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 @[simp]
 theorem pointwise_smul_le_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) {S T : AddSubgroup A} :
     a • S ≤ a • T ↔ S ≤ T :=
   set_smul_subset_set_smul_iff₀ ha
 #align add_subgroup.pointwise_smul_le_pointwise_smul_iff₀ AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀
 
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.pointwise_smul_le_iff₀ AddSubgroup.pointwise_smul_le_iff₀ₓ'. -/
 theorem pointwise_smul_le_iff₀ {a : α} (ha : a ≠ 0) {S T : AddSubgroup A} :
     a • S ≤ T ↔ S ≤ a⁻¹ • T :=
   set_smul_subset_iff₀ ha
 #align add_subgroup.pointwise_smul_le_iff₀ AddSubgroup.pointwise_smul_le_iff₀
 
-/- warning: add_subgroup.le_pointwise_smul_iff₀ -> AddSubgroup.le_pointwise_smul_iff₀ is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.le_pointwise_smul_iff₀ AddSubgroup.le_pointwise_smul_iff₀ₓ'. -/
 theorem le_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) {S T : AddSubgroup A} :
     S ≤ a • T ↔ a⁻¹ • S ≤ T :=
   subset_set_smul_iff₀ ha

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -62,10 +62,8 @@ but is expected to have type
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (S : Set.{u1} G), HasSubset.Subset.{u1} (Set.{u1} G) (Set.instHasSubsetSet.{u1} G) (Inv.inv.{u1} (Set.{u1} G) (Set.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1))))) S) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Subgroup.closure.{u1} G _inst_1 S))
 Case conversion may be inaccurate. Consider using '#align subgroup.inv_subset_closure Subgroup.inv_subset_closureₓ'. -/
 @[simp, to_additive]
-theorem inv_subset_closure (S : Set G) : S⁻¹ ⊆ closure S := fun s hs =>
-  by
-  rw [SetLike.mem_coe, ← Subgroup.inv_mem_iff]
-  exact subset_closure (mem_inv.mp hs)
+theorem inv_subset_closure (S : Set G) : S⁻¹ ⊆ closure S := fun s hs => by
+  rw [SetLike.mem_coe, ← Subgroup.inv_mem_iff]; exact subset_closure (mem_inv.mp hs)
 #align subgroup.inv_subset_closure Subgroup.inv_subset_closure
 #align add_subgroup.neg_subset_closure AddSubgroup.neg_subset_closure
 
@@ -251,11 +249,7 @@ Case conversion may be inaccurate. Consider using '#align subgroup.mul_normal Su
       "The carrier of `H ⊔ N` is just `↑H + ↑N` (pointwise set addition)\nwhen `N` is normal."]
 theorem mul_normal (H N : Subgroup G) [N.Normal] : (↑(H ⊔ N) : Set G) = H * N :=
   Set.Subset.antisymm
-    (show H ⊔ N ≤ mulNormalAux H N by
-      rw [sup_eq_closure]
-      apply sInf_le _
-      dsimp
-      rfl)
+    (show H ⊔ N ≤ mulNormalAux H N by rw [sup_eq_closure]; apply sInf_le _; dsimp; rfl)
     ((sup_eq_closure H N).symm ▸ subset_closure)
 #align subgroup.mul_normal Subgroup.mul_normal
 #align add_subgroup.add_normal AddSubgroup.add_normal
@@ -283,11 +277,7 @@ Case conversion may be inaccurate. Consider using '#align subgroup.normal_mul Su
       "The carrier of `N ⊔ H` is just `↑N + ↑H` (pointwise set addition)\nwhen `N` is normal."]
 theorem normal_mul (N H : Subgroup G) [N.Normal] : (↑(N ⊔ H) : Set G) = N * H :=
   Set.Subset.antisymm
-    (show N ⊔ H ≤ normalMulAux N H by
-      rw [sup_eq_closure]
-      apply sInf_le _
-      dsimp
-      rfl)
+    (show N ⊔ H ≤ normalMulAux N H by rw [sup_eq_closure]; apply sInf_le _; dsimp; rfl)
     ((sup_eq_closure N H).symm ▸ subset_closure)
 #align subgroup.normal_mul Subgroup.normal_mul
 #align add_subgroup.normal_add AddSubgroup.normal_add
@@ -358,11 +348,8 @@ instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_opposite_image_mul_preimage Subgroup.smul_opposite_image_mul_preimageₓ'. -/
 @[to_additive]
 theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.opposite) (s : Set G) :
-    (fun y => h • y) '' (Mul.mul g ⁻¹' s) = Mul.mul g ⁻¹' ((fun y => h • y) '' s) :=
-  by
-  ext x
-  cases h
-  simp [(· • ·), mul_assoc]
+    (fun y => h • y) '' (Mul.mul g ⁻¹' s) = Mul.mul g ⁻¹' ((fun y => h • y) '' s) := by ext x;
+  cases h; simp [(· • ·), mul_assoc]
 #align subgroup.smul_opposite_image_mul_preimage Subgroup.smul_opposite_image_mul_preimage
 #align add_subgroup.vadd_opposite_image_add_preimage AddSubgroup.vadd_opposite_image_add_preimage

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -239,7 +239,6 @@ private def mul_normal_aux (H N : Subgroup G) [hN : N.Normal] : Subgroup G
   inv_mem' := fun x ⟨h, n, hh, hn, hx⟩ =>
     ⟨h⁻¹, h * n⁻¹ * h⁻¹, H.inv_mem hh, hN.conj_mem _ (N.inv_mem hn) h, by
       rw [mul_assoc h, inv_mul_cancel_left, ← hx, mul_inv_rev]⟩
-#align subgroup.mul_normal_aux subgroup.mul_normal_aux
 
 /- warning: subgroup.mul_normal -> Subgroup.mul_normal is a dubious translation:
 lean 3 declaration is
@@ -272,7 +271,6 @@ private def normal_mul_aux (N H : Subgroup G) [hN : N.Normal] : Subgroup G
   inv_mem' := fun x ⟨n, h, hn, hh, hx⟩ =>
     ⟨h⁻¹ * n⁻¹ * h, h⁻¹, by simpa using hN.conj_mem _ (N.inv_mem hn) h⁻¹, H.inv_mem hh, by
       rw [mul_inv_cancel_right, ← mul_inv_rev, hx]⟩
-#align subgroup.normal_mul_aux subgroup.normal_mul_aux
 
 /- warning: subgroup.normal_mul -> Subgroup.normal_mul is a dubious translation:
 lean 3 declaration is
@@ -356,10 +354,7 @@ instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔
 #align subgroup.sup_normal Subgroup.sup_normal
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_opposite_image_mul_preimage Subgroup.smul_opposite_image_mul_preimageₓ'. -/
 @[to_additive]
 theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.opposite) (s : Set G) :
@@ -481,10 +476,7 @@ instance pointwise_isCentralScalar [MulDistribMulAction αᵐᵒᵖ G] [IsCentra
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_le_of_le Subgroup.conj_smul_le_of_leₓ'. -/
 theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.conj (h : G) • P ≤ H :=
   by
@@ -493,10 +485,7 @@ theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.co
 #align subgroup.conj_smul_le_of_le Subgroup.conj_smul_le_of_le
 
 /- warning: subgroup.conj_smul_subgroup_of -> Subgroup.conj_smul_subgroupOf is a dubious translation:
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G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, 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_inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G 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(MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_subgroup_of Subgroup.conj_smul_subgroupOfₓ'. -/
 theorem conj_smul_subgroupOf {P H : Subgroup G} (hP : P ≤ H) (h : H) :
     MulAut.conj h • P.subgroupOf H = (MulAut.conj (h : G) • P).subgroupOf H :=
@@ -659,10 +648,7 @@ theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (
 #align subgroup.normal.conj_act Subgroup.Normal.conjAct
 
 /- warning: subgroup.smul_normal -> Subgroup.smul_normal is a dubious translation:
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G 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+<too large>
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_normal Subgroup.smul_normalₓ'. -/
 @[simp]
 theorem smul_normal (g : G) (H : Subgroup G) [h : Normal H] : MulAut.conj g • H = H :=

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -359,7 +359,7 @@ instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔
 lean 3 declaration is
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 but is expected to have type
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(Set.preimage.{u1, u1} G G (fun (x._@.Mathlib.GroupTheory.Subgroup.Pointwise._hyg.2271 : G) => HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g x._@.Mathlib.GroupTheory.Subgroup.Pointwise._hyg.2271) (Set.image.{u1, u1} G G (fun (y : G) => HSMul.hSMul.{u1, u1, u1} (Subtype.{succ u1} (MulOpposite.{u1} G) (fun (x : MulOpposite.{u1} G) => Membership.mem.{u1, u1} (MulOpposite.{u1} G) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (SetLike.instMembership.{u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (MulOpposite.{u1} G) (Subgroup.instSetLikeSubgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H))) G G (instHSMul.{u1, u1} (Subtype.{succ u1} (MulOpposite.{u1} G) (fun (x : MulOpposite.{u1} G) => Membership.mem.{u1, u1} (MulOpposite.{u1} G) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (SetLike.instMembership.{u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (MulOpposite.{u1} G) (Subgroup.instSetLikeSubgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H))) G (Submonoid.smul.{u1, u1} (MulOpposite.{u1} G) G (Monoid.toMulOneClass.{u1} (MulOpposite.{u1} G) (DivInvMonoid.toMonoid.{u1} (MulOpposite.{u1} G) (Group.toDivInvMonoid.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)))) (Mul.toHasOppositeSMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.toSubmonoid.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H)))) h y) s))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Subgroup.{u1} G _inst_1} (g : G) (h : Subtype.{succ u1} (MulOpposite.{u1} G) (fun (x : MulOpposite.{u1} G) => Membership.mem.{u1, u1} (MulOpposite.{u1} G) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (SetLike.instMembership.{u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (MulOpposite.{u1} G) (Subgroup.instSetLikeSubgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H))) (s : Set.{u1} G), Eq.{succ u1} (Set.{u1} G) (Set.image.{u1, u1} G G (fun (y : G) => HSMul.hSMul.{u1, u1, u1} (Subtype.{succ u1} (MulOpposite.{u1} G) (fun (x : MulOpposite.{u1} G) => Membership.mem.{u1, u1} (MulOpposite.{u1} G) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (SetLike.instMembership.{u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (MulOpposite.{u1} G) (Subgroup.instSetLikeSubgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H))) G G (instHSMul.{u1, u1} (Subtype.{succ u1} (MulOpposite.{u1} G) (fun (x : MulOpposite.{u1} G) => Membership.mem.{u1, u1} (MulOpposite.{u1} G) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (SetLike.instMembership.{u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (MulOpposite.{u1} G) (Subgroup.instSetLikeSubgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H))) G (Submonoid.smul.{u1, u1} (MulOpposite.{u1} G) G (Monoid.toMulOneClass.{u1} (MulOpposite.{u1} G) (DivInvMonoid.toMonoid.{u1} (MulOpposite.{u1} G) (Group.toDivInvMonoid.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)))) (Mul.toHasOppositeSMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.toSubmonoid.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H)))) h y) (Set.preimage.{u1, u1} G G (fun (x._@.Mathlib.GroupTheory.Subgroup.Pointwise._hyg.2256 : G) => HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g x._@.Mathlib.GroupTheory.Subgroup.Pointwise._hyg.2256) s)) (Set.preimage.{u1, u1} G G (fun (x._@.Mathlib.GroupTheory.Subgroup.Pointwise._hyg.2271 : G) => HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g x._@.Mathlib.GroupTheory.Subgroup.Pointwise._hyg.2271) (Set.image.{u1, u1} G G (fun (y : G) => HSMul.hSMul.{u1, u1, u1} (Subtype.{succ u1} (MulOpposite.{u1} G) (fun (x : MulOpposite.{u1} G) => Membership.mem.{u1, u1} (MulOpposite.{u1} G) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (SetLike.instMembership.{u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (MulOpposite.{u1} G) (Subgroup.instSetLikeSubgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H))) G G (instHSMul.{u1, u1} (Subtype.{succ u1} (MulOpposite.{u1} G) (fun (x : MulOpposite.{u1} G) => Membership.mem.{u1, u1} (MulOpposite.{u1} G) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (SetLike.instMembership.{u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (MulOpposite.{u1} G) (Subgroup.instSetLikeSubgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H))) G (Submonoid.smul.{u1, u1} (MulOpposite.{u1} G) G (Monoid.toMulOneClass.{u1} (MulOpposite.{u1} G) (DivInvMonoid.toMonoid.{u1} (MulOpposite.{u1} G) (Group.toDivInvMonoid.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)))) (Mul.toHasOppositeSMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.toSubmonoid.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H)))) h y) s))
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_opposite_image_mul_preimage Subgroup.smul_opposite_image_mul_preimageₓ'. -/
 @[to_additive]
 theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.opposite) (s : Set G) :
@@ -399,7 +399,7 @@ open Pointwise
 lean 3 declaration is
   forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} (S : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) a S) (Subgroup.map.{u2, u2} G _inst_1 G _inst_1 (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.monoid.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (fun (_x : MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.monoid.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) => α -> (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))) (MonoidHom.hasCoeToFun.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.monoid.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MulDistribMulAction.toMonoidEnd.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4) a) S)
 but is expected to have type
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} (S : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a S) (Subgroup.map.{u2, u2} G _inst_1 G _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α _inst_3)) (MulOneClass.toMul.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))) (MonoidHom.monoidHomClass.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))))) (MulDistribMulAction.toMonoidEnd.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4) a) S)
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} (S : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a S) (Subgroup.map.{u2, u2} G _inst_1 G _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α _inst_3)) (MulOneClass.toMul.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))) (MonoidHom.monoidHomClass.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))))) (MulDistribMulAction.toMonoidEnd.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4) a) S)
 Case conversion may be inaccurate. Consider using '#align subgroup.pointwise_smul_def Subgroup.pointwise_smul_defₓ'. -/
 theorem pointwise_smul_def {a : α} (S : Subgroup G) :
     a • S = S.map (MulDistribMulAction.toMonoidEnd _ _ a) :=
@@ -484,7 +484,7 @@ instance pointwise_isCentralScalar [MulDistribMulAction αᵐᵒᵖ G] [IsCentra
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toHasLe.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) P H) -> (forall (h : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toHasLe.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (SMul.smul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (MulAction.toHasSmul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) G _inst_1 (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (fun (_x : MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) => G -> (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (MonoidHom.hasCoeToFun.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MulAut.conj.{u1} G _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x H))))) h)) P) H)
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) P H) -> (forall (h : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H)
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) P H) -> (forall (h : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H)
 Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_le_of_le Subgroup.conj_smul_le_of_leₓ'. -/
 theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.conj (h : G) • P ≤ H :=
   by
@@ -496,7 +496,7 @@ theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.co
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toHasLe.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) P H) -> (forall (h : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H), Eq.{succ u1} (Subgroup.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) (Subgroup.toGroup.{u1} G _inst_1 H)) (SMul.smul.{u1, u1} (MulAut.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) (MulOneClass.toHasMul.{u1} 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(MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MulAut.conj.{u1} G _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x H))))) h)) P) H))
 but is expected to have type
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_inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Group.toDivInvMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)))))))))))) (MulAut.conj.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)) h) (Subgroup.subgroupOf.{u1} G _inst_1 P H)) (Subgroup.subgroupOf.{u1} G _inst_1 (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G 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(DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) P H) -> (forall (h : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)), Eq.{succ u1} (Subgroup.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) => MulAut.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Monoid.toMulOneClass.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => 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(Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Monoid.toMulOneClass.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Group.toDivInvMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)))))) (MulAut.instGroupMulAut.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Monoid.toMulOneClass.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Group.toDivInvMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)))))))))))) (MulAut.conj.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)) h) (Subgroup.subgroupOf.{u1} G _inst_1 P H)) (Subgroup.subgroupOf.{u1} G _inst_1 (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H))
 Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_subgroup_of Subgroup.conj_smul_subgroupOfₓ'. -/
 theorem conj_smul_subgroupOf {P H : Subgroup G} (hP : P ≤ H) (h : H) :
     MulAut.conj h • P.subgroupOf H = (MulAut.conj (h : G) • P).subgroupOf H :=
@@ -662,7 +662,7 @@ theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (g : G) (H : Subgroup.{u1} G _inst_1) [h : Subgroup.Normal.{u1} G _inst_1 H], Eq.{succ u1} (Subgroup.{u1} G _inst_1) (SMul.smul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (MulAction.toHasSmul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) G _inst_1 (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (fun (_x : MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) => G -> (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (MonoidHom.hasCoeToFun.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MulAut.conj.{u1} G _inst_1) g) H) H
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (g : G) (H : Subgroup.{u1} G _inst_1) [h : Subgroup.Normal.{u1} G _inst_1 H], Eq.{succ u1} (Subgroup.{u1} G _inst_1) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) g) H) H
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (g : G) (H : Subgroup.{u1} G _inst_1) [h : Subgroup.Normal.{u1} G _inst_1 H], Eq.{succ u1} (Subgroup.{u1} G _inst_1) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) g) H) H
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_normal Subgroup.smul_normalₓ'. -/
 @[simp]
 theorem smul_normal (g : G) (H : Subgroup G) [h : Normal H] : MulAut.conj g • H = H :=

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -200,7 +200,7 @@ theorem iSup_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈
 
 /- warning: subgroup.closure_mul_le -> Subgroup.closure_mul_le is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (S : Set.{u1} G) (T : Set.{u1} G), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S T)) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) (Subgroup.closure.{u1} G _inst_1 S) (Subgroup.closure.{u1} G _inst_1 T))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (S : Set.{u1} G) (T : Set.{u1} G), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toHasLe.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S T)) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) (Subgroup.closure.{u1} G _inst_1 S) (Subgroup.closure.{u1} G _inst_1 T))
 but is expected to have type
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (S : Set.{u1} G) (T : Set.{u1} G), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S T)) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (Subgroup.closure.{u1} G _inst_1 S) (Subgroup.closure.{u1} G _inst_1 T))
 Case conversion may be inaccurate. Consider using '#align subgroup.closure_mul_le Subgroup.closure_mul_leₓ'. -/
@@ -296,7 +296,7 @@ theorem normal_mul (N H : Subgroup G) [N.Normal] : (↑(N ⊔ H) : Set G) = N *
 
 /- warning: subgroup.mul_inf_assoc -> Subgroup.mul_inf_assoc is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A C) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Inf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.hasInf.{u1} G _inst_1) B C))) (Inf.inf.{u1} (Set.{u1} G) (SemilatticeInf.toHasInf.{u1} (Set.{u1} G) (Lattice.toSemilatticeInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.completeBooleanAlgebra.{u1} G)))))))) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) B)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C)))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toHasLe.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A C) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Inf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.hasInf.{u1} G _inst_1) B C))) (Inf.inf.{u1} (Set.{u1} G) (SemilatticeInf.toHasInf.{u1} (Set.{u1} G) (Lattice.toSemilatticeInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.completeBooleanAlgebra.{u1} G)))))))) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) B)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C)))
 but is expected to have type
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) A C) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) A) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Inf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instInfSubgroup.{u1} G _inst_1) B C))) (Inf.inf.{u1} (Set.{u1} G) (Lattice.toInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.instCompleteBooleanAlgebraSet.{u1} G))))))) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) A) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) B)) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) C)))
 Case conversion may be inaccurate. Consider using '#align subgroup.mul_inf_assoc Subgroup.mul_inf_assocₓ'. -/
@@ -318,7 +318,7 @@ theorem mul_inf_assoc (A B C : Subgroup G) (h : A ≤ C) : (A : Set G) * ↑(B 
 
