group_theory.double_coset | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

4c19a16e

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

50832dae

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -72,7 +72,7 @@ theorem doset_eq_of_mem {H K : Subgroup G} {a b : G} (hb : b ∈ Doset.doset a H
 theorem mem_doset_of_not_disjoint {H K : Subgroup G} {a b : G}
     (h : ¬Disjoint (Doset.doset a H K) (Doset.doset b H K)) : b ∈ Doset.doset a H K :=
   by
-  rw [Set.not_disjoint_iff] at h 
+  rw [Set.not_disjoint_iff] at h
   simp only [mem_doset] at *
   obtain ⟨x, ⟨l, hl, r, hr, hrx⟩, y, hy, ⟨r', hr', rfl⟩⟩ := h
   refine' ⟨y⁻¹ * l, H.mul_mem (H.inv_mem hy) hl, r * r'⁻¹, K.mul_mem hr (K.inv_mem hr'), _⟩
@@ -85,7 +85,7 @@ theorem eq_of_not_disjoint {H K : Subgroup G} {a b : G}
     (h : ¬Disjoint (Doset.doset a H K) (Doset.doset b H K)) :
     Doset.doset a H K = Doset.doset b H K :=
   by
-  rw [disjoint_comm] at h 
+  rw [disjoint_comm] at h
   have ha : a ∈ Doset.doset b H K := mem_doset_of_not_disjoint h
   apply doset_eq_of_mem ha
 #align doset.eq_of_not_disjoint Doset.eq_of_not_disjoint
@@ -178,7 +178,7 @@ theorem mk_out'_eq_mul (H K : Subgroup G) (g : G) :
     ∃ h k : G, h ∈ H ∧ k ∈ K ∧ (mk H K g : Quotient ↑H ↑K).out' = h * g * k :=
   by
   have := Eq H K (mk H K g : Quotient ↑H ↑K).out' g
-  rw [out_eq'] at this 
+  rw [out_eq'] at this
   obtain ⟨h, h_h, k, hk, T⟩ := this.1 rfl
   refine' ⟨h⁻¹, k⁻¹, H.inv_mem h_h, K.inv_mem hk, eq_mul_inv_of_mul_eq (eq_inv_mul_of_mul_eq _)⟩
   rw [← mul_assoc, ← T]

50832dae

bump to nightly-2023-12-11-06

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

b0afba85

Diff

@@ -235,7 +235,7 @@ theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
 
 #print Doset.doset_union_leftCoset /-
 theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
-    (⋃ h : H, leftCoset (h * a : G) K) = Doset.doset a H K :=
+    (⋃ h : H, HSMul.hSMul (h * a : G) K) = Doset.doset a H K :=
   by
   ext x
   simp only [mem_leftCoset_iff, mul_inv_rev, Set.mem_iUnion, mem_doset]

50832dae

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,12 +3,12 @@ Copyright (c) 2021 Chris Birkbeck. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Birkbeck
 -/
-import Mathbin.Data.Setoid.Basic
-import Mathbin.GroupTheory.Subgroup.Basic
-import Mathbin.GroupTheory.Coset
-import Mathbin.GroupTheory.Subgroup.Pointwise
-import Mathbin.Data.Set.Basic
-import Mathbin.Tactic.Group
+import Data.Setoid.Basic
+import GroupTheory.Subgroup.Basic
+import GroupTheory.Coset
+import GroupTheory.Subgroup.Pointwise
+import Data.Set.Basic
+import Tactic.Group
 
 #align_import group_theory.double_coset from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"

50832dae

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Chris Birkbeck. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Birkbeck
-
-! This file was ported from Lean 3 source module group_theory.double_coset
-! leanprover-community/mathlib commit 50832daea47b195a48b5b33b1c8b2162c48c3afc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Setoid.Basic
 import Mathbin.GroupTheory.Subgroup.Basic
@@ -15,6 +10,8 @@ import Mathbin.GroupTheory.Subgroup.Pointwise
 import Mathbin.Data.Set.Basic
 import Mathbin.Tactic.Group
 
+#align_import group_theory.double_coset from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
+
 /-!
 # Double cosets

50832dae

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -121,7 +121,7 @@ theorem rel_iff {H K : Subgroup G} {x y : G} :
 theorem bot_rel_eq_leftRel (H : Subgroup G) :
     (setoid ↑(⊥ : Subgroup G) ↑H).Rel = (QuotientGroup.leftRel H).Rel :=
   by
-  ext (a b)
+  ext a b
   rw [rel_iff, Setoid.Rel, QuotientGroup.leftRel_apply]
   constructor
   · rintro ⟨a, rfl : a = 1, b, hb, rfl⟩
@@ -136,7 +136,7 @@ theorem bot_rel_eq_leftRel (H : Subgroup G) :
 theorem rel_bot_eq_right_group_rel (H : Subgroup G) :
     (setoid ↑H ↑(⊥ : Subgroup G)).Rel = (QuotientGroup.rightRel H).Rel :=
   by
-  ext (a b)
+  ext a b
   rw [rel_iff, Setoid.Rel, QuotientGroup.rightRel_apply]
   constructor
   · rintro ⟨b, hb, a, rfl : a = 1, rfl⟩

50832dae

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -46,16 +46,21 @@ def Doset.doset (a : α) (s t : Set α) : Set α :=
 #align doset Doset.doset
 -/
 
+#print Doset.mem_doset /-
 theorem mem_doset {s t : Set α} {a b : α} :
     b ∈ Doset.doset a s t ↔ ∃ x ∈ s, ∃ y ∈ t, b = x * a * y :=
   ⟨fun ⟨_, y, ⟨x, _, hx, rfl, rfl⟩, hy, h⟩ => ⟨x, hx, y, hy, h.symm⟩, fun ⟨x, hx, y, hy, h⟩ =>
     ⟨x * a, y, ⟨x, a, hx, rfl, rfl⟩, hy, h.symm⟩⟩
 #align doset.mem_doset Doset.mem_doset
+-/
 
+#print Doset.mem_doset_self /-
 theorem mem_doset_self (H K : Subgroup G) (a : G) : a ∈ Doset.doset a H K :=
   mem_doset.mpr ⟨1, H.one_mem, 1, K.one_mem, (one_mul a).symm.trans (mul_one (1 * a)).symm⟩
 #align doset.mem_doset_self Doset.mem_doset_self
+-/
 
+#print Doset.doset_eq_of_mem /-
 theorem doset_eq_of_mem {H K : Subgroup G} {a b : G} (hb : b ∈ Doset.doset a H K) :
     Doset.doset b H K = Doset.doset a H K :=
   by
@@ -64,7 +69,9 @@ theorem doset_eq_of_mem {H K : Subgroup G} {a b : G} (hb : b ∈ Doset.doset a H
     mul_assoc, mul_assoc, Subgroup.singleton_mul_subgroup hk, ← mul_assoc, ← mul_assoc,
     Subgroup.subgroup_mul_singleton hh]
 #align doset.doset_eq_of_mem Doset.doset_eq_of_mem
+-/
 
+#print Doset.mem_doset_of_not_disjoint /-
 theorem mem_doset_of_not_disjoint {H K : Subgroup G} {a b : G}
     (h : ¬Disjoint (Doset.doset a H K) (Doset.doset b H K)) : b ∈ Doset.doset a H K :=
   by
@@ -74,7 +81,9 @@ theorem mem_doset_of_not_disjoint {H K : Subgroup G} {a b : G}
   refine' ⟨y⁻¹ * l, H.mul_mem (H.inv_mem hy) hl, r * r'⁻¹, K.mul_mem hr (K.inv_mem hr'), _⟩
   rwa [mul_assoc, mul_assoc, eq_inv_mul_iff_mul_eq, ← mul_assoc, ← mul_assoc, eq_mul_inv_iff_mul_eq]
 #align doset.mem_doset_of_not_disjoint Doset.mem_doset_of_not_disjoint
+-/
 
+#print Doset.eq_of_not_disjoint /-
 theorem eq_of_not_disjoint {H K : Subgroup G} {a b : G}
     (h : ¬Disjoint (Doset.doset a H K) (Doset.doset b H K)) :
     Doset.doset a H K = Doset.doset b H K :=
@@ -83,6 +92,7 @@ theorem eq_of_not_disjoint {H K : Subgroup G} {a b : G}
   have ha : a ∈ Doset.doset b H K := mem_doset_of_not_disjoint h
   apply doset_eq_of_mem ha
 #align doset.eq_of_not_disjoint Doset.eq_of_not_disjoint
+-/
 