 /- warning: subgroup.inf_mul_assoc -> Subgroup.inf_mul_assoc is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C A) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Inf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.hasInf.{u1} G _inst_1) A B)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C)) (Inf.inf.{u1} (Set.{u1} G) (SemilatticeInf.toHasInf.{u1} (Set.{u1} G) (Lattice.toSemilatticeInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.completeBooleanAlgebra.{u1} G)))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) B) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C))))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toHasLe.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C A) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Inf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.hasInf.{u1} G _inst_1) A B)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C)) (Inf.inf.{u1} (Set.{u1} G) (SemilatticeInf.toHasInf.{u1} (Set.{u1} G) (Lattice.toSemilatticeInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.completeBooleanAlgebra.{u1} G)))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) B) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C))))
 but is expected to have type
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) C A) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Inf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instInfSubgroup.{u1} G _inst_1) A B)) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) C)) (Inf.inf.{u1} (Set.{u1} G) (Lattice.toInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.instCompleteBooleanAlgebraSet.{u1} G))))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) A) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) B) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) C))))
 Case conversion may be inaccurate. Consider using '#align subgroup.inf_mul_assoc Subgroup.inf_mul_assocₓ'. -/
@@ -482,7 +482,7 @@ instance pointwise_isCentralScalar [MulDistribMulAction αᵐᵒᵖ G] [IsCentra
 
 /- warning: subgroup.conj_smul_le_of_le -> Subgroup.conj_smul_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) P H) -> (forall (h : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (SMul.smul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (MulAction.toHasSmul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) G _inst_1 (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G 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(Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) => G -> (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (MonoidHom.hasCoeToFun.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MulAut.conj.{u1} G _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x H))))) h)) P) H)
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toHasLe.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) P H) -> (forall (h : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toHasLe.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (SMul.smul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (MulAction.toHasSmul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) G _inst_1 (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (fun (_x : MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) => G -> (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (MonoidHom.hasCoeToFun.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MulAut.conj.{u1} G _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x H))))) h)) P) H)
 but is expected to have type
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) P H) -> (forall (h : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H)
 Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_le_of_le Subgroup.conj_smul_le_of_leₓ'. -/
@@ -494,7 +494,7 @@ theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.co
 
 /- warning: subgroup.conj_smul_subgroup_of -> Subgroup.conj_smul_subgroupOf is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) P H) -> (forall (h : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H), Eq.{succ u1} (Subgroup.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) (Subgroup.toGroup.{u1} G _inst_1 H)) (SMul.smul.{u1, u1} (MulAut.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) (MulOneClass.toHasMul.{u1} 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(Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) => G -> (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (MonoidHom.hasCoeToFun.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MulAut.conj.{u1} G _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x H))))) h)) P) H))
 but is expected to have type
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) P H) -> (forall (h : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)), Eq.{succ u1} (Subgroup.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)) (HSMul.hSMul.{u1, u1, u1} ((fun 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_inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Group.toDivInvMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)))))))))))) (MulAut.conj.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)) h) (Subgroup.subgroupOf.{u1} G _inst_1 P H)) (Subgroup.subgroupOf.{u1} G _inst_1 (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H))
 Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_subgroup_of Subgroup.conj_smul_subgroupOfₓ'. -/
@@ -550,7 +550,7 @@ theorem mem_inv_pointwise_smul_iff {a : α} {S : Subgroup G} {x : G} : x ∈ a
 
 /- warning: subgroup.pointwise_smul_le_pointwise_smul_iff -> Subgroup.pointwise_smul_le_pointwise_smul_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a S) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S T)
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a S) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S T)
 but is expected to have type
   forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))))) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a S) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a T)) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))))) S T)
 Case conversion may be inaccurate. Consider using '#align subgroup.pointwise_smul_le_pointwise_smul_iff Subgroup.pointwise_smul_le_pointwise_smul_iffₓ'. -/
@@ -561,7 +561,7 @@ theorem pointwise_smul_le_pointwise_smul_iff {a : α} {S T : Subgroup G} : a •
 
 /- warning: subgroup.pointwise_smul_subset_iff -> Subgroup.pointwise_smul_subset_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a S) T) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) a) T))
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a S) T) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) a) T))
 but is expected to have type
   forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))))) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a S) T) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))))) S (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) (Inv.inv.{u1} α (InvOneClass.toInv.{u1} α (DivInvOneMonoid.toInvOneClass.{u1} α (DivisionMonoid.toDivInvOneMonoid.{u1} α (Group.toDivisionMonoid.{u1} α _inst_3)))) a) T))
 Case conversion may be inaccurate. Consider using '#align subgroup.pointwise_smul_subset_iff Subgroup.pointwise_smul_subset_iffₓ'. -/
@@ -571,7 +571,7 @@ theorem pointwise_smul_subset_iff {a : α} {S T : Subgroup G} : a • S ≤ T 
 
 /- warning: subgroup.subset_pointwise_smul_iff -> Subgroup.subset_pointwise_smul_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) a) S) T)
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) a) S) T)
 but is expected to have type
   forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))))) S (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a T)) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))))) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) (Inv.inv.{u1} α (InvOneClass.toInv.{u1} α (DivInvOneMonoid.toInvOneClass.{u1} α (DivisionMonoid.toDivInvOneMonoid.{u1} α (Group.toDivisionMonoid.{u1} α _inst_3)))) a) S) T)
 Case conversion may be inaccurate. Consider using '#align subgroup.subset_pointwise_smul_iff Subgroup.subset_pointwise_smul_iffₓ'. -/
@@ -713,7 +713,7 @@ theorem mem_inv_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : Subgroup G) (
 
 /- warning: subgroup.pointwise_smul_le_pointwise_smul_iff₀ -> Subgroup.pointwise_smul_le_pointwise_smul_iff₀ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a S) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S T))
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a S) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S T))
 but is expected to have type
   forall {α : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u1} G] [_inst_3 : GroupWithZero.{u2} α] [_inst_4 : MulDistribMulAction.{u2, u1} α G (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))] {a : α}, (Ne.{succ u2} α a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (MonoidWithZero.toZero.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3))))) -> (forall {S : Subgroup.{u1} G _inst_1} {T : Subgroup.{u1} G _inst_1}, Iff (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (HSMul.hSMul.{u2, u1, u1} α (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (Subgroup.pointwiseMulAction.{u2, u1} α G _inst_1 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) a S) (HSMul.hSMul.{u2, u1, u1} α (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (Subgroup.pointwiseMulAction.{u2, u1} α G _inst_1 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) a T)) (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) S T))
 Case conversion may be inaccurate. Consider using '#align subgroup.pointwise_smul_le_pointwise_smul_iff₀ Subgroup.pointwise_smul_le_pointwise_smul_iff₀ₓ'. -/
@@ -725,7 +725,7 @@ theorem pointwise_smul_le_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) {S T : S
 
 /- warning: subgroup.pointwise_smul_le_iff₀ -> Subgroup.pointwise_smul_le_iff₀ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a S) T) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α _inst_3)) a) T)))
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a S) T) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α _inst_3)) a) T)))
 but is expected to have type
   forall {α : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u1} G] [_inst_3 : GroupWithZero.{u2} α] [_inst_4 : MulDistribMulAction.{u2, u1} α G (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))] {a : α}, (Ne.{succ u2} α a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (MonoidWithZero.toZero.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3))))) -> (forall {S : Subgroup.{u1} G _inst_1} {T : Subgroup.{u1} G _inst_1}, Iff (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (HSMul.hSMul.{u2, u1, u1} α (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (Subgroup.pointwiseMulAction.{u2, u1} α G _inst_1 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) a S) T) (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) S (HSMul.hSMul.{u2, u1, u1} α (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (Subgroup.pointwiseMulAction.{u2, u1} α G _inst_1 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) (Inv.inv.{u2} α (GroupWithZero.toInv.{u2} α _inst_3) a) T)))
 Case conversion may be inaccurate. Consider using '#align subgroup.pointwise_smul_le_iff₀ Subgroup.pointwise_smul_le_iff₀ₓ'. -/
@@ -735,7 +735,7 @@ theorem pointwise_smul_le_iff₀ {a : α} (ha : a ≠ 0) {S T : Subgroup G} : a
 
 /- warning: subgroup.le_pointwise_smul_iff₀ -> Subgroup.le_pointwise_smul_iff₀ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toLE.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α _inst_3)) a) S) T))
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : Subgroup.{u2} G _inst_1} {T : Subgroup.{u2} G _inst_1}, Iff (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) S (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (Subgroup.{u2} G _inst_1) (Preorder.toHasLe.{u2} (Subgroup.{u2} G _inst_1) (PartialOrder.toPreorder.{u2} (Subgroup.{u2} G _inst_1) (SetLike.partialOrder.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α _inst_3)) a) S) T))
 but is expected to have type
   forall {α : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u1} G] [_inst_3 : GroupWithZero.{u2} α] [_inst_4 : MulDistribMulAction.{u2, u1} α G (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))] {a : α}, (Ne.{succ u2} α a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (MonoidWithZero.toZero.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3))))) -> (forall {S : Subgroup.{u1} G _inst_1} {T : Subgroup.{u1} G _inst_1}, Iff (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) S (HSMul.hSMul.{u2, u1, u1} α (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (Subgroup.pointwiseMulAction.{u2, u1} α G _inst_1 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) a T)) (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (HSMul.hSMul.{u2, u1, u1} α (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u2, u1} α (Subgroup.{u1} G _inst_1) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (Subgroup.pointwiseMulAction.{u2, u1} α G _inst_1 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) (Inv.inv.{u2} α (GroupWithZero.toInv.{u2} α _inst_3) a) S) T))
 Case conversion may be inaccurate. Consider using '#align subgroup.le_pointwise_smul_iff₀ Subgroup.le_pointwise_smul_iff₀ₓ'. -/
@@ -863,7 +863,7 @@ theorem mem_inv_pointwise_smul_iff {a : α} {S : AddSubgroup A} {x : A} : x ∈
 
 /- warning: add_subgroup.pointwise_smul_le_pointwise_smul_iff -> AddSubgroup.pointwise_smul_le_pointwise_smul_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Group.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α} {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a S) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S T)
+  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Group.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α} {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a S) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S T)
 but is expected to have type
   forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Group.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α} {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubgroup.{u2} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u2} A _inst_2))))) (HSMul.hSMul.{u1, u2, u2} α (AddSubgroup.{u2} A _inst_2) (AddSubgroup.{u2} A _inst_2) (instHSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a S) (HSMul.hSMul.{u1, u2, u2} α (AddSubgroup.{u2} A _inst_2) (AddSubgroup.{u2} A _inst_2) (instHSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a T)) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubgroup.{u2} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u2} A _inst_2))))) S T)
 Case conversion may be inaccurate. Consider using '#align add_subgroup.pointwise_smul_le_pointwise_smul_iff AddSubgroup.pointwise_smul_le_pointwise_smul_iffₓ'. -/
@@ -875,7 +875,7 @@ theorem pointwise_smul_le_pointwise_smul_iff {a : α} {S T : AddSubgroup A} :
 
 /- warning: add_subgroup.pointwise_smul_le_iff -> AddSubgroup.pointwise_smul_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Group.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α} {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a S) T) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) a) T))
+  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Group.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α} {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a S) T) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) a) T))
 but is expected to have type
   forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Group.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α} {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubgroup.{u2} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u2} A _inst_2))))) (HSMul.hSMul.{u1, u2, u2} α (AddSubgroup.{u2} A _inst_2) (AddSubgroup.{u2} A _inst_2) (instHSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a S) T) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubgroup.{u2} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u2} A _inst_2))))) S (HSMul.hSMul.{u1, u2, u2} α (AddSubgroup.{u2} A _inst_2) (AddSubgroup.{u2} A _inst_2) (instHSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) (Inv.inv.{u1} α (InvOneClass.toInv.{u1} α (DivInvOneMonoid.toInvOneClass.{u1} α (DivisionMonoid.toDivInvOneMonoid.{u1} α (Group.toDivisionMonoid.{u1} α _inst_3)))) a) T))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.pointwise_smul_le_iff AddSubgroup.pointwise_smul_le_iffₓ'. -/
@@ -885,7 +885,7 @@ theorem pointwise_smul_le_iff {a : α} {S T : AddSubgroup A} : a • S ≤ T ↔
 
 /- warning: add_subgroup.le_pointwise_smul_iff -> AddSubgroup.le_pointwise_smul_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Group.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α} {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) a) S) T)
+  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Group.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α} {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) a) S) T)
 but is expected to have type
   forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Group.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α} {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubgroup.{u2} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u2} A _inst_2))))) S (HSMul.hSMul.{u1, u2, u2} α (AddSubgroup.{u2} A _inst_2) (AddSubgroup.{u2} A _inst_2) (instHSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a T)) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubgroup.{u2} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubgroup.{u2} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u2} A _inst_2))))) (HSMul.hSMul.{u1, u2, u2} α (AddSubgroup.{u2} A _inst_2) (AddSubgroup.{u2} A _inst_2) (instHSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) (Inv.inv.{u1} α (InvOneClass.toInv.{u1} α (DivInvOneMonoid.toInvOneClass.{u1} α (DivisionMonoid.toDivInvOneMonoid.{u1} α (Group.toDivisionMonoid.{u1} α _inst_3)))) a) S) T)
 Case conversion may be inaccurate. Consider using '#align add_subgroup.le_pointwise_smul_iff AddSubgroup.le_pointwise_smul_iffₓ'. -/
@@ -937,7 +937,7 @@ theorem mem_inv_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) (S : AddSubgroup A
 
 /- warning: add_subgroup.pointwise_smul_le_pointwise_smul_iff₀ -> AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a S) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S T))
+  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a S) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S T))
 but is expected to have type
   forall {α : Type.{u2}} {A : Type.{u1}} [_inst_2 : AddGroup.{u1} A] [_inst_3 : GroupWithZero.{u2} α] [_inst_4 : DistribMulAction.{u2, u1} α A (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_2))] {a : α}, (Ne.{succ u2} α a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (MonoidWithZero.toZero.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3))))) -> (forall {S : AddSubgroup.{u1} A _inst_2} {T : AddSubgroup.{u1} A _inst_2}, Iff (LE.le.{u1} (AddSubgroup.{u1} A _inst_2) (Preorder.toLE.{u1} (AddSubgroup.{u1} A _inst_2) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} A _inst_2))))) (HSMul.hSMul.{u2, u1, u1} α (AddSubgroup.{u1} A _inst_2) (AddSubgroup.{u1} A _inst_2) (instHSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MulAction.toSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u2, u1} α A _inst_2 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) a S) (HSMul.hSMul.{u2, u1, u1} α (AddSubgroup.{u1} A _inst_2) (AddSubgroup.{u1} A _inst_2) (instHSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MulAction.toSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u2, u1} α A _inst_2 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) a T)) (LE.le.{u1} (AddSubgroup.{u1} A _inst_2) (Preorder.toLE.{u1} (AddSubgroup.{u1} A _inst_2) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} A _inst_2))))) S T))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.pointwise_smul_le_pointwise_smul_iff₀ AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀ₓ'. -/
@@ -949,7 +949,7 @@ theorem pointwise_smul_le_pointwise_smul_iff₀ {a : α} (ha : a ≠ 0) {S T : A
 
 /- warning: add_subgroup.pointwise_smul_le_iff₀ -> AddSubgroup.pointwise_smul_le_iff₀ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a S) T) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α _inst_3)) a) T)))
+  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a S) T) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α _inst_3)) a) T)))
 but is expected to have type
   forall {α : Type.{u2}} {A : Type.{u1}} [_inst_2 : AddGroup.{u1} A] [_inst_3 : GroupWithZero.{u2} α] [_inst_4 : DistribMulAction.{u2, u1} α A (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_2))] {a : α}, (Ne.{succ u2} α a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (MonoidWithZero.toZero.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3))))) -> (forall {S : AddSubgroup.{u1} A _inst_2} {T : AddSubgroup.{u1} A _inst_2}, Iff (LE.le.{u1} (AddSubgroup.{u1} A _inst_2) (Preorder.toLE.{u1} (AddSubgroup.{u1} A _inst_2) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} A _inst_2))))) (HSMul.hSMul.{u2, u1, u1} α (AddSubgroup.{u1} A _inst_2) (AddSubgroup.{u1} A _inst_2) (instHSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MulAction.toSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u2, u1} α A _inst_2 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) a S) T) (LE.le.{u1} (AddSubgroup.{u1} A _inst_2) (Preorder.toLE.{u1} (AddSubgroup.{u1} A _inst_2) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} A _inst_2))))) S (HSMul.hSMul.{u2, u1, u1} α (AddSubgroup.{u1} A _inst_2) (AddSubgroup.{u1} A _inst_2) (instHSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MulAction.toSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u2, u1} α A _inst_2 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) (Inv.inv.{u2} α (GroupWithZero.toInv.{u2} α _inst_3) a) T)))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.pointwise_smul_le_iff₀ AddSubgroup.pointwise_smul_le_iff₀ₓ'. -/
@@ -960,7 +960,7 @@ theorem pointwise_smul_le_iff₀ {a : α} (ha : a ≠ 0) {S T : AddSubgroup A} :
 
 /- warning: add_subgroup.le_pointwise_smul_iff₀ -> AddSubgroup.le_pointwise_smul_iff₀ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toLE.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α _inst_3)) a) S) T))
+  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : GroupWithZero.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] {a : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)))))))) -> (forall {S : AddSubgroup.{u2} A _inst_2} {T : AddSubgroup.{u2} A _inst_2}, Iff (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) S (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) a T)) (LE.le.{u2} (AddSubgroup.{u2} A _inst_2) (Preorder.toHasLe.{u2} (AddSubgroup.{u2} A _inst_2) (PartialOrder.toPreorder.{u2} (AddSubgroup.{u2} A _inst_2) (SetLike.partialOrder.{u2, u2} (AddSubgroup.{u2} A _inst_2) A (AddSubgroup.setLike.{u2} A _inst_2)))) (SMul.smul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 (MonoidWithZero.toMonoid.{u1} α (GroupWithZero.toMonoidWithZero.{u1} α _inst_3)) _inst_4)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α _inst_3)) a) S) T))
 but is expected to have type
   forall {α : Type.{u2}} {A : Type.{u1}} [_inst_2 : AddGroup.{u1} A] [_inst_3 : GroupWithZero.{u2} α] [_inst_4 : DistribMulAction.{u2, u1} α A (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_2))] {a : α}, (Ne.{succ u2} α a (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (MonoidWithZero.toZero.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3))))) -> (forall {S : AddSubgroup.{u1} A _inst_2} {T : AddSubgroup.{u1} A _inst_2}, Iff (LE.le.{u1} (AddSubgroup.{u1} A _inst_2) (Preorder.toLE.{u1} (AddSubgroup.{u1} A _inst_2) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} A _inst_2))))) S (HSMul.hSMul.{u2, u1, u1} α (AddSubgroup.{u1} A _inst_2) (AddSubgroup.{u1} A _inst_2) (instHSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MulAction.toSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u2, u1} α A _inst_2 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) a T)) (LE.le.{u1} (AddSubgroup.{u1} A _inst_2) (Preorder.toLE.{u1} (AddSubgroup.{u1} A _inst_2) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} A _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} A _inst_2) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} A _inst_2))))) (HSMul.hSMul.{u2, u1, u1} α (AddSubgroup.{u1} A _inst_2) (AddSubgroup.{u1} A _inst_2) (instHSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MulAction.toSMul.{u2, u1} α (AddSubgroup.{u1} A _inst_2) (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) (AddSubgroup.pointwiseMulAction.{u2, u1} α A _inst_2 (MonoidWithZero.toMonoid.{u2} α (GroupWithZero.toMonoidWithZero.{u2} α _inst_3)) _inst_4))) (Inv.inv.{u2} α (GroupWithZero.toInv.{u2} α _inst_3) a) S) T))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.le_pointwise_smul_iff₀ AddSubgroup.le_pointwise_smul_iff₀ₓ'. -/