 #print Doset.setoid /-
 /-- The setoid defined by the double_coset relation -/
@@ -98,13 +108,16 @@ def Quotient (H K : Set G) : Type _ :=
 #align doset.quotient Doset.Quotient
 -/
 
+#print Doset.rel_iff /-
 theorem rel_iff {H K : Subgroup G} {x y : G} :
     (setoid ↑H ↑K).Rel x y ↔ ∃ a ∈ H, ∃ b ∈ K, y = a * x * b :=
   Iff.trans
     ⟨fun hxy => (congr_arg _ hxy).mpr (mem_doset_self H K y), fun hxy => (doset_eq_of_mem hxy).symm⟩
     mem_doset
 #align doset.rel_iff Doset.rel_iff
+-/
 
+#print Doset.bot_rel_eq_leftRel /-
 theorem bot_rel_eq_leftRel (H : Subgroup G) :
     (setoid ↑(⊥ : Subgroup G) ↑H).Rel = (QuotientGroup.leftRel H).Rel :=
   by
@@ -117,7 +130,9 @@ theorem bot_rel_eq_leftRel (H : Subgroup G) :
   · rintro (h : a⁻¹ * b ∈ H)
     exact ⟨1, rfl, a⁻¹ * b, h, by rw [one_mul, mul_inv_cancel_left]⟩
 #align doset.bot_rel_eq_left_rel Doset.bot_rel_eq_leftRel
+-/
 
+#print Doset.rel_bot_eq_right_group_rel /-
 theorem rel_bot_eq_right_group_rel (H : Subgroup G) :
     (setoid ↑H ↑(⊥ : Subgroup G)).Rel = (QuotientGroup.rightRel H).Rel :=
   by
@@ -130,28 +145,38 @@ theorem rel_bot_eq_right_group_rel (H : Subgroup G) :
   · rintro (h : b * a⁻¹ ∈ H)
     exact ⟨b * a⁻¹, h, 1, rfl, by rw [mul_one, inv_mul_cancel_right]⟩
 #align doset.rel_bot_eq_right_group_rel Doset.rel_bot_eq_right_group_rel
+-/
 
+#print Doset.quotToDoset /-
 /-- Create a doset out of an element of `H \ G / K`-/
 def quotToDoset (H K : Subgroup G) (q : Quotient ↑H ↑K) : Set G :=
   Doset.doset q.out' H K
 #align doset.quot_to_doset Doset.quotToDoset
+-/
 
+#print Doset.mk /-
 /-- Map from `G` to `H \ G / K`-/
 abbrev mk (H K : Subgroup G) (a : G) : Quotient ↑H ↑K :=
   Quotient.mk'' a
 #align doset.mk Doset.mk
+-/
 
 instance (H K : Subgroup G) : Inhabited (Quotient ↑H ↑K) :=
   ⟨mk H K (1 : G)⟩
 
+#print Doset.eq /-
 theorem eq (H K : Subgroup G) (a b : G) : mk H K a = mk H K b ↔ ∃ h ∈ H, ∃ k ∈ K, b = h * a * k :=
   by rw [Quotient.eq'']; apply rel_iff
 #align doset.eq Doset.eq
+-/
 
+#print Doset.out_eq' /-
 theorem out_eq' (H K : Subgroup G) (q : Quotient ↑H ↑K) : mk H K q.out' = q :=
   Quotient.out_eq' q
 #align doset.out_eq' Doset.out_eq'
+-/
 
+#print Doset.mk_out'_eq_mul /-
 theorem mk_out'_eq_mul (H K : Subgroup G) (g : G) :
     ∃ h k : G, h ∈ H ∧ k ∈ K ∧ (mk H K g : Quotient ↑H ↑K).out' = h * g * k :=
   by
@@ -161,13 +186,17 @@ theorem mk_out'_eq_mul (H K : Subgroup G) (g : G) :
   refine' ⟨h⁻¹, k⁻¹, H.inv_mem h_h, K.inv_mem hk, eq_mul_inv_of_mul_eq (eq_inv_mul_of_mul_eq _)⟩
   rw [← mul_assoc, ← T]
 #align doset.mk_out'_eq_mul Doset.mk_out'_eq_mul
+-/
 
+#print Doset.mk_eq_of_doset_eq /-
 theorem mk_eq_of_doset_eq {H K : Subgroup G} {a b : G} (h : Doset.doset a H K = Doset.doset b H K) :
     mk H K a = mk H K b := by
   rw [Eq]
   exact mem_doset.mp (h.symm ▸ mem_doset_self H K b)
 #align doset.mk_eq_of_doset_eq Doset.mk_eq_of_doset_eq
+-/
 