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -152,19 +152,19 @@ theorem closure_induction'' {p : G → Prop} {x} (h : x ∈ closure s) (Hk : ∀
 #align subgroup.closure_induction'' Subgroup.closure_induction''
 #align add_subgroup.closure_induction'' AddSubgroup.closure_induction''
 
-/- warning: subgroup.supr_induction -> Subgroup.supᵢ_induction is a dubious translation:
+/- warning: subgroup.supr_induction -> Subgroup.iSup_induction is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Sort.{u2}} (S : ι -> (Subgroup.{u1} G _inst_1)) {C : G -> Prop} {x : G}, (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i))) -> (forall (i : ι) (x : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (S i)) -> (C x)) -> (C (OfNat.ofNat.{u1} G 1 (OfNat.mk.{u1} G 1 (One.one.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) -> (forall (x : G) (y : G), (C x) -> (C y) -> (C (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x y))) -> (C x)
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Sort.{u2}} (S : ι -> (Subgroup.{u1} G _inst_1)) {C : G -> Prop} {x : G}, (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i))) -> (forall (i : ι) (x : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (S i)) -> (C x)) -> (C (OfNat.ofNat.{u1} G 1 (OfNat.mk.{u1} G 1 (One.one.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) -> (forall (x : G) (y : G), (C x) -> (C y) -> (C (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x y))) -> (C x)
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Sort.{u2}} (S : ι -> (Subgroup.{u1} G _inst_1)) {C : G -> Prop} {x : G}, (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i))) -> (forall (i : ι) (x : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (S i)) -> (C x)) -> (C (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1))))))) -> (forall (x : G) (y : G), (C x) -> (C y) -> (C (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x y))) -> (C x)
-Case conversion may be inaccurate. Consider using '#align subgroup.supr_induction Subgroup.supᵢ_inductionₓ'. -/
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Sort.{u2}} (S : ι -> (Subgroup.{u1} G _inst_1)) {C : G -> Prop} {x : G}, (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i))) -> (forall (i : ι) (x : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (S i)) -> (C x)) -> (C (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1))))))) -> (forall (x : G) (y : G), (C x) -> (C y) -> (C (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x y))) -> (C x)
+Case conversion may be inaccurate. Consider using '#align subgroup.supr_induction Subgroup.iSup_inductionₓ'. -/
 /-- An induction principle for elements of `⨆ i, S i`.
 If `C` holds for `1` and all elements of `S i` for all `i`, and is preserved under multiplication,
 then it holds for all elements of the supremum of `S`. -/
 @[elab_as_elim,
   to_additive
       " An induction principle for elements of `⨆ i, S i`.\nIf `C` holds for `0` and all elements of `S i` for all `i`, and is preserved under addition,\nthen it holds for all elements of the supremum of `S`. "]
-theorem supᵢ_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
+theorem iSup_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
     (hp : ∀ (i), ∀ x ∈ S i, C x) (h1 : C 1) (hmul : ∀ x y, C x → C y → C (x * y)) : C x :=
   by
   rw [supr_eq_closure] at hx
@@ -173,19 +173,19 @@ theorem supᵢ_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop}
     exact hp _ _ hi
   · obtain ⟨i, hi⟩ := set.mem_Union.mp hx
     exact hp _ _ (inv_mem hi)
-#align subgroup.supr_induction Subgroup.supᵢ_induction
-#align add_subgroup.supr_induction AddSubgroup.supᵢ_induction
+#align subgroup.supr_induction Subgroup.iSup_induction
+#align add_subgroup.supr_induction AddSubgroup.iSup_induction
 
-/- warning: subgroup.supr_induction' -> Subgroup.supᵢ_induction' is a dubious translation:
+/- warning: subgroup.supr_induction' -> Subgroup.iSup_induction' is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Sort.{u2}} (S : ι -> (Subgroup.{u1} G _inst_1)) {C : forall (x : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i))) -> Prop}, (forall (i : ι) (x : G) (H : Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (S i)), C x (Subgroup.mem_supᵢ_of_mem.{u1, u2} G _inst_1 ι (fun (i : ι) => S i) i x H)) -> (C (OfNat.ofNat.{u1} G 1 (OfNat.mk.{u1} G 1 (One.one.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (OneMemClass.one_mem.{u1, u1} (Subgroup.{u1} G _inst_1) G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.setLike.{u1} G _inst_1) (SubmonoidClass.to_oneMemClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.setLike.{u1} G _inst_1) (SubgroupClass.to_submonoidClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Group.toDivInvMonoid.{u1} G _inst_1) (Subgroup.setLike.{u1} G _inst_1) (Subgroup.subgroupClass.{u1} G _inst_1))) (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i)))) -> (forall (x : G) (y : G) (hx : Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i))) (hy : Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i))), (C x hx) -> (C y hy) -> (C (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x y) (MulMemClass.mul_mem.{u1, u1} (Subgroup.{u1} G _inst_1) G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.setLike.{u1} G _inst_1) (SubmonoidClass.to_mulMemClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.setLike.{u1} G _inst_1) (SubgroupClass.to_submonoidClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Group.toDivInvMonoid.{u1} G _inst_1) (Subgroup.setLike.{u1} G _inst_1) (Subgroup.subgroupClass.{u1} G _inst_1))) (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i)) x y hx hy))) -> (forall {x : G} (hx : Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i))), C x hx)
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Sort.{u2}} (S : ι -> (Subgroup.{u1} G _inst_1)) {C : forall (x : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i))) -> Prop}, (forall (i : ι) (x : G) (H : Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (S i)), C x (Subgroup.mem_iSup_of_mem.{u1, u2} G _inst_1 ι (fun (i : ι) => S i) i x H)) -> (C (OfNat.ofNat.{u1} G 1 (OfNat.mk.{u1} G 1 (One.one.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (OneMemClass.one_mem.{u1, u1} (Subgroup.{u1} G _inst_1) G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.setLike.{u1} G _inst_1) (SubmonoidClass.to_oneMemClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.setLike.{u1} G _inst_1) (SubgroupClass.to_submonoidClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Group.toDivInvMonoid.{u1} G _inst_1) (Subgroup.setLike.{u1} G _inst_1) (Subgroup.subgroupClass.{u1} G _inst_1))) (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i)))) -> (forall (x : G) (y : G) (hx : Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i))) (hy : Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i))), (C x hx) -> (C y hy) -> (C (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x y) (MulMemClass.mul_mem.{u1, u1} (Subgroup.{u1} G _inst_1) G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.setLike.{u1} G _inst_1) (SubmonoidClass.to_mulMemClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.setLike.{u1} G _inst_1) (SubgroupClass.to_submonoidClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Group.toDivInvMonoid.{u1} G _inst_1) (Subgroup.setLike.{u1} G _inst_1) (Subgroup.subgroupClass.{u1} G _inst_1))) (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i)) x y hx hy))) -> (forall {x : G} (hx : Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => S i))), C x hx)
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Sort.{u2}} (S : ι -> (Subgroup.{u1} G _inst_1)) {C : forall (x : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i))) -> Prop}, (forall (i : ι) (x : G) (H : Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (S i)), C x (Subgroup.mem_supᵢ_of_mem.{u1, u2} G _inst_1 ι (fun (i : ι) => S i) i x H)) -> (C (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))))) (OneMemClass.one_mem.{u1, u1} (Subgroup.{u1} G _inst_1) G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (SubmonoidClass.toOneMemClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (SubgroupClass.toSubmonoidClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Group.toDivInvMonoid.{u1} G _inst_1) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Subgroup.instSubgroupClassSubgroupToDivInvMonoidInstSetLikeSubgroup.{u1} G _inst_1))) (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i)))) -> (forall (x : G) (y : G) (hx : Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i))) (hy : Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i))), (C x hx) -> (C y hy) -> (C (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x y) (MulMemClass.mul_mem.{u1, u1} (Subgroup.{u1} G _inst_1) G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (SubmonoidClass.toMulMemClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (SubgroupClass.toSubmonoidClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Group.toDivInvMonoid.{u1} G _inst_1) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Subgroup.instSubgroupClassSubgroupToDivInvMonoidInstSetLikeSubgroup.{u1} G _inst_1))) (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i)) x y hx hy))) -> (forall {x : G} (hx : Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (supᵢ.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i))), C x hx)
-Case conversion may be inaccurate. Consider using '#align subgroup.supr_induction' Subgroup.supᵢ_induction'ₓ'. -/
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Sort.{u2}} (S : ι -> (Subgroup.{u1} G _inst_1)) {C : forall (x : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i))) -> Prop}, (forall (i : ι) (x : G) (H : Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (S i)), C x (Subgroup.mem_iSup_of_mem.{u1, u2} G _inst_1 ι (fun (i : ι) => S i) i x H)) -> (C (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))))) (OneMemClass.one_mem.{u1, u1} (Subgroup.{u1} G _inst_1) G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (SubmonoidClass.toOneMemClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (SubgroupClass.toSubmonoidClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Group.toDivInvMonoid.{u1} G _inst_1) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Subgroup.instSubgroupClassSubgroupToDivInvMonoidInstSetLikeSubgroup.{u1} G _inst_1))) (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i)))) -> (forall (x : G) (y : G) (hx : Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i))) (hy : Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i))), (C x hx) -> (C y hy) -> (C (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x y) (MulMemClass.mul_mem.{u1, u1} (Subgroup.{u1} G _inst_1) G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (SubmonoidClass.toMulMemClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (SubgroupClass.toSubmonoidClass.{u1, u1} (Subgroup.{u1} G _inst_1) G (Group.toDivInvMonoid.{u1} G _inst_1) (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Subgroup.instSubgroupClassSubgroupToDivInvMonoidInstSetLikeSubgroup.{u1} G _inst_1))) (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i)) x y hx hy))) -> (forall {x : G} (hx : Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (iSup.{u1, u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))) ι (fun (i : ι) => S i))), C x hx)
+Case conversion may be inaccurate. Consider using '#align subgroup.supr_induction' Subgroup.iSup_induction'ₓ'. -/
 /-- A dependent version of `subgroup.supr_induction`. -/
 @[elab_as_elim, to_additive "A dependent version of `add_subgroup.supr_induction`. "]
-theorem supᵢ_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
-    (hp : ∀ (i), ∀ x ∈ S i, C x (mem_supᵢ_of_mem i ‹_›)) (h1 : C 1 (one_mem _))
+theorem iSup_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
+    (hp : ∀ (i), ∀ x ∈ S i, C x (mem_iSup_of_mem i ‹_›)) (h1 : C 1 (one_mem _))
     (hmul : ∀ x y hx hy, C x hx → C y hy → C (x * y) (mul_mem ‹_› ‹_›)) {x : G}
     (hx : x ∈ ⨆ i, S i) : C x hx :=
   by
@@ -195,8 +195,8 @@ theorem supᵢ_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x 
   · exact ⟨_, h1⟩
   · rintro ⟨_, Cx⟩ ⟨_, Cy⟩
     refine' ⟨_, hmul _ _ _ _ Cx Cy⟩
-#align subgroup.supr_induction' Subgroup.supᵢ_induction'
-#align add_subgroup.supr_induction' AddSubgroup.supᵢ_induction'
+#align subgroup.supr_induction' Subgroup.iSup_induction'
+#align add_subgroup.supr_induction' AddSubgroup.iSup_induction'
 
 /- warning: subgroup.closure_mul_le -> Subgroup.closure_mul_le is a dubious translation:
 lean 3 declaration is
@@ -206,7 +206,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align subgroup.closure_mul_le Subgroup.closure_mul_leₓ'. -/
 @[to_additive]
 theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure T :=
-  infₛ_le fun x ⟨s, t, hs, ht, hx⟩ =>
+  sInf_le fun x ⟨s, t, hs, ht, hx⟩ =>
     hx ▸
       (closure S ⊔ closure T).mul_mem (SetLike.le_def.mp le_sup_left <| subset_closure hs)
         (SetLike.le_def.mp le_sup_right <| subset_closure ht)
@@ -254,7 +254,7 @@ theorem mul_normal (H N : Subgroup G) [N.Normal] : (↑(H ⊔ N) : Set G) = H *
   Set.Subset.antisymm
     (show H ⊔ N ≤ mulNormalAux H N by
       rw [sup_eq_closure]
-      apply infₛ_le _
+      apply sInf_le _
       dsimp
       rfl)
     ((sup_eq_closure H N).symm ▸ subset_closure)
@@ -287,7 +287,7 @@ theorem normal_mul (N H : Subgroup G) [N.Normal] : (↑(N ⊔ H) : Set G) = N *
   Set.Subset.antisymm
     (show N ⊔ H ≤ normalMulAux N H by
       rw [sup_eq_closure]
-      apply infₛ_le _
+      apply sInf_le _
       dsimp
       rfl)
     ((sup_eq_closure N H).symm ▸ subset_closure)

bump to nightly-2023-04-05-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

ea95f542

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module group_theory.subgroup.pointwise
-! leanprover-community/mathlib commit c10e724be91096453ee3db13862b9fb9a992fef2
+! leanprover-community/mathlib commit e655e4ea5c6d02854696f97494997ba4c31be802
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -94,7 +94,9 @@ lean 3 declaration is
 but is expected to have type
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {s : Set.{u1} G} {p : G -> Prop} {x : G}, (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (Subgroup.closure.{u1} G _inst_1 s)) -> (p (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1))))))) -> (forall (x : G), (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x s) -> (forall (y : G), (p y) -> (p (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x y)))) -> (forall (x : G), (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x s) -> (forall (y : G), (p y) -> (p (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))) x) y)))) -> (p x)
 Case conversion may be inaccurate. Consider using '#align subgroup.closure_induction_left Subgroup.closure_induction_leftₓ'. -/
-@[to_additive]
+/-- For subgroups generated by a single element, see the simpler `zpow_induction_left`. -/
+@[to_additive
+      "For additive subgroups generated by a single element, see the simpler\n`zsmul_induction_left`."]
 theorem closure_induction_left {p : G → Prop} {x : G} (h : x ∈ closure s) (H1 : p 1)
     (Hmul : ∀ x ∈ s, ∀ (y), p y → p (x * y)) (Hinv : ∀ x ∈ s, ∀ (y), p y → p (x⁻¹ * y)) : p x :=
   let key := (closure_toSubmonoid s).le
@@ -109,7 +111,9 @@ lean 3 declaration is
 but is expected to have type
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {s : Set.{u1} G} {p : G -> Prop} {x : G}, (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (Subgroup.closure.{u1} G _inst_1 s)) -> (p (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1))))))) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) y s) -> (p x) -> (p (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x y))) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) y s) -> (p x) -> (p (HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) x (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))) y)))) -> (p x)
 Case conversion may be inaccurate. Consider using '#align subgroup.closure_induction_right Subgroup.closure_induction_rightₓ'. -/
-@[to_additive]
+/-- For subgroups generated by a single element, see the simpler `zpow_induction_right`. -/
+@[to_additive
+      "For additive subgroups generated by a single element, see the simpler\n`zsmul_induction_right`."]
 theorem closure_induction_right {p : G → Prop} {x : G} (h : x ∈ closure s) (H1 : p 1)
     (Hmul : ∀ (x), ∀ y ∈ s, p x → p (x * y)) (Hinv : ∀ (x), ∀ y ∈ s, p x → p (x * y⁻¹)) : p x :=
   let key := (closure_toSubmonoid s).le

bump to nightly-2023-03-24-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

5b87f9bb

Diff

@@ -355,7 +355,7 @@ instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Subgroup.{u1} G _inst_1} (g : G) (h : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) (MulOpposite.{u1} G) (Subgroup.setLike.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (fun (_x : Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) => (Subgroup.{u1} G _inst_1) -> (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H)) (s : Set.{u1} G), 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 but is expected to have type
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(Set.preimage.{u1, u1} G G (fun (x._@.Mathlib.GroupTheory.Subgroup.Pointwise._hyg.2271 : G) => HMul.hMul.{u1, u1, u1} G G G (instHMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g x._@.Mathlib.GroupTheory.Subgroup.Pointwise._hyg.2271) (Set.image.{u1, u1} G G (fun (y : G) => HSMul.hSMul.{u1, u1, u1} (Subtype.{succ u1} (MulOpposite.{u1} G) (fun (x : MulOpposite.{u1} G) => Membership.mem.{u1, u1} (MulOpposite.{u1} G) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (SetLike.instMembership.{u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) H) (MulOpposite.{u1} G) (Subgroup.instSetLikeSubgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} 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(MulOpposite.{u1} G) (Subgroup.instSetLikeSubgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H))) G (Submonoid.smul.{u1, u1} (MulOpposite.{u1} G) G (Monoid.toMulOneClass.{u1} (MulOpposite.{u1} G) (DivInvMonoid.toMonoid.{u1} (MulOpposite.{u1} G) (Group.toDivInvMonoid.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)))) (Mul.toHasOppositeSMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.toSubmonoid.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.group.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H)))) h y) s))
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_opposite_image_mul_preimage Subgroup.smul_opposite_image_mul_preimageₓ'. -/
 @[to_additive]
 theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.opposite) (s : Set G) :
@@ -469,16 +469,12 @@ theorem smul_closure (a : α) (s : Set G) : a • closure s = closure (a • s)
 #align subgroup.smul_closure Subgroup.smul_closure
 -/
 
-/- warning: subgroup.pointwise_central_scalar -> Subgroup.pointwise_isCentralScalar is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] [_inst_5 : MulDistribMulAction.{u1, u2} (MulOpposite.{u1} α) G (MulOpposite.monoid.{u1} α _inst_3) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] [_inst_6 : IsCentralScalar.{u1, u2} α G (MulAction.toHasSmul.{u1, u2} α G _inst_3 (MulDistribMulAction.toMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4)) (MulAction.toHasSmul.{u1, u2} (MulOpposite.{u1} α) G (MulOpposite.monoid.{u1} α _inst_3) (MulDistribMulAction.toMulAction.{u1, u2} (MulOpposite.{u1} α) G (MulOpposite.monoid.{u1} α _inst_3) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_5))], IsCentralScalar.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) (MulAction.toHasSmul.{u1, u2} (MulOpposite.{u1} α) (Subgroup.{u2} G _inst_1) (MulOpposite.monoid.{u1} α _inst_3) (Subgroup.pointwiseMulAction.{u1, u2} (MulOpposite.{u1} α) G _inst_1 (MulOpposite.monoid.{u1} α _inst_3) _inst_5))
-but is expected to have type
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] [_inst_5 : MulDistribMulAction.{u1, u2} (MulOpposite.{u1} α) G (MulOpposite.instMonoidMulOpposite.{u1} α _inst_3) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] [_inst_6 : IsCentralScalar.{u1, u2} α G (MulAction.toSMul.{u1, u2} α G _inst_3 (MulDistribMulAction.toMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4)) (MulAction.toSMul.{u1, u2} (MulOpposite.{u1} α) G (MulOpposite.instMonoidMulOpposite.{u1} α _inst_3) (MulDistribMulAction.toMulAction.{u1, u2} (MulOpposite.{u1} α) G (MulOpposite.instMonoidMulOpposite.{u1} α _inst_3) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_5))], IsCentralScalar.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) (MulAction.toSMul.{u1, u2} (MulOpposite.{u1} α) (Subgroup.{u2} G _inst_1) (MulOpposite.instMonoidMulOpposite.{u1} α _inst_3) (Subgroup.pointwiseMulAction.{u1, u2} (MulOpposite.{u1} α) G _inst_1 (MulOpposite.instMonoidMulOpposite.{u1} α _inst_3) _inst_5))
-Case conversion may be inaccurate. Consider using '#align subgroup.pointwise_central_scalar Subgroup.pointwise_isCentralScalarₓ'. -/
+#print Subgroup.pointwise_isCentralScalar /-
 instance pointwise_isCentralScalar [MulDistribMulAction αᵐᵒᵖ G] [IsCentralScalar α G] :
     IsCentralScalar α (Subgroup G) :=
   ⟨fun a S => (congr_arg fun f => S.map f) <| MonoidHom.ext <| op_smul_eq_smul _⟩
 #align subgroup.pointwise_central_scalar Subgroup.pointwise_isCentralScalar
+-/
 