+#print Doset.disjoint_out' /-
 theorem disjoint_out' {H K : Subgroup G} {a b : Quotient H.1 K} :
     a ≠ b → Disjoint (Doset.doset a.out' H K) (Doset.doset b.out' H K) :=
   by
@@ -175,7 +204,9 @@ theorem disjoint_out' {H K : Subgroup G} {a b : Quotient H.1 K} :
   intro h
   simpa [out_eq'] using mk_eq_of_doset_eq (eq_of_not_disjoint h)
 #align doset.disjoint_out' Doset.disjoint_out'
+-/
 
+#print Doset.union_quotToDoset /-
 theorem union_quotToDoset (H K : Subgroup G) : (⋃ q, quotToDoset H K q) = Set.univ :=
   by
   ext x
@@ -186,7 +217,9 @@ theorem union_quotToDoset (H K : Subgroup G) : (⋃ q, quotToDoset H K q) = Set.
   refine' ⟨h⁻¹, H.inv_mem h3, k⁻¹, K.inv_mem h4, _⟩
   simp only [h5, Subgroup.coe_mk, ← mul_assoc, one_mul, mul_left_inv, mul_inv_cancel_right]
 #align doset.union_quot_to_doset Doset.union_quotToDoset
+-/
 
+#print Doset.doset_union_rightCoset /-
 theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
     (⋃ k : K, rightCoset (↑H) (a * k)) = Doset.doset a H K :=
   by
@@ -201,7 +234,9 @@ theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
     refine' ⟨⟨y, hy⟩, _⟩
     simp only [hxy, ← mul_assoc, hx, mul_inv_cancel_right, Subgroup.coe_mk]
 #align doset.doset_union_right_coset Doset.doset_union_rightCoset
+-/
 
+#print Doset.doset_union_leftCoset /-
 theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
     (⋃ h : H, leftCoset (h * a : G) K) = Doset.doset a H K :=
   by
@@ -215,7 +250,9 @@ theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
     refine' ⟨⟨x, hx⟩, _⟩
     simp only [hxy, ← mul_assoc, hy, one_mul, mul_left_inv, Subgroup.coe_mk, inv_mul_cancel_right]
 #align doset.doset_union_left_coset Doset.doset_union_leftCoset
+-/
 
+#print Doset.left_bot_eq_left_quot /-
 theorem left_bot_eq_left_quot (H : Subgroup G) : Quotient (⊥ : Subgroup G).1 H = (G ⧸ H) :=
   by
   unfold Quotient
@@ -224,7 +261,9 @@ theorem left_bot_eq_left_quot (H : Subgroup G) : Quotient (⊥ : Subgroup G).1 H
   simp_rw [← bot_rel_eq_left_rel H]
   rfl
 #align doset.left_bot_eq_left_quot Doset.left_bot_eq_left_quot
+-/
 
+#print Doset.right_bot_eq_right_quot /-
 theorem right_bot_eq_right_quot (H : Subgroup G) :
     Quotient H.1 (⊥ : Subgroup G) = Quotient (QuotientGroup.rightRel H) :=
   by
@@ -234,6 +273,7 @@ theorem right_bot_eq_right_quot (H : Subgroup G) :
   simp_rw [← rel_bot_eq_right_group_rel H]
   rfl
 #align doset.right_bot_eq_right_quot Doset.right_bot_eq_right_quot
+-/
 
 end Doset.doset

50832dae

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -68,7 +68,7 @@ theorem doset_eq_of_mem {H K : Subgroup G} {a b : G} (hb : b ∈ Doset.doset a H
 theorem mem_doset_of_not_disjoint {H K : Subgroup G} {a b : G}
     (h : ¬Disjoint (Doset.doset a H K) (Doset.doset b H K)) : b ∈ Doset.doset a H K :=
   by
-  rw [Set.not_disjoint_iff] at h
+  rw [Set.not_disjoint_iff] at h 
   simp only [mem_doset] at *
   obtain ⟨x, ⟨l, hl, r, hr, hrx⟩, y, hy, ⟨r', hr', rfl⟩⟩ := h
   refine' ⟨y⁻¹ * l, H.mul_mem (H.inv_mem hy) hl, r * r'⁻¹, K.mul_mem hr (K.inv_mem hr'), _⟩
@@ -79,7 +79,7 @@ theorem eq_of_not_disjoint {H K : Subgroup G} {a b : G}
     (h : ¬Disjoint (Doset.doset a H K) (Doset.doset b H K)) :
     Doset.doset a H K = Doset.doset b H K :=
   by
-  rw [disjoint_comm] at h
+  rw [disjoint_comm] at h 
   have ha : a ∈ Doset.doset b H K := mem_doset_of_not_disjoint h
   apply doset_eq_of_mem ha
 #align doset.eq_of_not_disjoint Doset.eq_of_not_disjoint
@@ -156,7 +156,7 @@ theorem mk_out'_eq_mul (H K : Subgroup G) (g : G) :
     ∃ h k : G, h ∈ H ∧ k ∈ K ∧ (mk H K g : Quotient ↑H ↑K).out' = h * g * k :=
   by
   have := Eq H K (mk H K g : Quotient ↑H ↑K).out' g
-  rw [out_eq'] at this
+  rw [out_eq'] at this 
   obtain ⟨h, h_h, k, hk, T⟩ := this.1 rfl
   refine' ⟨h⁻¹, k⁻¹, H.inv_mem h_h, K.inv_mem hk, eq_mul_inv_of_mul_eq (eq_inv_mul_of_mul_eq _)⟩
   rw [← mul_assoc, ← T]

50832dae

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -37,7 +37,7 @@ variable {G : Type _} [Group G] {α : Type _} [Mul α] (J : Subgroup G) (g : G)
 
 namespace Doset.doset
 
-open Pointwise
+open scoped Pointwise
 
 #print Doset.doset /-
 /-- The double_coset as an element of `set α` corresponding to `s a t` -/

50832dae

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -46,34 +46,16 @@ def Doset.doset (a : α) (s t : Set α) : Set α :=
 #align doset Doset.doset
 -/
 
-/- warning: doset.mem_doset -> Doset.mem_doset is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_2 : Mul.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α} {a : α} {b : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Doset.doset.{u1} α _inst_2 a s t)) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => Eq.{succ u1} α b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_2) x a) y))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_2 : Mul.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α} {a : α} {b : α}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Doset.doset.{u1} α _inst_2 a s t)) (Exists.{succ u1} α (fun (x : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (Eq.{succ u1} α b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_2) x a) y))))))
-Case conversion may be inaccurate. Consider using '#align doset.mem_doset Doset.mem_dosetₓ'. -/
 theorem mem_doset {s t : Set α} {a b : α} :
     b ∈ Doset.doset a s t ↔ ∃ x ∈ s, ∃ y ∈ t, b = x * a * y :=
   ⟨fun ⟨_, y, ⟨x, _, hx, rfl, rfl⟩, hy, h⟩ => ⟨x, hx, y, hy, h.symm⟩, fun ⟨x, hx, y, hy, h⟩ =>
     ⟨x * a, y, ⟨x, a, hx, rfl, rfl⟩, hy, h.symm⟩⟩
 #align doset.mem_doset Doset.mem_doset
 
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 theorem mem_doset_self (H K : Subgroup G) (a : G) : a ∈ Doset.doset a H K :=
   mem_doset.mpr ⟨1, H.one_mem, 1, K.one_mem, (one_mul a).symm.trans (mul_one (1 * a)).symm⟩
 #align doset.mem_doset_self Doset.mem_doset_self
 
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-Case conversion may be inaccurate. Consider using '#align doset.doset_eq_of_mem Doset.doset_eq_of_memₓ'. -/
 theorem doset_eq_of_mem {H K : Subgroup G} {a b : G} (hb : b ∈ Doset.doset a H K) :
     Doset.doset b H K = Doset.doset a H K :=
   by
@@ -83,12 +65,6 @@ theorem doset_eq_of_mem {H K : Subgroup G} {a b : G} (hb : b ∈ Doset.doset a H
     Subgroup.subgroup_mul_singleton hh]
 #align doset.doset_eq_of_mem Doset.doset_eq_of_mem
 