 /- warning: subgroup.conj_smul_le_of_le -> Subgroup.conj_smul_le_of_le is a dubious translation:
 lean 3 declaration is
@@ -814,7 +810,7 @@ theorem mem_smul_pointwise_iff_exists (m : A) (a : α) (S : AddSubgroup A) :
 lean 3 declaration is
   forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Monoid.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A _inst_3 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] [_inst_5 : DistribMulAction.{u1, u2} (MulOpposite.{u1} α) A (MulOpposite.monoid.{u1} α _inst_3) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] [_inst_6 : IsCentralScalar.{u1, u2} α A (SMulZeroClass.toHasSmul.{u1, u2} α A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} α A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} α A _inst_3 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)) _inst_4))) (SMulZeroClass.toHasSmul.{u1, u2} (MulOpposite.{u1} α) A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} (MulOpposite.{u1} α) A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} (MulOpposite.{u1} α) A (MulOpposite.monoid.{u1} α _inst_3) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)) _inst_5)))], IsCentralScalar.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toHasSmul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) _inst_3 (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 _inst_3 _inst_4)) (MulAction.toHasSmul.{u1, u2} (MulOpposite.{u1} α) (AddSubgroup.{u2} A _inst_2) (MulOpposite.monoid.{u1} α _inst_3) (AddSubgroup.pointwiseMulAction.{u1, u2} (MulOpposite.{u1} α) A _inst_2 (MulOpposite.monoid.{u1} α _inst_3) _inst_5))
 but is expected to have type
-  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Monoid.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A _inst_3 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] [_inst_5 : DistribMulAction.{u1, u2} (MulOpposite.{u1} α) A (MulOpposite.instMonoidMulOpposite.{u1} α _inst_3) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] [_inst_6 : IsCentralScalar.{u1, u2} α A (SMulZeroClass.toSMul.{u1, u2} α A (NegZeroClass.toZero.{u2} A (SubNegZeroMonoid.toNegZeroClass.{u2} A (SubtractionMonoid.toSubNegZeroMonoid.{u2} A (AddGroup.toSubtractionMonoid.{u2} A _inst_2)))) (DistribSMul.toSMulZeroClass.{u1, u2} α A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} α A _inst_3 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)) _inst_4))) (SMulZeroClass.toSMul.{u1, u2} (MulOpposite.{u1} α) A (NegZeroClass.toZero.{u2} A (SubNegZeroMonoid.toNegZeroClass.{u2} A (SubtractionMonoid.toSubNegZeroMonoid.{u2} A (AddGroup.toSubtractionMonoid.{u2} A _inst_2)))) (DistribSMul.toSMulZeroClass.{u1, u2} (MulOpposite.{u1} α) A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} (MulOpposite.{u1} α) A (MulOpposite.instMonoidMulOpposite.{u1} α _inst_3) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)) _inst_5)))], IsCentralScalar.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) _inst_3 (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 _inst_3 _inst_4)) (MulAction.toSMul.{u1, u2} (MulOpposite.{u1} α) (AddSubgroup.{u2} A _inst_2) (MulOpposite.instMonoidMulOpposite.{u1} α _inst_3) (AddSubgroup.pointwiseMulAction.{u1, u2} (MulOpposite.{u1} α) A _inst_2 (MulOpposite.instMonoidMulOpposite.{u1} α _inst_3) _inst_5))
+  forall {α : Type.{u1}} {A : Type.{u2}} [_inst_2 : AddGroup.{u2} A] [_inst_3 : Monoid.{u1} α] [_inst_4 : DistribMulAction.{u1, u2} α A _inst_3 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] [_inst_5 : DistribMulAction.{u1, u2} (MulOpposite.{u1} α) A (MulOpposite.monoid.{u1} α _inst_3) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))] [_inst_6 : IsCentralScalar.{u1, u2} α A (SMulZeroClass.toSMul.{u1, u2} α A (NegZeroClass.toZero.{u2} A (SubNegZeroMonoid.toNegZeroClass.{u2} A (SubtractionMonoid.toSubNegZeroMonoid.{u2} A (AddGroup.toSubtractionMonoid.{u2} A _inst_2)))) (DistribSMul.toSMulZeroClass.{u1, u2} α A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} α A _inst_3 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)) _inst_4))) (SMulZeroClass.toSMul.{u1, u2} (MulOpposite.{u1} α) A (NegZeroClass.toZero.{u2} A (SubNegZeroMonoid.toNegZeroClass.{u2} A (SubtractionMonoid.toSubNegZeroMonoid.{u2} A (AddGroup.toSubtractionMonoid.{u2} A _inst_2)))) (DistribSMul.toSMulZeroClass.{u1, u2} (MulOpposite.{u1} α) A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} (MulOpposite.{u1} α) A (MulOpposite.monoid.{u1} α _inst_3) (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_2)) _inst_5)))], IsCentralScalar.{u1, u2} α (AddSubgroup.{u2} A _inst_2) (MulAction.toSMul.{u1, u2} α (AddSubgroup.{u2} A _inst_2) _inst_3 (AddSubgroup.pointwiseMulAction.{u1, u2} α A _inst_2 _inst_3 _inst_4)) (MulAction.toSMul.{u1, u2} (MulOpposite.{u1} α) (AddSubgroup.{u2} A _inst_2) (MulOpposite.monoid.{u1} α _inst_3) (AddSubgroup.pointwiseMulAction.{u1, u2} (MulOpposite.{u1} α) A _inst_2 (MulOpposite.monoid.{u1} α _inst_3) _inst_5))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.pointwise_central_scalar AddSubgroup.pointwise_isCentralScalarₓ'. -/
 instance pointwise_isCentralScalar [DistribMulAction αᵐᵒᵖ A] [IsCentralScalar α A] :
     IsCentralScalar α (AddSubgroup A) :=

bump to nightly-2023-03-17-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

624c906c

Diff

@@ -590,17 +590,17 @@ theorem smul_inf (a : α) (S T : Subgroup G) : a • (S ⊓ T) = a • S ⊓ a 
   simp [SetLike.ext_iff, mem_pointwise_smul_iff_inv_smul_mem]
 #align subgroup.smul_inf Subgroup.smul_inf
 
-/- warning: subgroup.equiv_smul -> Subgroup.equivSmul is a dubious translation:
+/- warning: subgroup.equiv_smul -> Subgroup.equivSMul is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] (a : α) (H : Subgroup.{u2} G _inst_1), MulEquiv.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subgroup.{u2} G _inst_1) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)) H) (coeSort.{succ u2, succ (succ u2)} (Subgroup.{u2} G _inst_1) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.setLike.{u2} G _inst_1)) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a H)) (Subgroup.mul.{u2} G _inst_1 H) (Subgroup.mul.{u2} G _inst_1 (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a H))
 but is expected to have type
   forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] (a : α) (H : Subgroup.{u2} G _inst_1), MulEquiv.{u2, u2} (Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x H)) (Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a H))) (Subgroup.mul.{u2} G _inst_1 H) (Subgroup.mul.{u2} G _inst_1 (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a H))
-Case conversion may be inaccurate. Consider using '#align subgroup.equiv_smul Subgroup.equivSmulₓ'. -/
+Case conversion may be inaccurate. Consider using '#align subgroup.equiv_smul Subgroup.equivSMulₓ'. -/
 /-- Applying a `mul_distrib_mul_action` results in an isomorphic subgroup -/
 @[simps]
-def equivSmul (a : α) (H : Subgroup G) : H ≃* (a • H : Subgroup G) :=
+def equivSMul (a : α) (H : Subgroup G) : H ≃* (a • H : Subgroup G) :=
   (MulDistribMulAction.toMulEquiv G a).subgroupMap H
-#align subgroup.equiv_smul Subgroup.equivSmul
+#align subgroup.equiv_smul Subgroup.equivSMul
 
 /- warning: subgroup.subgroup_mul_singleton -> Subgroup.subgroup_mul_singleton is a dubious translation:
 lean 3 declaration is

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -355,7 +355,7 @@ instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔
 lean 3 declaration is
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(MulOpposite.instGroupMulOpposite.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.instGroupMulOpposite.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H))) G (Submonoid.smul.{u1, u1} (MulOpposite.{u1} G) G (Monoid.toMulOneClass.{u1} (MulOpposite.{u1} G) (DivInvMonoid.toMonoid.{u1} (MulOpposite.{u1} G) (Group.toDivInvMonoid.{u1} (MulOpposite.{u1} G) (MulOpposite.instGroupMulOpposite.{u1} G _inst_1)))) (Mul.toHasOppositeSMul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.toSubmonoid.{u1} (MulOpposite.{u1} G) (MulOpposite.instGroupMulOpposite.{u1} G _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.instGroupMulOpposite.{u1} G _inst_1))) (Subgroup.{u1} G _inst_1) (fun (a : Subgroup.{u1} G _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subgroup.{u1} G _inst_1) => Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.instGroupMulOpposite.{u1} G _inst_1)) a) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Subgroup.{u1} (MulOpposite.{u1} G) (MulOpposite.instGroupMulOpposite.{u1} G _inst_1))) (Subgroup.opposite.{u1} G _inst_1) H)))) h y) s))
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_opposite_image_mul_preimage Subgroup.smul_opposite_image_mul_preimageₓ'. -/
 @[to_additive]
 theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.opposite) (s : Set G) :
@@ -395,7 +395,7 @@ open Pointwise
 lean 3 declaration is
   forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} (S : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) a S) (Subgroup.map.{u2, u2} G _inst_1 G _inst_1 (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.monoid.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (fun (_x : MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.monoid.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) => α -> (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))) (MonoidHom.hasCoeToFun.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.monoid.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MulDistribMulAction.toMonoidEnd.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4) a) S)
 but is expected to have type
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} (S : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a S) (Subgroup.map.{u2, u2} G _inst_1 G _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α _inst_3)) (MulOneClass.toMul.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))) (MonoidHom.monoidHomClass.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))))) (MulDistribMulAction.toMonoidEnd.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4) a) S)
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} (S : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a S) (Subgroup.map.{u2, u2} G _inst_1 G _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α _inst_3)) (MulOneClass.toMul.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))) (MonoidHom.monoidHomClass.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))))) (MulDistribMulAction.toMonoidEnd.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4) a) S)
 Case conversion may be inaccurate. Consider using '#align subgroup.pointwise_smul_def Subgroup.pointwise_smul_defₓ'. -/
 theorem pointwise_smul_def {a : α} (S : Subgroup G) :
     a • S = S.map (MulDistribMulAction.toMonoidEnd _ _ a) :=
@@ -484,7 +484,7 @@ instance pointwise_isCentralScalar [MulDistribMulAction αᵐᵒᵖ G] [IsCentra
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) P H) -> (forall (h : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (SMul.smul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (MulAction.toHasSmul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) G _inst_1 (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (fun (_x : MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) => G -> (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (MonoidHom.hasCoeToFun.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MulAut.conj.{u1} G _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x H))))) h)) P) H)
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) P H) -> (forall (h : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => 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(DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H)
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) P H) -> (forall (h : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H)
 Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_le_of_le Subgroup.conj_smul_le_of_leₓ'. -/
 theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.conj (h : G) • P ≤ H :=
   by
@@ -496,7 +496,7 @@ theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.co
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) P H) -> (forall (h : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H), Eq.{succ u1} (Subgroup.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) (Subgroup.toGroup.{u1} G _inst_1 H)) (SMul.smul.{u1, u1} (MulAut.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) (MulOneClass.toHasMul.{u1} 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(coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x H))))) h)) P) H))
 but is expected to have type
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_inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Group.toDivInvMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)))))))))))) (MulAut.conj.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)) h) (Subgroup.subgroupOf.{u1} G _inst_1 P H)) (Subgroup.subgroupOf.{u1} G _inst_1 (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H))
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) => MulAut.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Monoid.toMulOneClass.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => 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(MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H))
 Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_subgroup_of Subgroup.conj_smul_subgroupOfₓ'. -/
 theorem conj_smul_subgroupOf {P H : Subgroup G} (hP : P ≤ H) (h : H) :
     MulAut.conj h • P.subgroupOf H = (MulAut.conj (h : G) • P).subgroupOf H :=
@@ -662,7 +662,7 @@ theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (g : G) (H : Subgroup.{u1} G _inst_1) [h : Subgroup.Normal.{u1} G _inst_1 H], Eq.{succ u1} (Subgroup.{u1} G _inst_1) (SMul.smul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (MulAction.toHasSmul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) G _inst_1 (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (fun (_x : MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) => G -> (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (MonoidHom.hasCoeToFun.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MulAut.conj.{u1} G _inst_1) g) H) H
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (g : G) (H : Subgroup.{u1} G _inst_1) [h : Subgroup.Normal.{u1} G _inst_1 H], Eq.{succ u1} (Subgroup.{u1} G _inst_1) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) g) H) H
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (g : G) (H : Subgroup.{u1} G _inst_1) [h : Subgroup.Normal.{u1} G _inst_1 H], Eq.{succ u1} (Subgroup.{u1} G _inst_1) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) g) H) H
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_normal Subgroup.smul_normalₓ'. -/
 @[simp]
 theorem smul_normal (g : G) (H : Subgroup G) [h : Normal H] : MulAut.conj g • H = H :=

bump to nightly-2023-03-08-18

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

10f15343

Diff

@@ -395,7 +395,7 @@ open Pointwise
 lean 3 declaration is
   forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} (S : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) a S) (Subgroup.map.{u2, u2} G _inst_1 G _inst_1 (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.monoid.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (fun (_x : MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.monoid.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) => α -> (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))) (MonoidHom.hasCoeToFun.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.monoid.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MulDistribMulAction.toMonoidEnd.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4) a) S)
 but is expected to have type
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} (S : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a S) (Subgroup.map.{u2, u2} G _inst_1 G _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α _inst_3)) (MulOneClass.toMul.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))) (MonoidHom.monoidHomClass.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))))) (MulDistribMulAction.toMonoidEnd.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4) a) S)
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] {a : α} (S : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a S) (Subgroup.map.{u2, u2} G _inst_1 G _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α _inst_3)) (MulOneClass.toMul.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))) (MonoidHom.monoidHomClass.{u1, u2} α (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.toMulOneClass.{u1} α _inst_3) (Monoid.toMulOneClass.{u2} (Monoid.End.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (Monoid.End.instMonoidEnd.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))))) (MulDistribMulAction.toMonoidEnd.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) _inst_4) a) S)
 Case conversion may be inaccurate. Consider using '#align subgroup.pointwise_smul_def Subgroup.pointwise_smul_defₓ'. -/
 theorem pointwise_smul_def {a : α} (S : Subgroup G) :
     a • S = S.map (MulDistribMulAction.toMonoidEnd _ _ a) :=
@@ -484,7 +484,7 @@ instance pointwise_isCentralScalar [MulDistribMulAction αᵐᵒᵖ G] [IsCentra
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) P H) -> (forall (h : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (SMul.smul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (MulAction.toHasSmul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) G _inst_1 (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (fun (_x : MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) => G -> (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (MonoidHom.hasCoeToFun.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MulAut.conj.{u1} G _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x H))))) h)) P) H)
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) P H) -> (forall (h : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H)
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) P H) -> (forall (h : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H)
 Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_le_of_le Subgroup.conj_smul_le_of_leₓ'. -/
 theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.conj (h : G) • P ≤ H :=
   by
@@ -496,7 +496,7 @@ theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) : MulAut.co
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) P H) -> (forall (h : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H), Eq.{succ u1} (Subgroup.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) (Subgroup.toGroup.{u1} G _inst_1 H)) (SMul.smul.{u1, u1} (MulAut.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) (MulOneClass.toHasMul.{u1} 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(coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) H) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x H))))) h)) P) H))
 but is expected to have type
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_inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Group.toDivInvMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)))))))))))) (MulAut.conj.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)) h) (Subgroup.subgroupOf.{u1} G _inst_1 P H)) (Subgroup.subgroupOf.{u1} G _inst_1 (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G 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(DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {P : Subgroup.{u1} G _inst_1} {H : Subgroup.{u1} G _inst_1}, (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) P H) -> (forall (h : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)), Eq.{succ u1} (Subgroup.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) => MulAut.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Monoid.toMulOneClass.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => 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(Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Monoid.toMulOneClass.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Group.toDivInvMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)))))) (MulAut.instGroupMulAut.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (MulOneClass.toMul.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Monoid.toMulOneClass.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (DivInvMonoid.toMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Group.toDivInvMonoid.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)))))))))))) (MulAut.conj.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x H)) (Subgroup.toGroup.{u1} G _inst_1 H)) h) (Subgroup.subgroupOf.{u1} G _inst_1 P H)) (Subgroup.subgroupOf.{u1} G _inst_1 (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) (Subtype.val.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H)) h)) P) H))
 Case conversion may be inaccurate. Consider using '#align subgroup.conj_smul_subgroup_of Subgroup.conj_smul_subgroupOfₓ'. -/
 theorem conj_smul_subgroupOf {P H : Subgroup G} (hP : P ≤ H) (h : H) :
     MulAut.conj h • P.subgroupOf H = (MulAut.conj (h : G) • P).subgroupOf H :=
@@ -662,7 +662,7 @@ theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (g : G) (H : Subgroup.{u1} G _inst_1) [h : Subgroup.Normal.{u1} G _inst_1 H], Eq.{succ u1} (Subgroup.{u1} G _inst_1) (SMul.smul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (MulAction.toHasSmul.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) G _inst_1 (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (fun (_x : MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) => G -> (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (MonoidHom.hasCoeToFun.{u1, u1} G (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.group.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MulAut.conj.{u1} G _inst_1) g) H) H
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (g : G) (H : Subgroup.{u1} G _inst_1) [h : Subgroup.Normal.{u1} G _inst_1 H], Eq.{succ u1} (Subgroup.{u1} G _inst_1) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) g) H) H
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (g : G) (H : Subgroup.{u1} G _inst_1) [h : Subgroup.Normal.{u1} G _inst_1 H], Eq.{succ u1} (Subgroup.{u1} G _inst_1) (HSMul.hSMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (Subgroup.{u1} G _inst_1) (instHSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (MulAction.toSMul.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Subgroup.{u1} G _inst_1) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (Subgroup.pointwiseMulAction.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) G _inst_1 (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) g) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))) (MulAut.applyMulDistribMulAction.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))) G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u1} G (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))) (MulAut.instGroupMulAut.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))))))))))) (MulAut.conj.{u1} G _inst_1) g) H) H
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_normal Subgroup.smul_normalₓ'. -/
 @[simp]
 theorem smul_normal (g : G) (H : Subgroup G) [h : Normal H] : MulAut.conj g • H = H :=

bump to nightly-2023-03-03-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

7fe4dd24

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module group_theory.subgroup.pointwise
-! leanprover-community/mathlib commit f16e7a22e11fc09c71f25446ac1db23a24e8a0bd
+! leanprover-community/mathlib commit c10e724be91096453ee3db13862b9fb9a992fef2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -37,22 +37,22 @@ open Set
 
 open Pointwise
 
-variable {α G A S : Type _} [Group G] [AddGroup A] {s : Set G}
+variable {α G A S : Type _}
 