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-Case conversion may be inaccurate. Consider using '#align doset.mem_doset_of_not_disjoint Doset.mem_doset_of_not_disjointₓ'. -/
 theorem mem_doset_of_not_disjoint {H K : Subgroup G} {a b : G}
     (h : ¬Disjoint (Doset.doset a H K) (Doset.doset b H K)) : b ∈ Doset.doset a H K :=
   by
@@ -99,12 +75,6 @@ theorem mem_doset_of_not_disjoint {H K : Subgroup G} {a b : G}
   rwa [mul_assoc, mul_assoc, eq_inv_mul_iff_mul_eq, ← mul_assoc, ← mul_assoc, eq_mul_inv_iff_mul_eq]
 #align doset.mem_doset_of_not_disjoint Doset.mem_doset_of_not_disjoint
 
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 theorem eq_of_not_disjoint {H K : Subgroup G} {a b : G}
     (h : ¬Disjoint (Doset.doset a H K) (Doset.doset b H K)) :
     Doset.doset a H K = Doset.doset b H K :=
@@ -128,12 +98,6 @@ def Quotient (H K : Set G) : Type _ :=
 #align doset.quotient Doset.Quotient
 -/
 
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-Case conversion may be inaccurate. Consider using '#align doset.rel_iff Doset.rel_iffₓ'. -/
 theorem rel_iff {H K : Subgroup G} {x y : G} :
     (setoid ↑H ↑K).Rel x y ↔ ∃ a ∈ H, ∃ b ∈ K, y = a * x * b :=
   Iff.trans
@@ -141,12 +105,6 @@ theorem rel_iff {H K : Subgroup G} {x y : G} :
     mem_doset
 #align doset.rel_iff Doset.rel_iff
 
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 theorem bot_rel_eq_leftRel (H : Subgroup G) :
     (setoid ↑(⊥ : Subgroup G) ↑H).Rel = (QuotientGroup.leftRel H).Rel :=
   by
@@ -160,12 +118,6 @@ theorem bot_rel_eq_leftRel (H : Subgroup G) :
     exact ⟨1, rfl, a⁻¹ * b, h, by rw [one_mul, mul_inv_cancel_left]⟩
 #align doset.bot_rel_eq_left_rel Doset.bot_rel_eq_leftRel
 
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 theorem rel_bot_eq_right_group_rel (H : Subgroup G) :
     (setoid ↑H ↑(⊥ : Subgroup G)).Rel = (QuotientGroup.rightRel H).Rel :=
   by
@@ -179,23 +131,11 @@ theorem rel_bot_eq_right_group_rel (H : Subgroup G) :
     exact ⟨b * a⁻¹, h, 1, rfl, by rw [mul_one, inv_mul_cancel_right]⟩
 #align doset.rel_bot_eq_right_group_rel Doset.rel_bot_eq_right_group_rel
 
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 /-- Create a doset out of an element of `H \ G / K`-/
 def quotToDoset (H K : Subgroup G) (q : Quotient ↑H ↑K) : Set G :=
   Doset.doset q.out' H K
 #align doset.quot_to_doset Doset.quotToDoset
 
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 /-- Map from `G` to `H \ G / K`-/
 abbrev mk (H K : Subgroup G) (a : G) : Quotient ↑H ↑K :=
   Quotient.mk'' a
@@ -204,32 +144,14 @@ abbrev mk (H K : Subgroup G) (a : G) : Quotient ↑H ↑K :=
 instance (H K : Subgroup G) : Inhabited (Quotient ↑H ↑K) :=
   ⟨mk H K (1 : G)⟩
 
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 theorem eq (H K : Subgroup G) (a b : G) : mk H K a = mk H K b ↔ ∃ h ∈ H, ∃ k ∈ K, b = h * a * k :=
   by rw [Quotient.eq'']; apply rel_iff
 #align doset.eq Doset.eq
 
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 theorem out_eq' (H K : Subgroup G) (q : Quotient ↑H ↑K) : mk H K q.out' = q :=
   Quotient.out_eq' q
 #align doset.out_eq' Doset.out_eq'
 
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 theorem mk_out'_eq_mul (H K : Subgroup G) (g : G) :
     ∃ h k : G, h ∈ H ∧ k ∈ K ∧ (mk H K g : Quotient ↑H ↑K).out' = h * g * k :=
   by
@@ -240,24 +162,12 @@ theorem mk_out'_eq_mul (H K : Subgroup G) (g : G) :
   rw [← mul_assoc, ← T]
 #align doset.mk_out'_eq_mul Doset.mk_out'_eq_mul
 
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 theorem mk_eq_of_doset_eq {H K : Subgroup G} {a b : G} (h : Doset.doset a H K = Doset.doset b H K) :
     mk H K a = mk H K b := by
   rw [Eq]
   exact mem_doset.mp (h.symm ▸ mem_doset_self H K b)
 #align doset.mk_eq_of_doset_eq Doset.mk_eq_of_doset_eq
 
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-Case conversion may be inaccurate. Consider using '#align doset.disjoint_out' Doset.disjoint_out'ₓ'. -/
 theorem disjoint_out' {H K : Subgroup G} {a b : Quotient H.1 K} :
     a ≠ b → Disjoint (Doset.doset a.out' H K) (Doset.doset b.out' H K) :=
   by
@@ -266,12 +176,6 @@ theorem disjoint_out' {H K : Subgroup G} {a b : Quotient H.1 K} :
   simpa [out_eq'] using mk_eq_of_doset_eq (eq_of_not_disjoint h)
 #align doset.disjoint_out' Doset.disjoint_out'
 
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 theorem union_quotToDoset (H K : Subgroup G) : (⋃ q, quotToDoset H K q) = Set.univ :=
   by
   ext x
@@ -283,12 +187,6 @@ theorem union_quotToDoset (H K : Subgroup G) : (⋃ q, quotToDoset H K q) = Set.
   simp only [h5, Subgroup.coe_mk, ← mul_assoc, one_mul, mul_left_inv, mul_inv_cancel_right]
 #align doset.union_quot_to_doset Doset.union_quotToDoset
 
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 theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
     (⋃ k : K, rightCoset (↑H) (a * k)) = Doset.doset a H K :=
   by
@@ -304,12 +202,6 @@ theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
     simp only [hxy, ← mul_assoc, hx, mul_inv_cancel_right, Subgroup.coe_mk]
 #align doset.doset_union_right_coset Doset.doset_union_rightCoset
 
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 theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
     (⋃ h : H, leftCoset (h * a : G) K) = Doset.doset a H K :=
   by
@@ -324,12 +216,6 @@ theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
     simp only [hxy, ← mul_assoc, hy, one_mul, mul_left_inv, Subgroup.coe_mk, inv_mul_cancel_right]
 #align doset.doset_union_left_coset Doset.doset_union_leftCoset
 
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 theorem left_bot_eq_left_quot (H : Subgroup G) : Quotient (⊥ : Subgroup G).1 H = (G ⧸ H) :=
   by
   unfold Quotient
@@ -339,12 +225,6 @@ theorem left_bot_eq_left_quot (H : Subgroup G) : Quotient (⊥ : Subgroup G).1 H
   rfl
 #align doset.left_bot_eq_left_quot Doset.left_bot_eq_left_quot
 
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-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1), Eq.{succ (succ u1)} Type.{u1} (Doset.Quotient.{u1} G _inst_1 (Subgroup.carrier.{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)))) (Bot.bot.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.hasBot.{u1} G _inst_1)))) (Quotient.{succ u1} G (QuotientGroup.rightRel.{u1} G _inst_1 H))
-but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1), Eq.{succ (succ u1)} Type.{u1} (Doset.Quotient.{u1} G _inst_1 (SetLike.coe.{u1, u1} (Submonoid.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) G (Submonoid.instSetLikeSubmonoid.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.toSubmonoid.{u1} G _inst_1 H)) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) (Bot.bot.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instBotSubgroup.{u1} G _inst_1)))) (Quotient.{succ u1} G (QuotientGroup.rightRel.{u1} G _inst_1 H))
-Case conversion may be inaccurate. Consider using '#align doset.right_bot_eq_right_quot Doset.right_bot_eq_right_quotₓ'. -/
 theorem right_bot_eq_right_quot (H : Subgroup G) :
     Quotient H.1 (⊥ : Subgroup G) = Quotient (QuotientGroup.rightRel H) :=
   by

50832dae

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -211,9 +211,7 @@ 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) (a : G) (b : G), Iff (Eq.{succ u1} (Doset.Quotient.{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)) (Doset.mk.{u1} G _inst_1 H K a) (Doset.mk.{u1} G _inst_1 H K b)) (Exists.{succ u1} G (fun (h : G) => And (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)) h H) (Exists.{succ u1} G (fun (k : G) => And (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)) k K) (Eq.{succ u1} G b (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))))) (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))))) h a) k))))))
 Case conversion may be inaccurate. Consider using '#align doset.eq Doset.eqₓ'. -/
 theorem eq (H K : Subgroup G) (a b : G) : mk H K a = mk H K b ↔ ∃ h ∈ H, ∃ k ∈ K, b = h * a * k :=
-  by
-  rw [Quotient.eq'']
-  apply rel_iff
+  by rw [Quotient.eq'']; apply rel_iff
 #align doset.eq Doset.eq
 