 /- warning: inv_coe_set -> inv_coe_set is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} {S : Type.{u2}} [_inst_1 : Group.{u1} G] [_inst_3 : SetLike.{u2, u1} S G] [_inst_4 : SubgroupClass.{u2, u1} S G (Group.toDivInvMonoid.{u1} G _inst_1) _inst_3] {H : S}, Eq.{succ u1} (Set.{u1} G) (Inv.inv.{u1} (Set.{u1} G) (Set.inv.{u1} G (DivInvMonoid.toHasInv.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) ((fun (a : Type.{u2}) (b : Type.{u1}) [self : HasLiftT.{succ u2, succ u1} a b] => self.0) S (Set.{u1} G) (HasLiftT.mk.{succ u2, succ u1} S (Set.{u1} G) (CoeTCₓ.coe.{succ u2, succ u1} S (Set.{u1} G) (SetLike.Set.hasCoeT.{u2, u1} S G _inst_3))) H)) ((fun (a : Type.{u2}) (b : Type.{u1}) [self : HasLiftT.{succ u2, succ u1} a b] => self.0) S (Set.{u1} G) (HasLiftT.mk.{succ u2, succ u1} S (Set.{u1} G) (CoeTCₓ.coe.{succ u2, succ u1} S (Set.{u1} G) (SetLike.Set.hasCoeT.{u2, u1} S G _inst_3))) H)
+  forall {G : Type.{u1}} {S : Type.{u2}} [_inst_1 : InvolutiveInv.{u1} G] [_inst_2 : SetLike.{u2, u1} S G] [_inst_3 : InvMemClass.{u2, u1} S G (InvolutiveInv.toHasInv.{u1} G _inst_1) _inst_2] {H : S}, Eq.{succ u1} (Set.{u1} G) (Inv.inv.{u1} (Set.{u1} G) (Set.inv.{u1} G (InvolutiveInv.toHasInv.{u1} G _inst_1)) ((fun (a : Type.{u2}) (b : Type.{u1}) [self : HasLiftT.{succ u2, succ u1} a b] => self.0) S (Set.{u1} G) (HasLiftT.mk.{succ u2, succ u1} S (Set.{u1} G) (CoeTCₓ.coe.{succ u2, succ u1} S (Set.{u1} G) (SetLike.Set.hasCoeT.{u2, u1} S G _inst_2))) H)) ((fun (a : Type.{u2}) (b : Type.{u1}) [self : HasLiftT.{succ u2, succ u1} a b] => self.0) S (Set.{u1} G) (HasLiftT.mk.{succ u2, succ u1} S (Set.{u1} G) (CoeTCₓ.coe.{succ u2, succ u1} S (Set.{u1} G) (SetLike.Set.hasCoeT.{u2, u1} S G _inst_2))) H)
 but is expected to have type
-  forall {G : Type.{u2}} {S : Type.{u1}} [_inst_1 : InvolutiveInv.{u2} G] [_inst_3 : SetLike.{u1, u2} S G] [_inst_4 : InvMemClass.{u1, u2} S G (InvolutiveInv.toInv.{u2} G _inst_1) _inst_3] {H : S}, Eq.{succ u2} (Set.{u2} G) (Inv.inv.{u2} (Set.{u2} G) (Set.inv.{u2} G (InvolutiveInv.toInv.{u2} G _inst_1)) (SetLike.coe.{u1, u2} S G _inst_3 H)) (SetLike.coe.{u1, u2} S G _inst_3 H)
+  forall {G : Type.{u2}} {S : Type.{u1}} [_inst_1 : InvolutiveInv.{u2} G] [_inst_2 : SetLike.{u1, u2} S G] [_inst_3 : InvMemClass.{u1, u2} S G (InvolutiveInv.toInv.{u2} G _inst_1) _inst_2] {H : S}, Eq.{succ u2} (Set.{u2} G) (Inv.inv.{u2} (Set.{u2} G) (Set.inv.{u2} G (InvolutiveInv.toInv.{u2} G _inst_1)) (SetLike.coe.{u1, u2} S G _inst_2 H)) (SetLike.coe.{u1, u2} S G _inst_2 H)
 Case conversion may be inaccurate. Consider using '#align inv_coe_set inv_coe_setₓ'. -/
 @[simp, to_additive]
-theorem inv_coe_set [SetLike S G] [SubgroupClass S G] {H : S} : (H : Set G)⁻¹ = H :=
-  by
-  ext
-  simp
+theorem inv_coe_set [InvolutiveInv G] [SetLike S G] [InvMemClass S G] {H : S} : (H : Set G)⁻¹ = H :=
+  Set.ext fun _ => inv_mem_iff
 #align inv_coe_set inv_coe_set
 #align neg_coe_set neg_coe_set
 
+variable [Group G] [AddGroup A] {s : Set G}
+
 namespace Subgroup
 
 /- warning: subgroup.inv_subset_closure -> Subgroup.inv_subset_closure is a dubious translation:

f16e7a22

bump to nightly-2023-03-03-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

04b5c979

Diff

@@ -43,7 +43,7 @@ variable {α G A S : Type _} [Group G] [AddGroup A] {s : Set G}
 lean 3 declaration is
   forall {G : Type.{u1}} {S : Type.{u2}} [_inst_1 : Group.{u1} G] [_inst_3 : SetLike.{u2, u1} S G] [_inst_4 : SubgroupClass.{u2, u1} S G (Group.toDivInvMonoid.{u1} G _inst_1) _inst_3] {H : S}, Eq.{succ u1} (Set.{u1} G) (Inv.inv.{u1} (Set.{u1} G) (Set.inv.{u1} G (DivInvMonoid.toHasInv.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) ((fun (a : Type.{u2}) (b : Type.{u1}) [self : HasLiftT.{succ u2, succ u1} a b] => self.0) S (Set.{u1} G) (HasLiftT.mk.{succ u2, succ u1} S (Set.{u1} G) (CoeTCₓ.coe.{succ u2, succ u1} S (Set.{u1} G) (SetLike.Set.hasCoeT.{u2, u1} S G _inst_3))) H)) ((fun (a : Type.{u2}) (b : Type.{u1}) [self : HasLiftT.{succ u2, succ u1} a b] => self.0) S (Set.{u1} G) (HasLiftT.mk.{succ u2, succ u1} S (Set.{u1} G) (CoeTCₓ.coe.{succ u2, succ u1} S (Set.{u1} G) (SetLike.Set.hasCoeT.{u2, u1} S G _inst_3))) H)
 but is expected to have type
-  forall {G : Type.{u1}} {S : Type.{u2}} [_inst_1 : Group.{u1} G] [_inst_3 : SetLike.{u2, u1} S G] [_inst_4 : SubgroupClass.{u2, u1} S G (Group.toDivInvMonoid.{u1} G _inst_1) _inst_3] {H : S}, Eq.{succ u1} (Set.{u1} G) (Inv.inv.{u1} (Set.{u1} G) (Set.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1))))) (SetLike.coe.{u2, u1} S G _inst_3 H)) (SetLike.coe.{u2, u1} S G _inst_3 H)
+  forall {G : Type.{u2}} {S : Type.{u1}} [_inst_1 : InvolutiveInv.{u2} G] [_inst_3 : SetLike.{u1, u2} S G] [_inst_4 : InvMemClass.{u1, u2} S G (InvolutiveInv.toInv.{u2} G _inst_1) _inst_3] {H : S}, Eq.{succ u2} (Set.{u2} G) (Inv.inv.{u2} (Set.{u2} G) (Set.inv.{u2} G (InvolutiveInv.toInv.{u2} G _inst_1)) (SetLike.coe.{u1, u2} S G _inst_3 H)) (SetLike.coe.{u1, u2} S G _inst_3 H)
 Case conversion may be inaccurate. Consider using '#align inv_coe_set inv_coe_setₓ'. -/
 @[simp, to_additive]
 theorem inv_coe_set [SetLike S G] [SubgroupClass S G] {H : S} : (H : Set G)⁻¹ = H :=

f16e7a22

bump to nightly-2023-02-28-04

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

2097f8af

Diff

@@ -196,9 +196,9 @@ theorem supᵢ_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x 
 
 /- warning: subgroup.closure_mul_le -> Subgroup.closure_mul_le is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (S : Set.{u1} G) (T : Set.{u1} G), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S T)) (HasSup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) (Subgroup.closure.{u1} G _inst_1 S) (Subgroup.closure.{u1} G _inst_1 T))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (S : Set.{u1} G) (T : Set.{u1} G), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S T)) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) (Subgroup.closure.{u1} G _inst_1 S) (Subgroup.closure.{u1} G _inst_1 T))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (S : Set.{u1} G) (T : Set.{u1} G), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S T)) (HasSup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (Subgroup.closure.{u1} G _inst_1 S) (Subgroup.closure.{u1} G _inst_1 T))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (S : Set.{u1} G) (T : Set.{u1} G), LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S T)) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) (Subgroup.closure.{u1} G _inst_1 S) (Subgroup.closure.{u1} G _inst_1 T))
 Case conversion may be inaccurate. Consider using '#align subgroup.closure_mul_le Subgroup.closure_mul_leₓ'. -/
 @[to_additive]
 theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure T :=
@@ -211,9 +211,9 @@ theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure
 
 /- warning: subgroup.sup_eq_closure -> Subgroup.sup_eq_closure is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1), Eq.{succ u1} (Subgroup.{u1} G _inst_1) (HasSup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) H K) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) H) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) K)))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1), Eq.{succ u1} (Subgroup.{u1} G _inst_1) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) H K) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) H) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) K)))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1), Eq.{succ u1} (Subgroup.{u1} G _inst_1) (HasSup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) H K) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) K)))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1), Eq.{succ u1} (Subgroup.{u1} G _inst_1) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) H K) (Subgroup.closure.{u1} G _inst_1 (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) K)))
 Case conversion may be inaccurate. Consider using '#align subgroup.sup_eq_closure Subgroup.sup_eq_closureₓ'. -/
 @[to_additive]
 theorem sup_eq_closure (H K : Subgroup G) : H ⊔ K = closure (H * K) :=
@@ -239,9 +239,9 @@ private def mul_normal_aux (H N : Subgroup G) [hN : N.Normal] : Subgroup G
 
 /- warning: subgroup.mul_normal -> Subgroup.mul_normal is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (N : Subgroup.{u1} G _inst_1) [_inst_3 : Subgroup.Normal.{u1} G _inst_1 N], Eq.{succ u1} (Set.{u1} G) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (HasSup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) H N)) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) H) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) N))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (N : Subgroup.{u1} G _inst_1) [_inst_3 : Subgroup.Normal.{u1} G _inst_1 N], Eq.{succ u1} (Set.{u1} G) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) H N)) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) H) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) N))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (N : Subgroup.{u1} G _inst_1) [_inst_3 : Subgroup.Normal.{u1} G _inst_1 N], Eq.{succ u1} (Set.{u1} G) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (HasSup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) H N)) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) N))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (N : Subgroup.{u1} G _inst_1) [_inst_3 : Subgroup.Normal.{u1} G _inst_1 N], Eq.{succ u1} (Set.{u1} G) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) H N)) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) N))
 Case conversion may be inaccurate. Consider using '#align subgroup.mul_normal Subgroup.mul_normalₓ'. -/
 /-- The carrier of `H ⊔ N` is just `↑H * ↑N` (pointwise set product) when `N` is normal. -/
 @[to_additive
@@ -272,9 +272,9 @@ private def normal_mul_aux (N H : Subgroup G) [hN : N.Normal] : Subgroup G
 
 /- warning: subgroup.normal_mul -> Subgroup.normal_mul is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (N : Subgroup.{u1} G _inst_1) (H : Subgroup.{u1} G _inst_1) [_inst_3 : Subgroup.Normal.{u1} G _inst_1 N], Eq.{succ u1} (Set.{u1} G) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (HasSup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) N H)) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) N) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) H))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (N : Subgroup.{u1} G _inst_1) (H : Subgroup.{u1} G _inst_1) [_inst_3 : Subgroup.Normal.{u1} G _inst_1 N], Eq.{succ u1} (Set.{u1} G) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) N H)) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) N) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) H))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (N : Subgroup.{u1} G _inst_1) (H : Subgroup.{u1} G _inst_1) [_inst_3 : Subgroup.Normal.{u1} G _inst_1 N], Eq.{succ u1} (Set.{u1} G) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (HasSup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) N H)) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) N) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (N : Subgroup.{u1} G _inst_1) (H : Subgroup.{u1} G _inst_1) [_inst_3 : Subgroup.Normal.{u1} G _inst_1 N], Eq.{succ u1} (Set.{u1} G) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) N H)) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) N) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) H))
 Case conversion may be inaccurate. Consider using '#align subgroup.normal_mul Subgroup.normal_mulₓ'. -/
 /-- The carrier of `N ⊔ H` is just `↑N * ↑H` (pointwise set product) when `N` is normal. -/
 @[to_additive
@@ -292,9 +292,9 @@ theorem normal_mul (N H : Subgroup G) [N.Normal] : (↑(N ⊔ H) : Set G) = N *
 
 /- warning: subgroup.mul_inf_assoc -> Subgroup.mul_inf_assoc is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A C) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (HasInf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.hasInf.{u1} G _inst_1) B C))) (HasInf.inf.{u1} (Set.{u1} G) (SemilatticeInf.toHasInf.{u1} (Set.{u1} G) (Lattice.toSemilatticeInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.completeBooleanAlgebra.{u1} G)))))))) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) B)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C)))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A C) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Inf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.hasInf.{u1} G _inst_1) B C))) (Inf.inf.{u1} (Set.{u1} G) (SemilatticeInf.toHasInf.{u1} (Set.{u1} G) (Lattice.toSemilatticeInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.completeBooleanAlgebra.{u1} G)))))))) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) B)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C)))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) A C) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) A) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (HasInf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instHasInfSubgroup.{u1} G _inst_1) B C))) (HasInf.inf.{u1} (Set.{u1} G) (Lattice.toHasInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.instCompleteBooleanAlgebraSet.{u1} G))))))) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) A) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) B)) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) C)))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) A C) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) A) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Inf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instInfSubgroup.{u1} G _inst_1) B C))) (Inf.inf.{u1} (Set.{u1} G) (Lattice.toInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.instCompleteBooleanAlgebraSet.{u1} G))))))) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) A) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) B)) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) C)))
 Case conversion may be inaccurate. Consider using '#align subgroup.mul_inf_assoc Subgroup.mul_inf_assocₓ'. -/
 @[to_additive]
 theorem mul_inf_assoc (A B C : Subgroup G) (h : A ≤ C) : (A : Set G) * ↑(B ⊓ C) = A * B ⊓ C :=
@@ -314,9 +314,9 @@ theorem mul_inf_assoc (A B C : Subgroup G) (h : A ≤ C) : (A : Set G) * ↑(B 
 
 /- warning: subgroup.inf_mul_assoc -> Subgroup.inf_mul_assoc is a dubious translation:
 lean 3 declaration is
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+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (SetLike.partialOrder.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C A) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) (Inf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.hasInf.{u1} G _inst_1) A B)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C)) (Inf.inf.{u1} (Set.{u1} G) (SemilatticeInf.toHasInf.{u1} (Set.{u1} G) (Lattice.toSemilatticeInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.completeBooleanAlgebra.{u1} G)))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) A) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) B) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subgroup.{u1} G _inst_1) (Set.{u1} G) (HasLiftT.mk.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (CoeTCₓ.coe.{succ u1, succ u1} (Subgroup.{u1} G _inst_1) (Set.{u1} G) (SetLike.Set.hasCoeT.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)))) C))))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) C A) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (HasInf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instHasInfSubgroup.{u1} G _inst_1) A B)) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) C)) (HasInf.inf.{u1} (Set.{u1} G) (Lattice.toHasInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.instCompleteBooleanAlgebraSet.{u1} G))))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) A) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) B) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) C))))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (A : Subgroup.{u1} G _inst_1) (B : Subgroup.{u1} G _inst_1) (C : Subgroup.{u1} G _inst_1), (LE.le.{u1} (Subgroup.{u1} G _inst_1) (Preorder.toLE.{u1} (Subgroup.{u1} G _inst_1) (PartialOrder.toPreorder.{u1} (Subgroup.{u1} G _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) C A) -> (Eq.{succ u1} (Set.{u1} G) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Inf.inf.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instInfSubgroup.{u1} G _inst_1) A B)) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) C)) (Inf.inf.{u1} (Set.{u1} G) (Lattice.toInf.{u1} (Set.{u1} G) (ConditionallyCompleteLattice.toLattice.{u1} (Set.{u1} G) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Set.{u1} G) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} G) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} G) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} G) (Set.instCompleteBooleanAlgebraSet.{u1} G))))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) A) (HMul.hMul.{u1, u1, u1} (Set.{u1} G) (Set.{u1} G) (Set.{u1} G) (instHMul.{u1} (Set.{u1} G) (Set.mul.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) B) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) C))))
 Case conversion may be inaccurate. Consider using '#align subgroup.inf_mul_assoc Subgroup.inf_mul_assocₓ'. -/
 @[to_additive]
 theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
@@ -337,9 +337,9 @@ theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
 
 /- warning: subgroup.sup_normal -> Subgroup.sup_normal is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1) [hH : Subgroup.Normal.{u1} G _inst_1 H] [hK : Subgroup.Normal.{u1} G _inst_1 K], Subgroup.Normal.{u1} G _inst_1 (HasSup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) H K)
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1) [hH : Subgroup.Normal.{u1} G _inst_1 H] [hK : Subgroup.Normal.{u1} G _inst_1 K], Subgroup.Normal.{u1} G _inst_1 (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))))) H K)
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1) [hH : Subgroup.Normal.{u1} G _inst_1 H] [hK : Subgroup.Normal.{u1} G _inst_1 K], Subgroup.Normal.{u1} G _inst_1 (HasSup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) H K)
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1) [hH : Subgroup.Normal.{u1} G _inst_1 H] [hK : Subgroup.Normal.{u1} G _inst_1 K], Subgroup.Normal.{u1} G _inst_1 (Sup.sup.{u1} (Subgroup.{u1} G _inst_1) (SemilatticeSup.toSup.{u1} (Subgroup.{u1} G _inst_1) (Lattice.toSemilatticeSup.{u1} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1))))) H K)
 Case conversion may be inaccurate. Consider using '#align subgroup.sup_normal Subgroup.sup_normalₓ'. -/
 instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔ K).Normal
     where conj_mem n hmem g := by
@@ -455,9 +455,9 @@ theorem smul_bot (a : α) : a • (⊥ : Subgroup G) = ⊥ :=
 
 /- warning: subgroup.smul_sup -> Subgroup.smul_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] (a : α) (S : Subgroup.{u2} G _inst_1) (T : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) a (HasSup.sup.{u2} (Subgroup.{u2} G _inst_1) (SemilatticeSup.toHasSup.{u2} (Subgroup.{u2} G _inst_1) (Lattice.toSemilatticeSup.{u2} (Subgroup.{u2} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.completeLattice.{u2} G _inst_1))))) S T)) (HasSup.sup.{u2} (Subgroup.{u2} G _inst_1) (SemilatticeSup.toHasSup.{u2} (Subgroup.{u2} G _inst_1) (Lattice.toSemilatticeSup.{u2} (Subgroup.{u2} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.completeLattice.{u2} G _inst_1))))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) a S) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) a T))
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] (a : α) (S : Subgroup.{u2} G _inst_1) (T : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) a (Sup.sup.{u2} (Subgroup.{u2} G _inst_1) (SemilatticeSup.toHasSup.{u2} (Subgroup.{u2} G _inst_1) (Lattice.toSemilatticeSup.{u2} (Subgroup.{u2} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.completeLattice.{u2} G _inst_1))))) S T)) (Sup.sup.{u2} (Subgroup.{u2} G _inst_1) (SemilatticeSup.toHasSup.{u2} (Subgroup.{u2} G _inst_1) (Lattice.toSemilatticeSup.{u2} (Subgroup.{u2} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.completeLattice.{u2} G _inst_1))))) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) a S) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4)) a T))
 but is expected to have type
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] (a : α) (S : Subgroup.{u2} G _inst_1) (T : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a (HasSup.sup.{u2} (Subgroup.{u2} G _inst_1) (SemilatticeSup.toHasSup.{u2} (Subgroup.{u2} G _inst_1) (Lattice.toSemilatticeSup.{u2} (Subgroup.{u2} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))))) S T)) (HasSup.sup.{u2} (Subgroup.{u2} G _inst_1) (SemilatticeSup.toHasSup.{u2} (Subgroup.{u2} G _inst_1) (Lattice.toSemilatticeSup.{u2} (Subgroup.{u2} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))))) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a S) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a T))
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Monoid.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G _inst_3 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] (a : α) (S : Subgroup.{u2} G _inst_1) (T : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a (Sup.sup.{u2} (Subgroup.{u2} G _inst_1) (SemilatticeSup.toSup.{u2} (Subgroup.{u2} G _inst_1) (Lattice.toSemilatticeSup.{u2} (Subgroup.{u2} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))))) S T)) (Sup.sup.{u2} (Subgroup.{u2} G _inst_1) (SemilatticeSup.toSup.{u2} (Subgroup.{u2} G _inst_1) (Lattice.toSemilatticeSup.{u2} (Subgroup.{u2} G _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))))) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a S) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) _inst_3 (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 _inst_3 _inst_4))) a T))
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_sup Subgroup.smul_supₓ'. -/
 theorem smul_sup (a : α) (S T : Subgroup G) : a • (S ⊔ T) = a • S ⊔ a • T :=
   map_sup _ _ _
@@ -581,9 +581,9 @@ theorem subset_pointwise_smul_iff {a : α} {S T : Subgroup G} : S ≤ a • T 
 
 /- warning: subgroup.smul_inf -> Subgroup.smul_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] (a : α) (S : Subgroup.{u2} G _inst_1) (T : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a (HasInf.inf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.hasInf.{u2} G _inst_1) S T)) (HasInf.inf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.hasInf.{u2} G _inst_1) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a S) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a T))
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] (a : α) (S : Subgroup.{u2} G _inst_1) (T : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a (Inf.inf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.hasInf.{u2} G _inst_1) S T)) (Inf.inf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.hasInf.{u2} G _inst_1) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a S) (SMul.smul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toHasSmul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4)) a T))
 but is expected to have type
-  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] (a : α) (S : Subgroup.{u2} G _inst_1) (T : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a (HasInf.inf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instHasInfSubgroup.{u2} G _inst_1) S T)) (HasInf.inf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instHasInfSubgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a S) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a T))
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_3 : Group.{u1} α] [_inst_4 : MulDistribMulAction.{u1, u2} α G (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))] (a : α) (S : Subgroup.{u2} G _inst_1) (T : Subgroup.{u2} G _inst_1), Eq.{succ u2} (Subgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a (Inf.inf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instInfSubgroup.{u2} G _inst_1) S T)) (Inf.inf.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instInfSubgroup.{u2} G _inst_1) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a S) (HSMul.hSMul.{u1, u2, u2} α (Subgroup.{u2} G _inst_1) (Subgroup.{u2} G _inst_1) (instHSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (MulAction.toSMul.{u1, u2} α (Subgroup.{u2} G _inst_1) (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) (Subgroup.pointwiseMulAction.{u1, u2} α G _inst_1 (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α _inst_3)) _inst_4))) a T))
 Case conversion may be inaccurate. Consider using '#align subgroup.smul_inf Subgroup.smul_infₓ'. -/
 @[simp]
 theorem smul_inf (a : α) (S T : Subgroup G) : a • (S ⊓ T) = a • S ⊓ a • T := by

f16e7a22

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

feat: pointwise scalar multiplication is monotone (#11809)

Everywhere we have a smul_mem_pointwise_smul lemma, I've added this result.

5f4e6d8b

Diff

@@ -330,6 +330,9 @@ theorem smul_mem_pointwise_smul (m : G) (a : α) (S : Subgroup G) : m ∈ S →
   (Set.smul_mem_smul_set : _ → _ ∈ a • (S : Set G))
 #align subgroup.smul_mem_pointwise_smul Subgroup.smul_mem_pointwise_smul
 
+instance : CovariantClass α (Subgroup G) HSMul.hSMul LE.le :=
+  ⟨fun _ _ => image_subset _⟩
+
 theorem mem_smul_pointwise_iff_exists (m : G) (a : α) (S : Subgroup G) :
     m ∈ a • S ↔ ∃ s : G, s ∈ S ∧ a • s = m :=
   (Set.mem_smul_set : m ∈ a • (S : Set G) ↔ _)

chore(GroupTheory): rename induction arguments for Sub{semigroup,monoid,group} (#11461)

The additive version are still incorrectly named, but these can easily be tracked down later (#11462) by searching for to_additive (attr := elab_as_elim).

7339b9f2

Diff

@@ -134,13 +134,13 @@ the closure of `k`. -/
   elements of `k` and their negation, and is preserved under addition, then `p` holds for all
   elements of the additive closure of `k`."]
 theorem closure_induction'' {p : (g : G) → g ∈ closure s → Prop}
-    (Hk : ∀ x (hx : x ∈ s), p x (subset_closure hx))
-    (Hk_inv : ∀ x (hx : x ∈ s), p x⁻¹ (inv_mem (subset_closure hx)))
-    (H1 : p 1 (one_mem _))
-    (Hmul : ∀ x y hx hy, p x hx → p y hy → p (x * y) (mul_mem hx hy))
+    (mem : ∀ x (hx : x ∈ s), p x (subset_closure hx))
+    (inv_mem : ∀ x (hx : x ∈ s), p x⁻¹ (inv_mem (subset_closure hx)))
+    (one : p 1 (one_mem _))
+    (mul : ∀ x y hx hy, p x hx → p y hy → p (x * y) (mul_mem hx hy))
     {x} (h : x ∈ closure s) : p x h :=
-  closure_induction_left H1 (fun x hx y _ hy => Hmul x y _ _ (Hk x hx) hy)
-    (fun x hx y _ => Hmul x⁻¹ y _ _ <| Hk_inv x hx) h
+  closure_induction_left one (fun x hx y _ hy => mul x y _ _ (mem x hx) hy)
+    (fun x hx y _ => mul x⁻¹ y _ _ <| inv_mem x hx) h
 #align subgroup.closure_induction'' Subgroup.closure_induction''
 #align add_subgroup.closure_induction'' AddSubgroup.closure_induction''
 
@@ -151,17 +151,17 @@ then it holds for all elements of the supremum of `S`. -/
 If `C` holds for `0` and all elements of `S i` for all `i`, and is preserved under addition,
 then it holds for all elements of the supremum of `S`. "]
 theorem iSup_induction {ι : Sort*} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
-    (hp : ∀ (i), ∀ x ∈ S i, C x) (h1 : C 1) (hmul : ∀ x y, C x → C y → C (x * y)) : C x := by
+    (mem : ∀ (i), ∀ x ∈ S i, C x) (one : C 1) (mul : ∀ x y, C x → C y → C (x * y)) : C x := by
   rw [iSup_eq_closure] at hx
   induction hx using closure_induction'' with
-  | H1 => exact h1
-  | Hk x hx =>
+  | one => exact one
+  | mem x hx =>
     obtain ⟨i, hi⟩ := Set.mem_iUnion.mp hx
-    exact hp _ _ hi
-  | Hk_inv x hx =>
+    exact mem _ _ hi
+  | inv_mem x hx =>
     obtain ⟨i, hi⟩ := Set.mem_iUnion.mp hx
-    exact hp _ _ (inv_mem hi)
-  | Hmul x y _ _ ihx ihy => exact hmul x y ihx ihy
+    exact mem _ _ (inv_mem hi)
+  | mul x y _ _ ihx ihy => exact mul x y ihx ihy
 #align subgroup.supr_induction Subgroup.iSup_induction
 #align add_subgroup.supr_induction AddSubgroup.iSup_induction
 
@@ -210,13 +210,13 @@ theorem mul_normal (H N : Subgroup G) [hN : N.Normal] : (↑(H ⊔ N) : Set G) =
   rw [sup_eq_closure_mul]
   refine Set.Subset.antisymm (fun x hx => ?_) subset_closure
   induction hx using closure_induction'' with
-  | H1 => exact ⟨1, one_mem _, 1, one_mem _, mul_one 1⟩
-  | Hk _ hx => exact hx
-  | Hk_inv x hx =>
+  | one => exact ⟨1, one_mem _, 1, one_mem _, mul_one 1⟩
+  | mem _ hx => exact hx
+  | inv_mem x hx =>
     obtain ⟨x, hx, y, hy, rfl⟩ := hx
     simpa only [mul_inv_rev, mul_assoc, inv_inv, inv_mul_cancel_left]
       using mul_mem_mul (inv_mem hx) (hN.conj_mem _ (inv_mem hy) x)
-  | Hmul x' x' _ _ hx hx' =>
+  | mul x' x' _ _ hx hx' =>
     obtain ⟨x, hx, y, hy, rfl⟩ := hx
     obtain ⟨x', hx', y', hy', rfl⟩ := hx'
     refine ⟨x * x', mul_mem hx hx', x'⁻¹ * y * x' * y', mul_mem ?_ hy', ?_⟩

chore: classify new lemma porting notes (#11217)

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

"new lemma"
"added lemma"

68df7d0d

Diff

@@ -274,7 +274,7 @@ instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔
     simp only [mul_assoc, inv_mul_cancel_left]
 #align subgroup.sup_normal Subgroup.sup_normal
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 @[to_additive]
 theorem smul_opposite_image_mul_preimage' (g : G) (h : Gᵐᵒᵖ) (s : Set G) :
     (fun y => h • y) '' ((g * ·) ⁻¹' s) = (g * ·) ⁻¹' ((fun y => h • y) '' s) := by

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -274,13 +274,13 @@ instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔
     simp only [mul_assoc, inv_mul_cancel_left]
 #align subgroup.sup_normal Subgroup.sup_normal
 
--- porting note: new lemma
+-- Porting note: new lemma
 @[to_additive]
 theorem smul_opposite_image_mul_preimage' (g : G) (h : Gᵐᵒᵖ) (s : Set G) :
     (fun y => h • y) '' ((g * ·) ⁻¹' s) = (g * ·) ⁻¹' ((fun y => h • y) '' s) := by
   simp [preimage_preimage, mul_assoc]
 
--- porting note: deprecate?
+-- Porting note: deprecate?
 @[to_additive]
 theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.op) (s : Set G) :
     (fun y => h • y) '' ((g * ·) ⁻¹' s) = (g * ·) ⁻¹' ((fun y => h • y) '' s) :=

feat: IsTorsionFree M ↔ NoZeroSMulDivisors ℕ M (#10918)

and some subgroup results.

From PFR

a424c094

Diff

@@ -33,7 +33,7 @@ open Pointwise
 
 variable {α G A S : Type*}
 
-@[to_additive (attr := simp)]
+@[to_additive (attr := simp, norm_cast)]
 theorem inv_coe_set [InvolutiveInv G] [SetLike S G] [InvMemClass S G] {H : S} : (H : Set G)⁻¹ = H :=
   Set.ext fun _ => inv_mem_iff
 #align inv_coe_set inv_coe_set
@@ -49,6 +49,14 @@ lemma op_smul_coe_set [Group G] [SetLike S G] [SubgroupClass S G] {s : S} {a : G
     MulOpposite.op a • (s : Set G) = s := by
   ext; simp [Set.mem_smul_set_iff_inv_smul_mem, mul_mem_cancel_right, ha]
 
+@[to_additive (attr := simp, norm_cast)]
+lemma coe_mul_coe [SetLike S G] [DivInvMonoid G] [SubgroupClass S G] (H : S) :
+    H * H = (H : Set G) := by aesop (add simp mem_mul)
+
+@[to_additive (attr := simp, norm_cast)]
+lemma coe_div_coe [SetLike S G] [DivisionMonoid G] [SubgroupClass S G] (H : S) :
+    H / H = (H : Set G) := by simp [div_eq_mul_inv]
+
 variable [Group G] [AddGroup A] {s : Set G}
 
 namespace Subgroup

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -168,7 +168,7 @@ theorem iSup_induction' {ι : Sort*} (S : ι → Subgroup G) {C : ∀ x, (x ∈
   · exact ⟨_, hp i _ hx⟩
   · exact ⟨_, h1⟩
   · rintro ⟨_, Cx⟩ ⟨_, Cy⟩
-    refine' ⟨_, hmul _ _ _ _ Cx Cy⟩
+    exact ⟨_, hmul _ _ _ _ Cx Cy⟩
 #align subgroup.supr_induction' Subgroup.iSup_induction'
 #align add_subgroup.supr_induction' AddSubgroup.iSup_induction'

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

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

This follows on from #6964.

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

a13e8040

Diff

@@ -163,7 +163,7 @@ theorem iSup_induction' {ι : Sort*} (S : ι → Subgroup G) {C : ∀ x, (x ∈
     (hp : ∀ (i), ∀ x (hx : x ∈ S i), C x (mem_iSup_of_mem i hx)) (h1 : C 1 (one_mem _))
     (hmul : ∀ x y hx hy, C x hx → C y hy → C (x * y) (mul_mem ‹_› ‹_›)) {x : G}
     (hx : x ∈ ⨆ i, S i) : C x hx := by
-  suffices : ∃ h, C x h; exact this.snd
+  suffices ∃ h, C x h from this.snd
   refine' iSup_induction S (C := fun x => ∃ h, C x h) hx (fun i x hx => _) _ fun x y => _
   · exact ⟨_, hp i _ hx⟩
   · exact ⟨_, h1⟩

feat: change Subgroup and Submonoid induction principles to work with induction (#9861)

Induction principles have to be fully dependent in order to work with the induction tactic. This is usually a good thing anyway, since the dependent version is often more convenient to use, and avoids the caller having to fumble with generalizing over an existential.

This changes the following induction principles (and their additive versions):

Submonoid.closure_induction_{left,right}
Subgroup.closure_induction_{left,right}
Subgroup.closure_induction'' (no submonoid version exists)

Arguments to these lemmas have also been renamed to drop the H, as seems to be preferred for induction lemmas.

28dae78b

Diff

@@ -74,24 +74,41 @@ theorem closure_toSubmonoid (S : Set G) :
 #align add_subgroup.closure_to_add_submonoid AddSubgroup.closure_toAddSubmonoid
 
 /-- For subgroups generated by a single element, see the simpler `zpow_induction_left`. -/
-@[to_additive "For additive subgroups generated by a single element, see the simpler
-`zsmul_induction_left`."]
-theorem closure_induction_left {p : G → Prop} {x : G} (h : x ∈ closure s) (H1 : p 1)
-    (Hmul : ∀ x ∈ s, ∀ (y), p y → p (x * y)) (Hinv : ∀ x ∈ s, ∀ (y), p y → p (x⁻¹ * y)) : p x :=
-  let key := (closure_toSubmonoid s).le
-  Submonoid.closure_induction_left (key h) H1 fun x hx => hx.elim (Hmul x) fun hx y hy =>
-    inv_inv x ▸ Hinv x⁻¹ hx y hy
+@[to_additive (attr := elab_as_elim)
+  "For additive subgroups generated by a single element, see the simpler
+  `zsmul_induction_left`."]
+theorem closure_induction_left {p : (x : G) → x ∈ closure s → Prop} (one : p 1 (one_mem _))
+    (mul_left : ∀ x (hx : x ∈ s), ∀ (y) hy, p y hy → p (x * y) (mul_mem (subset_closure hx) hy))
+    (mul_left_inv : ∀ x (hx : x ∈ s), ∀ (y) hy, p y hy →
+      p (x⁻¹ * y) (mul_mem (inv_mem (subset_closure hx)) hy))
+    {x : G} (h : x ∈ closure s) : p x h := by
+  revert h
+  simp_rw [← mem_toSubmonoid, closure_toSubmonoid] at *
+  intro h
+  induction h using Submonoid.closure_induction_left with
+  | one => exact one
+  | mul_left x hx y hy ih =>
+    cases hx with
+    | inl hx => exact mul_left _ hx _ hy ih
+    | inr hx => simpa only [inv_inv] using mul_left_inv _ hx _ hy ih
 #align subgroup.closure_induction_left Subgroup.closure_induction_left
 #align add_subgroup.closure_induction_left AddSubgroup.closure_induction_left
 
 /-- For subgroups generated by a single element, see the simpler `zpow_induction_right`. -/
-@[to_additive "For additive subgroups generated by a single element, see the simpler
-`zsmul_induction_right`."]
-theorem closure_induction_right {p : G → Prop} {x : G} (h : x ∈ closure s) (H1 : p 1)
-    (Hmul : ∀ (x), ∀ y ∈ s, p x → p (x * y)) (Hinv : ∀ (x), ∀ y ∈ s, p x → p (x * y⁻¹)) : p x :=
-  let key := (closure_toSubmonoid s).le
-  Submonoid.closure_induction_right (key h) H1 fun x y hy => hy.elim (Hmul x y) fun hy hx =>
-    inv_inv y ▸ Hinv x y⁻¹ hy hx
+@[to_additive (attr := elab_as_elim)
+  "For additive subgroups generated by a single element, see the simpler
+  `zsmul_induction_right`."]
+theorem closure_induction_right {p : (x : G) → x ∈ closure s → Prop} (one : p 1 (one_mem _))
+    (mul_right : ∀ (x) hx, ∀ y (hy : y ∈ s), p x hx → p (x * y) (mul_mem hx (subset_closure hy)))
+    (mul_right_inv : ∀ (x) hx, ∀ y (hy : y ∈ s), p x hx →
+      p (x * y⁻¹) (mul_mem hx (inv_mem (subset_closure hy))))
+    {x : G} (h : x ∈ closure s) : p x h :=
+  closure_induction_left (s := MulOpposite.unop ⁻¹' s)
+    (p := fun m hm => p m.unop <| by rwa [← op_closure] at hm)
+    one
+    (fun _x hx _y hy => mul_right _ _ _ hx)
+    (fun _x hx _y hy => mul_right_inv _ _ _ hx)
+    (by rwa [← op_closure])
 #align subgroup.closure_induction_right Subgroup.closure_induction_right
 #align add_subgroup.closure_induction_right AddSubgroup.closure_induction_right
 
@@ -104,13 +121,18 @@ theorem closure_inv (s : Set G) : closure s⁻¹ = closure s := by
 /-- An induction principle for closure membership. If `p` holds for `1` and all elements of
 `k` and their inverse, and is preserved under multiplication, then `p` holds for all elements of
 the closure of `k`. -/
-@[to_additive "An induction principle for additive closure membership. If `p` holds for `0` and all
-elements of `k` and their negation, and is preserved under addition, then `p` holds for all
-elements of the additive closure of `k`."]
-theorem closure_induction'' {p : G → Prop} {x} (h : x ∈ closure s) (Hk : ∀ x ∈ s, p x)
-    (Hk_inv : ∀ x ∈ s, p x⁻¹) (H1 : p 1) (Hmul : ∀ x y, p x → p y → p (x * y)) : p x :=
-  closure_induction_left h H1 (fun x hx y hy => Hmul x y (Hk x hx) hy) fun x hx y =>
-    Hmul x⁻¹ y <| Hk_inv x hx
+@[to_additive (attr := elab_as_elim)
+  "An induction principle for additive closure membership. If `p` holds for `0` and all
+  elements of `k` and their negation, and is preserved under addition, then `p` holds for all
+  elements of the additive closure of `k`."]
+theorem closure_induction'' {p : (g : G) → g ∈ closure s → Prop}
+    (Hk : ∀ x (hx : x ∈ s), p x (subset_closure hx))
+    (Hk_inv : ∀ x (hx : x ∈ s), p x⁻¹ (inv_mem (subset_closure hx)))
+    (H1 : p 1 (one_mem _))
+    (Hmul : ∀ x y hx hy, p x hx → p y hy → p (x * y) (mul_mem hx hy))
+    {x} (h : x ∈ closure s) : p x h :=
+  closure_induction_left H1 (fun x hx y _ hy => Hmul x y _ _ (Hk x hx) hy)
+    (fun x hx y _ => Hmul x⁻¹ y _ _ <| Hk_inv x hx) h
 #align subgroup.closure_induction'' Subgroup.closure_induction''
 #align add_subgroup.closure_induction'' AddSubgroup.closure_induction''
 
@@ -123,11 +145,15 @@ then it holds for all elements of the supremum of `S`. "]
 theorem iSup_induction {ι : Sort*} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
     (hp : ∀ (i), ∀ x ∈ S i, C x) (h1 : C 1) (hmul : ∀ x y, C x → C y → C (x * y)) : C x := by
   rw [iSup_eq_closure] at hx
-  refine' closure_induction'' hx (fun x hx => _) (fun x hx => _) h1 hmul
-  · obtain ⟨i, hi⟩ := Set.mem_iUnion.mp hx
+  induction hx using closure_induction'' with
+  | H1 => exact h1
+  | Hk x hx =>
+    obtain ⟨i, hi⟩ := Set.mem_iUnion.mp hx
     exact hp _ _ hi
-  · obtain ⟨i, hi⟩ := Set.mem_iUnion.mp hx
+  | Hk_inv x hx =>
+    obtain ⟨i, hi⟩ := Set.mem_iUnion.mp hx
     exact hp _ _ (inv_mem hi)
+  | Hmul x y _ _ ihx ihy => exact hmul x y ihx ihy
 #align subgroup.supr_induction Subgroup.iSup_induction
 #align add_subgroup.supr_induction AddSubgroup.iSup_induction
 
@@ -175,14 +201,16 @@ when `N` is normal."]
 theorem mul_normal (H N : Subgroup G) [hN : N.Normal] : (↑(H ⊔ N) : Set G) = H * N := by
   rw [sup_eq_closure_mul]
   refine Set.Subset.antisymm (fun x hx => ?_) subset_closure
-  refine closure_induction'' (p := fun x => x ∈ (H : Set G) * (N : Set G)) hx ?_ ?_ ?_ ?_
-  · rintro _ ⟨x, hx, y, hy, rfl⟩
-    exact mul_mem_mul hx hy
-  · rintro _ ⟨x, hx, y, hy, rfl⟩
+  induction hx using closure_induction'' with
+  | H1 => exact ⟨1, one_mem _, 1, one_mem _, mul_one 1⟩
+  | Hk _ hx => exact hx
+  | Hk_inv x hx =>
+    obtain ⟨x, hx, y, hy, rfl⟩ := hx
     simpa only [mul_inv_rev, mul_assoc, inv_inv, inv_mul_cancel_left]
       using mul_mem_mul (inv_mem hx) (hN.conj_mem _ (inv_mem hy) x)
-  · exact ⟨1, one_mem _, 1, one_mem _, mul_one 1⟩
-  · rintro _ _ ⟨x, hx, y, hy, rfl⟩ ⟨x', hx', y', hy', rfl⟩
+  | Hmul x' x' _ _ hx hx' =>
+    obtain ⟨x, hx, y, hy, rfl⟩ := hx
+    obtain ⟨x', hx', y', hy', rfl⟩ := hx'
     refine ⟨x * x', mul_mem hx hx', x'⁻¹ * y * x' * y', mul_mem ?_ hy', ?_⟩
     · simpa using hN.conj_mem _ hy x'⁻¹
     · simp only [mul_assoc, mul_inv_cancel_left]

refactor(*): change definition of Set.image2 etc (#9275)

Redefine Set.image2 to use ∃ a ∈ s, ∃ b ∈ t, f a b = c instead of ∃ a b, a ∈ s ∧ b ∈ t ∧ f a b = c.
Redefine Set.seq as Set.image2. The new definition is equal to the old one but rw [Set.seq] gives a different result.
Redefine Filter.map₂ to use ∃ u ∈ f, ∃ v ∈ g, image2 m u v ⊆ s instead of ∃ u v, u ∈ f ∧ v ∈ g ∧ ...
Update lemmas like Set.mem_image2, Finset.mem_image₂, Set.mem_mul, Finset.mem_div etc

The two reasons to make the change are:

∃ a ∈ s, ∃ b ∈ t, _ is a simp-normal form, and
it looks a bit nicer.

8f17470f

Diff

@@ -148,7 +148,7 @@ theorem iSup_induction' {ι : Sort*} (S : ι → Subgroup G) {C : ∀ x, (x ∈
 
 @[to_additive]
 theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure T :=
-  sInf_le fun _x ⟨_s, _t, hs, ht, hx⟩ => hx ▸
+  sInf_le fun _x ⟨_s, hs, _t, ht, hx⟩ => hx ▸
     (closure S ⊔ closure T).mul_mem (SetLike.le_def.mp le_sup_left <| subset_closure hs)
       (SetLike.le_def.mp le_sup_right <| subset_closure ht)
 #align subgroup.closure_mul_le Subgroup.closure_mul_le
@@ -157,8 +157,8 @@ theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure
 @[to_additive]
 theorem sup_eq_closure_mul (H K : Subgroup G) : H ⊔ K = closure ((H : Set G) * (K : Set G)) :=
   le_antisymm
-    (sup_le (fun h hh => subset_closure ⟨h, 1, hh, K.one_mem, mul_one h⟩) fun k hk =>
-      subset_closure ⟨1, k, H.one_mem, hk, one_mul k⟩)
+    (sup_le (fun h hh => subset_closure ⟨h, hh, 1, K.one_mem, mul_one h⟩) fun k hk =>
+      subset_closure ⟨1, H.one_mem, k, hk, one_mul k⟩)
     ((closure_mul_le _ _).trans <| by rw [closure_eq, closure_eq])
 #align subgroup.sup_eq_closure Subgroup.sup_eq_closure_mul
 #align add_subgroup.sup_eq_closure AddSubgroup.sup_eq_closure_add
@@ -176,14 +176,14 @@ theorem mul_normal (H N : Subgroup G) [hN : N.Normal] : (↑(H ⊔ N) : Set G) =
   rw [sup_eq_closure_mul]
   refine Set.Subset.antisymm (fun x hx => ?_) subset_closure
   refine closure_induction'' (p := fun x => x ∈ (H : Set G) * (N : Set G)) hx ?_ ?_ ?_ ?_
-  · rintro _ ⟨x, y, hx, hy, rfl⟩
+  · rintro _ ⟨x, hx, y, hy, rfl⟩
     exact mul_mem_mul hx hy
-  · rintro _ ⟨x, y, hx, hy, rfl⟩
+  · rintro _ ⟨x, hx, y, hy, rfl⟩
     simpa only [mul_inv_rev, mul_assoc, inv_inv, inv_mul_cancel_left]
       using mul_mem_mul (inv_mem hx) (hN.conj_mem _ (inv_mem hy) x)
-  · exact ⟨1, 1, one_mem _, one_mem _, mul_one 1⟩
-  · rintro _ _ ⟨x, y, hx, hy, rfl⟩ ⟨x', y', hx', hy', rfl⟩
-    refine ⟨x * x', x'⁻¹ * y * x' * y', mul_mem hx hx', mul_mem ?_ hy', ?_⟩
+  · exact ⟨1, one_mem _, 1, one_mem _, mul_one 1⟩
+  · rintro _ _ ⟨x, hx, y, hy, rfl⟩ ⟨x', hx', y', hy', rfl⟩
+    refine ⟨x * x', mul_mem hx hx', x'⁻¹ * y * x' * y', mul_mem ?_ hy', ?_⟩
     · simpa using hN.conj_mem _ hy x'⁻¹
     · simp only [mul_assoc, mul_inv_cancel_left]
 #align subgroup.mul_normal Subgroup.mul_normal
@@ -203,11 +203,11 @@ theorem mul_inf_assoc (A B C : Subgroup G) (h : A ≤ C) :
   ext
   simp only [coe_inf, Set.mem_mul, Set.mem_inter_iff]
   constructor
-  · rintro ⟨y, z, hy, ⟨hzB, hzC⟩, rfl⟩
+  · rintro ⟨y, hy, z, ⟨hzB, hzC⟩, rfl⟩
     refine' ⟨_, mul_mem (h hy) hzC⟩
-    exact ⟨y, z, hy, hzB, rfl⟩
-  rintro ⟨⟨y, z, hy, hz, rfl⟩, hyz⟩
-  refine' ⟨y, z, hy, ⟨hz, _⟩, rfl⟩
+    exact ⟨y, hy, z, hzB, rfl⟩
+  rintro ⟨⟨y, hy, z, hz, rfl⟩, hyz⟩
+  refine' ⟨y, hy, z, ⟨hz, _⟩, rfl⟩
   suffices y⁻¹ * (y * z) ∈ C by simpa
   exact mul_mem (inv_mem (h hy)) hyz
 #align subgroup.mul_inf_assoc Subgroup.mul_inf_assoc
@@ -219,11 +219,11 @@ theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
   ext
   simp only [coe_inf, Set.mem_mul, Set.mem_inter_iff]
   constructor
-  · rintro ⟨y, z, ⟨hyA, hyB⟩, hz, rfl⟩
+  · rintro ⟨y, ⟨hyA, hyB⟩, z, hz, rfl⟩
     refine' ⟨A.mul_mem hyA (h hz), _⟩
-    exact ⟨y, z, hyB, hz, rfl⟩
-  rintro ⟨hyz, y, z, hy, hz, rfl⟩
-  refine' ⟨y, z, ⟨_, hy⟩, hz, rfl⟩
+    exact ⟨y, hyB, z, hz, rfl⟩
+  rintro ⟨hyz, y, hy, z, hz, rfl⟩
+  refine' ⟨y, ⟨_, hy⟩, z, hz, rfl⟩
   suffices y * z * z⁻¹ ∈ A by simpa
   exact mul_mem hyz (inv_mem (h hz))
 #align subgroup.inf_mul_assoc Subgroup.inf_mul_assoc
@@ -233,8 +233,8 @@ theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
 instance sup_normal (H K : Subgroup G) [hH : H.Normal] [hK : K.Normal] : (H ⊔ K).Normal where
   conj_mem n hmem g := by
     rw [← SetLike.mem_coe, normal_mul] at hmem ⊢
-    rcases hmem with ⟨h, k, hh, hk, rfl⟩
-    refine ⟨g * h * g⁻¹, g * k * g⁻¹, hH.conj_mem h hh g, hK.conj_mem k hk g, ?_⟩
+    rcases hmem with ⟨h, hh, k, hk, rfl⟩
+    refine ⟨g * h * g⁻¹, hH.conj_mem h hh g, g * k * g⁻¹, hK.conj_mem k hk g, ?_⟩
     simp only [mul_assoc, inv_mul_cancel_left]
 #align subgroup.sup_normal Subgroup.sup_normal

chore(Subgroup/Pointwise): golf, use ∩ (#9208)

e9294e6f

Diff

@@ -166,10 +166,8 @@ theorem sup_eq_closure_mul (H K : Subgroup G) : H ⊔ K = closure ((H : Set G) *
 @[to_additive]
 theorem set_mul_normal_comm (s : Set G) (N : Subgroup G) [hN : N.Normal] :
     s * (N : Set G) = (N : Set G) * s := by
-  ext x
-  refine (exists_congr fun y => ?_).trans exists_swap
-  simp only [exists_and_left, @and_left_comm _ (y ∈ s), ← eq_inv_mul_iff_mul_eq (b := y),
-    ← eq_mul_inv_iff_mul_eq (c := y), exists_eq_right, SetLike.mem_coe, hN.mem_comm_iff]
+  rw [← iUnion_mul_left_image, ← iUnion_mul_right_image]
+  simp only [image_mul_left, image_mul_right, Set.preimage, SetLike.mem_coe, hN.mem_comm_iff]
 
 /-- The carrier of `H ⊔ N` is just `↑H * ↑N` (pointwise set product) when `N` is normal. -/
 @[to_additive "The carrier of `H ⊔ N` is just `↑H + ↑N` (pointwise set addition)
@@ -199,12 +197,11 @@ theorem normal_mul (N H : Subgroup G) [N.Normal] : (↑(N ⊔ H) : Set G) = N *
 #align subgroup.normal_mul Subgroup.normal_mul
 #align add_subgroup.normal_add AddSubgroup.normal_add
 
--- porting note: todo: use `∩` in the RHS
 @[to_additive]
 theorem mul_inf_assoc (A B C : Subgroup G) (h : A ≤ C) :
-    (A : Set G) * ↑(B ⊓ C) = (A : Set G) * (B : Set G) ⊓ C := by
+    (A : Set G) * ↑(B ⊓ C) = (A : Set G) * (B : Set G) ∩ C := by
   ext
-  simp only [coe_inf, Set.inf_eq_inter, Set.mem_mul, Set.mem_inter_iff]
+  simp only [coe_inf, Set.mem_mul, Set.mem_inter_iff]
   constructor
   · rintro ⟨y, z, hy, ⟨hzB, hzC⟩, rfl⟩
     refine' ⟨_, mul_mem (h hy) hzC⟩
@@ -216,12 +213,11 @@ theorem mul_inf_assoc (A B C : Subgroup G) (h : A ≤ C) :
 #align subgroup.mul_inf_assoc Subgroup.mul_inf_assoc
 #align add_subgroup.add_inf_assoc AddSubgroup.add_inf_assoc
 
--- porting note: todo: use `∩` in the RHS
 @[to_additive]
 theorem inf_mul_assoc (A B C : Subgroup G) (h : C ≤ A) :
-    ((A ⊓ B : Subgroup G) : Set G) * C = (A : Set G) ⊓ ↑B * ↑C := by
+    ((A ⊓ B : Subgroup G) : Set G) * C = (A : Set G) ∩ (↑B * ↑C) := by
   ext
-  simp only [coe_inf, Set.inf_eq_inter, Set.mem_mul, Set.mem_inter_iff]
+  simp only [coe_inf, Set.mem_mul, Set.mem_inter_iff]
   constructor
   · rintro ⟨y, z, ⟨hyA, hyB⟩, hz, rfl⟩
     refine' ⟨A.mul_mem hyA (h hz), _⟩

refactor: Remove leftCoset/rightCoset (#8877)

Those two definitions are completely obsolete now that we have the pointwise API. This PR removes them but not the corresponding API. A much more tedious subsequent PR will be needed to merge the two API.

Note that I need to tweak simp lemmas to keep confluence since I'm merging two pairs of head keys together.

aa99c9f6

Diff

@@ -39,6 +39,16 @@ theorem inv_coe_set [InvolutiveInv G] [SetLike S G] [InvMemClass S G] {H : S} :
 #align inv_coe_set inv_coe_set
 #align neg_coe_set neg_coe_set
 
+@[to_additive (attr := simp)]
+lemma smul_coe_set [Group G] [SetLike S G] [SubgroupClass S G] {s : S} {a : G} (ha : a ∈ s) :
+    a • (s : Set G) = s := by
+  ext; simp [Set.mem_smul_set_iff_inv_smul_mem, mul_mem_cancel_left, ha]
+
+@[to_additive (attr := simp)]
+lemma op_smul_coe_set [Group G] [SetLike S G] [SubgroupClass S G] {s : S} {a : G} (ha : a ∈ s) :
+    MulOpposite.op a • (s : Set G) = s := by
+  ext; simp [Set.mem_smul_set_iff_inv_smul_mem, mul_mem_cancel_right, ha]
+
 variable [Group G] [AddGroup A] {s : Set G}
 
 namespace Subgroup

feat: sup_eq_closure for Submonoid and Subgroup (#7468)

71442323

Diff

@@ -145,13 +145,13 @@ theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure
 #align add_subgroup.closure_add_le AddSubgroup.closure_add_le
 
 @[to_additive]
-theorem sup_eq_closure (H K : Subgroup G) : H ⊔ K = closure ((H : Set G) * (K : Set G)) :=
+theorem sup_eq_closure_mul (H K : Subgroup G) : H ⊔ K = closure ((H : Set G) * (K : Set G)) :=
   le_antisymm
     (sup_le (fun h hh => subset_closure ⟨h, 1, hh, K.one_mem, mul_one h⟩) fun k hk =>
       subset_closure ⟨1, k, H.one_mem, hk, one_mul k⟩)
     ((closure_mul_le _ _).trans <| by rw [closure_eq, closure_eq])
-#align subgroup.sup_eq_closure Subgroup.sup_eq_closure
-#align add_subgroup.sup_eq_closure AddSubgroup.sup_eq_closure
+#align subgroup.sup_eq_closure Subgroup.sup_eq_closure_mul
+#align add_subgroup.sup_eq_closure AddSubgroup.sup_eq_closure_add
 
 @[to_additive]
 theorem set_mul_normal_comm (s : Set G) (N : Subgroup G) [hN : N.Normal] :
@@ -165,7 +165,7 @@ theorem set_mul_normal_comm (s : Set G) (N : Subgroup G) [hN : N.Normal] :
 @[to_additive "The carrier of `H ⊔ N` is just `↑H + ↑N` (pointwise set addition)
 when `N` is normal."]
 theorem mul_normal (H N : Subgroup G) [hN : N.Normal] : (↑(H ⊔ N) : Set G) = H * N := by
-  rw [sup_eq_closure]
+  rw [sup_eq_closure_mul]
   refine Set.Subset.antisymm (fun x hx => ?_) subset_closure
   refine closure_induction'' (p := fun x => x ∈ (H : Set G) * (N : Set G)) hx ?_ ?_ ?_ ?_
   · rintro _ ⟨x, y, hx, hy, rfl⟩

feat(GroupTheory/Submonoid): add opposite submonoids (#7415)

We already have API for the multiplicative opposite of subgroups.

This tidies the API for subgroups by introducing separate .op and .unop definitions (as dot notation on .opposite worked in Lean 3 but not Lean 4), and adds the same API for submonoids.

edaa10ad

Diff

@@ -240,7 +240,7 @@ theorem smul_opposite_image_mul_preimage' (g : G) (h : Gᵐᵒᵖ) (s : Set G) :
 
 -- porting note: deprecate?
 @[to_additive]
-theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : opposite H) (s : Set G) :
+theorem smul_opposite_image_mul_preimage {H : Subgroup G} (g : G) (h : H.op) (s : Set G) :
     (fun y => h • y) '' ((g * ·) ⁻¹' s) = (g * ·) ⁻¹' ((fun y => h • y) '' s) :=
   smul_opposite_image_mul_preimage' g h s
 #align subgroup.smul_opposite_image_mul_preimage Subgroup.smul_opposite_image_mul_preimage

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -31,7 +31,7 @@ open Set
 
 open Pointwise
 
-variable {α G A S : Type _}
+variable {α G A S : Type*}
 
 @[to_additive (attr := simp)]
 theorem inv_coe_set [InvolutiveInv G] [SetLike S G] [InvMemClass S G] {H : S} : (H : Set G)⁻¹ = H :=
@@ -110,7 +110,7 @@ then it holds for all elements of the supremum of `S`. -/
 @[to_additive (attr := elab_as_elim) " An induction principle for elements of `⨆ i, S i`.
 If `C` holds for `0` and all elements of `S i` for all `i`, and is preserved under addition,
 then it holds for all elements of the supremum of `S`. "]
-theorem iSup_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
+theorem iSup_induction {ι : Sort*} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
     (hp : ∀ (i), ∀ x ∈ S i, C x) (h1 : C 1) (hmul : ∀ x y, C x → C y → C (x * y)) : C x := by
   rw [iSup_eq_closure] at hx
   refine' closure_induction'' hx (fun x hx => _) (fun x hx => _) h1 hmul
@@ -123,7 +123,7 @@ theorem iSup_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x
 
 /-- A dependent version of `Subgroup.iSup_induction`. -/
 @[to_additive (attr := elab_as_elim) "A dependent version of `AddSubgroup.iSup_induction`. "]
-theorem iSup_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
+theorem iSup_induction' {ι : Sort*} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
     (hp : ∀ (i), ∀ x (hx : x ∈ S i), C x (mem_iSup_of_mem i hx)) (h1 : C 1 (one_mem _))
     (hmul : ∀ x y hx hy, C x hx → C y hy → C (x * y) (mul_mem ‹_› ‹_›)) {x : G}
     (hx : x ∈ ⨆ i, S i) : C x hx := by
@@ -380,7 +380,7 @@ theorem singleton_mul_subgroup {H : Subgroup G} {h : G} (hh : h ∈ H) : {h} * (
   rfl
 #align subgroup.singleton_mul_subgroup Subgroup.singleton_mul_subgroup
 
-theorem Normal.conjAct {G : Type _} [Group G] {H : Subgroup G} (hH : H.Normal) (g : ConjAct G) :
+theorem Normal.conjAct {G : Type*} [Group G] {H : Subgroup G} (hH : H.Normal) (g : ConjAct G) :
     g • H = H :=
   have : ∀ g : ConjAct G, g • H ≤ H :=
     fun _ => map_le_iff_le_comap.2 fun _ h => hH.conj_mem _ h _

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module group_theory.subgroup.pointwise
-! leanprover-community/mathlib commit e655e4ea5c6d02854696f97494997ba4c31be802
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.Subgroup.MulOpposite
 import Mathlib.GroupTheory.Submonoid.Pointwise
 import Mathlib.GroupTheory.GroupAction.ConjAct
 
+#align_import group_theory.subgroup.pointwise from "leanprover-community/mathlib"@"e655e4ea5c6d02854696f97494997ba4c31be802"
+
 /-! # Pointwise instances on `Subgroup` and `AddSubgroup`s
 
 This file provides the actions

chore: cleanup whitespace (#5988)

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

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

12343aa5

Diff

@@ -162,7 +162,7 @@ theorem set_mul_normal_comm (s : Set G) (N : Subgroup G) [hN : N.Normal] :
   ext x
   refine (exists_congr fun y => ?_).trans exists_swap
   simp only [exists_and_left, @and_left_comm _ (y ∈ s), ← eq_inv_mul_iff_mul_eq (b := y),
-    ← eq_mul_inv_iff_mul_eq  (c := y), exists_eq_right, SetLike.mem_coe, hN.mem_comm_iff]
+    ← eq_mul_inv_iff_mul_eq (c := y), exists_eq_right, SetLike.mem_coe, hN.mem_comm_iff]
 
 /-- The carrier of `H ⊔ N` is just `↑H * ↑N` (pointwise set product) when `N` is normal. -/
 @[to_additive "The carrier of `H ⊔ N` is just `↑H + ↑N` (pointwise set addition)

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

supₛ → sSup
infₛ → sInf
supᵢ → iSup
infᵢ → iInf
bsupₛ → bsSup
binfₛ → bsInf
bsupᵢ → biSup
binfᵢ → biInf
csupₛ → csSup
cinfₛ → csInf
csupᵢ → ciSup
cinfᵢ → ciInf
unionₛ → sUnion
interₛ → sInter
unionᵢ → iUnion
interᵢ → iInter
bunionₛ → bsUnion
binterₛ → bsInter
bunionᵢ → biUnion
binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

d1eb6264

Diff

@@ -113,35 +113,35 @@ then it holds for all elements of the supremum of `S`. -/
 @[to_additive (attr := elab_as_elim) " An induction principle for elements of `⨆ i, S i`.
 If `C` holds for `0` and all elements of `S i` for all `i`, and is preserved under addition,
 then it holds for all elements of the supremum of `S`. "]
-theorem supᵢ_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
+theorem iSup_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
     (hp : ∀ (i), ∀ x ∈ S i, C x) (h1 : C 1) (hmul : ∀ x y, C x → C y → C (x * y)) : C x := by
-  rw [supᵢ_eq_closure] at hx
+  rw [iSup_eq_closure] at hx
   refine' closure_induction'' hx (fun x hx => _) (fun x hx => _) h1 hmul
-  · obtain ⟨i, hi⟩ := Set.mem_unionᵢ.mp hx
+  · obtain ⟨i, hi⟩ := Set.mem_iUnion.mp hx
     exact hp _ _ hi
-  · obtain ⟨i, hi⟩ := Set.mem_unionᵢ.mp hx
+  · obtain ⟨i, hi⟩ := Set.mem_iUnion.mp hx
     exact hp _ _ (inv_mem hi)
-#align subgroup.supr_induction Subgroup.supᵢ_induction
-#align add_subgroup.supr_induction AddSubgroup.supᵢ_induction
+#align subgroup.supr_induction Subgroup.iSup_induction
+#align add_subgroup.supr_induction AddSubgroup.iSup_induction
 
-/-- A dependent version of `Subgroup.supᵢ_induction`. -/
-@[to_additive (attr := elab_as_elim) "A dependent version of `AddSubgroup.supᵢ_induction`. "]
-theorem supᵢ_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
-    (hp : ∀ (i), ∀ x (hx : x ∈ S i), C x (mem_supᵢ_of_mem i hx)) (h1 : C 1 (one_mem _))
+/-- A dependent version of `Subgroup.iSup_induction`. -/
+@[to_additive (attr := elab_as_elim) "A dependent version of `AddSubgroup.iSup_induction`. "]
+theorem iSup_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
+    (hp : ∀ (i), ∀ x (hx : x ∈ S i), C x (mem_iSup_of_mem i hx)) (h1 : C 1 (one_mem _))
     (hmul : ∀ x y hx hy, C x hx → C y hy → C (x * y) (mul_mem ‹_› ‹_›)) {x : G}
     (hx : x ∈ ⨆ i, S i) : C x hx := by
   suffices : ∃ h, C x h; exact this.snd
-  refine' supᵢ_induction S (C := fun x => ∃ h, C x h) hx (fun i x hx => _) _ fun x y => _
+  refine' iSup_induction S (C := fun x => ∃ h, C x h) hx (fun i x hx => _) _ fun x y => _
   · exact ⟨_, hp i _ hx⟩
   · exact ⟨_, h1⟩
   · rintro ⟨_, Cx⟩ ⟨_, Cy⟩
     refine' ⟨_, hmul _ _ _ _ Cx Cy⟩
-#align subgroup.supr_induction' Subgroup.supᵢ_induction'
-#align add_subgroup.supr_induction' AddSubgroup.supᵢ_induction'
+#align subgroup.supr_induction' Subgroup.iSup_induction'
+#align add_subgroup.supr_induction' AddSubgroup.iSup_induction'
 
 @[to_additive]
 theorem closure_mul_le (S T : Set G) : closure (S * T) ≤ closure S ⊔ closure T :=
-  infₛ_le fun _x ⟨_s, _t, hs, ht, hx⟩ => hx ▸
+  sInf_le fun _x ⟨_s, _t, hs, ht, hx⟩ => hx ▸
     (closure S ⊔ closure T).mul_mem (SetLike.le_def.mp le_sup_left <| subset_closure hs)
       (SetLike.le_def.mp le_sup_right <| subset_closure ht)
 #align subgroup.closure_mul_le Subgroup.closure_mul_le

https://github.com/leanprover-community/mathlib/pull/18668

feat: Induction principle for powers (#3278)

f8369997

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module group_theory.subgroup.pointwise
-! leanprover-community/mathlib commit c10e724be91096453ee3db13862b9fb9a992fef2
+! leanprover-community/mathlib commit e655e4ea5c6d02854696f97494997ba4c31be802
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -66,7 +66,9 @@ theorem closure_toSubmonoid (S : Set G) :
 #align subgroup.closure_to_submonoid Subgroup.closure_toSubmonoid
 #align add_subgroup.closure_to_add_submonoid AddSubgroup.closure_toAddSubmonoid
 
-@[to_additive]
+/-- For subgroups generated by a single element, see the simpler `zpow_induction_left`. -/
+@[to_additive "For additive subgroups generated by a single element, see the simpler
+`zsmul_induction_left`."]
 theorem closure_induction_left {p : G → Prop} {x : G} (h : x ∈ closure s) (H1 : p 1)
     (Hmul : ∀ x ∈ s, ∀ (y), p y → p (x * y)) (Hinv : ∀ x ∈ s, ∀ (y), p y → p (x⁻¹ * y)) : p x :=
   let key := (closure_toSubmonoid s).le
@@ -75,7 +77,9 @@ theorem closure_induction_left {p : G → Prop} {x : G} (h : x ∈ closure s) (H
 #align subgroup.closure_induction_left Subgroup.closure_induction_left
 #align add_subgroup.closure_induction_left AddSubgroup.closure_induction_left
 
-@[to_additive]
+/-- For subgroups generated by a single element, see the simpler `zpow_induction_right`. -/
+@[to_additive "For additive subgroups generated by a single element, see the simpler
+`zsmul_induction_right`."]
 theorem closure_induction_right {p : G → Prop} {x : G} (h : x ∈ closure s) (H1 : p 1)
     (Hmul : ∀ (x), ∀ y ∈ s, p x → p (x * y)) (Hinv : ∀ (x), ∀ y ∈ s, p x → p (x * y⁻¹)) : p x :=
   let key := (closure_toSubmonoid s).le

chore: tidy various files (#2950)

f03c405e

Diff

@@ -365,9 +365,9 @@ theorem smul_inf (a : α) (S T : Subgroup G) : a • (S ⊓ T) = a • S ⊓ a 
 
 /-- Applying a `MulDistribMulAction` results in an isomorphic subgroup -/
 @[simps!]
-def equivSmul (a : α) (H : Subgroup G) : H ≃* (a • H : Subgroup G) :=
+def equivSMul (a : α) (H : Subgroup G) : H ≃* (a • H : Subgroup G) :=
   (MulDistribMulAction.toMulEquiv G a).subgroupMap H
-#align subgroup.equiv_smul Subgroup.equivSmul
+#align subgroup.equiv_smul Subgroup.equivSMul
 
 theorem subgroup_mul_singleton {H : Subgroup G} {h : G} (hh : h ∈ H) : (H : Set G) * {h} = H :=
   suffices { x : G | x ∈ H } = ↑H by simpa [preimage, mul_mem_cancel_right (inv_mem hh)]

Fix: Move more attributes to the attr argument of to_additive (#2558)

e8072f65

Diff

@@ -106,7 +106,7 @@ theorem closure_induction'' {p : G → Prop} {x} (h : x ∈ closure s) (Hk : ∀
 /-- An induction principle for elements of `⨆ i, S i`.
 If `C` holds for `1` and all elements of `S i` for all `i`, and is preserved under multiplication,
 then it holds for all elements of the supremum of `S`. -/
-@[elab_as_elim, to_additive " An induction principle for elements of `⨆ i, S i`.
+@[to_additive (attr := elab_as_elim) " An induction principle for elements of `⨆ i, S i`.
 If `C` holds for `0` and all elements of `S i` for all `i`, and is preserved under addition,
 then it holds for all elements of the supremum of `S`. "]
 theorem supᵢ_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop} {x : G} (hx : x ∈ ⨆ i, S i)
@@ -121,7 +121,7 @@ theorem supᵢ_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop}
 #align add_subgroup.supr_induction AddSubgroup.supᵢ_induction
 
 /-- A dependent version of `Subgroup.supᵢ_induction`. -/
-@[elab_as_elim, to_additive "A dependent version of `AddSubgroup.supᵢ_induction`. "]
+@[to_additive (attr := elab_as_elim) "A dependent version of `AddSubgroup.supᵢ_induction`. "]
 theorem supᵢ_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
     (hp : ∀ (i), ∀ x (hx : x ∈ S i), C x (mem_supᵢ_of_mem i hx)) (h1 : C 1 (one_mem _))
     (hmul : ∀ x y hx hy, C x hx → C y hy → C (x * y) (mul_mem ‹_› ‹_›)) {x : G}

feat: add units.embedding_val₀ (#2590)

Forward-port #18536

3155a57a

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module group_theory.subgroup.pointwise
-! leanprover-community/mathlib commit 59694bd07f0a39c5beccba34bd9f413a160782bf
+! leanprover-community/mathlib commit c10e724be91096453ee3db13862b9fb9a992fef2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -34,15 +34,16 @@ open Set
 
 open Pointwise
 
-variable {α G A S : Type _} [Group G] [AddGroup A] {s : Set G}
+variable {α G A S : Type _}
 
 @[to_additive (attr := simp)]
-theorem inv_coe_set [SetLike S G] [SubgroupClass S G] {H : S} : (H : Set G)⁻¹ = H := by
-  ext
-  simp
+theorem inv_coe_set [InvolutiveInv G] [SetLike S G] [InvMemClass S G] {H : S} : (H : Set G)⁻¹ = H :=
+  Set.ext fun _ => inv_mem_iff
 #align inv_coe_set inv_coe_set
 #align neg_coe_set neg_coe_set
 
+variable [Group G] [AddGroup A] {s : Set G}
+
 namespace Subgroup
 
 @[to_additive (attr := simp)]

feat: require @[simps!] if simps runs in expensive mode (#1885)

This does not change the behavior of simps, just raises a linter error if you run simps in a more expensive mode without writing !.
Fixed some incorrect occurrences of to_additive, simps. Will do that systematically in future PR.
Fix port of OmegaCompletePartialOrder.ContinuousHom.ofMono a bit

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

52c04a34

Diff

@@ -363,7 +363,7 @@ theorem smul_inf (a : α) (S T : Subgroup G) : a • (S ⊓ T) = a • S ⊓ a 
 #align subgroup.smul_inf Subgroup.smul_inf
 
 /-- Applying a `MulDistribMulAction` results in an isomorphic subgroup -/
-@[simps]
+@[simps!]
 def equivSmul (a : α) (H : Subgroup G) : H ≃* (a • H : Subgroup G) :=
   (MulDistribMulAction.toMulEquiv G a).subgroupMap H
 #align subgroup.equiv_smul Subgroup.equivSmul

chore: tidy various files (#2009)

ec8fde78

Diff

@@ -19,7 +19,7 @@ This file provides the actions
 * `Subgroup.pointwiseMulAction`
 * `AddSubgroup.pointwiseMulAction`
 
-which matches the action of `mul_action_set`.
+which matches the action of `Set.mulActionSet`.
 
 These actions are available in the `Pointwise` locale.
 
@@ -120,7 +120,7 @@ theorem supᵢ_induction {ι : Sort _} (S : ι → Subgroup G) {C : G → Prop}
 #align add_subgroup.supr_induction AddSubgroup.supᵢ_induction
 
 /-- A dependent version of `Subgroup.supᵢ_induction`. -/
-@[elab_as_elim, to_additive "A dependent version of `add_subgroup.supr_induction`. "]
+@[elab_as_elim, to_additive "A dependent version of `AddSubgroup.supᵢ_induction`. "]
 theorem supᵢ_induction' {ι : Sort _} (S : ι → Subgroup G) {C : ∀ x, (x ∈ ⨆ i, S i) → Prop}
     (hp : ∀ (i), ∀ x (hx : x ∈ S i), C x (mem_supᵢ_of_mem i hx)) (h1 : C 1 (one_mem _))
     (hmul : ∀ x y hx hy, C x hx → C y hy → C (x * y) (mul_mem ‹_› ‹_›)) {x : G}
@@ -304,10 +304,10 @@ theorem smul_closure (a : α) (s : Set G) : a • closure s = closure (a • s)
   MonoidHom.map_closure _ _
 #align subgroup.smul_closure Subgroup.smul_closure
 
-instance pointwise_central_scalar [MulDistribMulAction αᵐᵒᵖ G] [IsCentralScalar α G] :
+instance pointwise_isCentralScalar [MulDistribMulAction αᵐᵒᵖ G] [IsCentralScalar α G] :
     IsCentralScalar α (Subgroup G) :=
   ⟨fun _ S => (congr_arg fun f => S.map f) <| MonoidHom.ext <| op_smul_eq_smul _⟩
-#align subgroup.pointwise_central_scalar Subgroup.pointwise_central_scalar
+#align subgroup.pointwise_central_scalar Subgroup.pointwise_isCentralScalar
 
 theorem conj_smul_le_of_le {P H : Subgroup G} (hP : P ≤ H) (h : H) :
     MulAut.conj (h : G) • P ≤ H := by
@@ -471,10 +471,10 @@ theorem mem_smul_pointwise_iff_exists (m : A) (a : α) (S : AddSubgroup A) :
   (Set.mem_smul_set : m ∈ a • (S : Set A) ↔ _)
 #align add_subgroup.mem_smul_pointwise_iff_exists AddSubgroup.mem_smul_pointwise_iff_exists
 
-instance pointwise_central_scalar [DistribMulAction αᵐᵒᵖ A] [IsCentralScalar α A] :
+instance pointwise_isCentralScalar [DistribMulAction αᵐᵒᵖ A] [IsCentralScalar α A] :
     IsCentralScalar α (AddSubgroup A) :=
   ⟨fun _ S => (congr_arg fun f => S.map f) <| AddMonoidHom.ext <| op_smul_eq_smul _⟩
-#align add_subgroup.pointwise_central_scalar AddSubgroup.pointwise_central_scalar
+#align add_subgroup.pointwise_central_scalar AddSubgroup.pointwise_isCentralScalar
 
 end Monoid