 /- warning: doset.out_eq' -> Doset.out_eq' is a dubious translation:

50832dae

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -270,14 +270,14 @@ theorem disjoint_out' {H K : Subgroup G} {a b : Quotient H.1 K} :
 
 /- warning: doset.union_quot_to_doset -> Doset.union_quotToDoset 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} (Set.{u1} G) (Set.unionᵢ.{u1, succ u1} G (Doset.Quotient.{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)) (fun (q : Doset.Quotient.{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)) => Doset.quotToDoset.{u1} G _inst_1 H K q)) (Set.univ.{u1} G)
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1), Eq.{succ u1} (Set.{u1} G) (Set.iUnion.{u1, succ u1} G (Doset.Quotient.{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)) (fun (q : Doset.Quotient.{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)) => Doset.quotToDoset.{u1} G _inst_1 H K q)) (Set.univ.{u1} G)
 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} (Set.{u1} G) (Set.unionᵢ.{u1, succ u1} G (Doset.Quotient.{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)) (fun (q : Doset.Quotient.{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)) => Doset.quotToDoset.{u1} G _inst_1 H K q)) (Set.univ.{u1} G)
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1), Eq.{succ u1} (Set.{u1} G) (Set.iUnion.{u1, succ u1} G (Doset.Quotient.{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)) (fun (q : Doset.Quotient.{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)) => Doset.quotToDoset.{u1} G _inst_1 H K q)) (Set.univ.{u1} G)
 Case conversion may be inaccurate. Consider using '#align doset.union_quot_to_doset Doset.union_quotToDosetₓ'. -/
 theorem union_quotToDoset (H K : Subgroup G) : (⋃ q, quotToDoset H K q) = Set.univ :=
   by
   ext x
-  simp only [Set.mem_unionᵢ, quot_to_doset, mem_doset, SetLike.mem_coe, exists_prop, Set.mem_univ,
+  simp only [Set.mem_iUnion, quot_to_doset, mem_doset, SetLike.mem_coe, exists_prop, Set.mem_univ,
     iff_true_iff]
   use mk H K x
   obtain ⟨h, k, h3, h4, h5⟩ := mk_out'_eq_mul H K x
@@ -287,15 +287,15 @@ theorem union_quotToDoset (H K : Subgroup G) : (⋃ q, quotToDoset H K q) = Set.
 
 /- warning: doset.doset_union_right_coset -> Doset.doset_union_rightCoset is a dubious translation:
 lean 3 declaration is
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+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1) (a : G), Eq.{succ u1} (Set.{u1} G) (Set.iUnion.{u1, succ u1} G (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)) K) (fun (k : 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)) K) => rightCoset.{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) (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))))) a ((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)) K) 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)) K) 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)) K) 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)) K) 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 K))))) k)))) (Doset.doset.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{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)))) 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) (a : G), Eq.{succ u1} (Set.{u1} G) (Set.unionᵢ.{u1, succ u1} G (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 K)) (fun (k : 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 K)) => rightCoset.{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) (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))))) a (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) K)) k)))) (Doset.doset.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) a (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) (a : G), Eq.{succ u1} (Set.{u1} G) (Set.iUnion.{u1, succ u1} G (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 K)) (fun (k : 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 K)) => rightCoset.{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) (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))))) a (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) K)) k)))) (Doset.doset.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) a (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 doset.doset_union_right_coset Doset.doset_union_rightCosetₓ'. -/
 theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
     (⋃ k : K, rightCoset (↑H) (a * k)) = Doset.doset a H K :=
   by
   ext x
-  simp only [mem_rightCoset_iff, exists_prop, mul_inv_rev, Set.mem_unionᵢ, mem_doset,
+  simp only [mem_rightCoset_iff, exists_prop, mul_inv_rev, Set.mem_iUnion, mem_doset,
     Subgroup.mem_carrier, SetLike.mem_coe]
   constructor
   · rintro ⟨y, h_h⟩
@@ -308,15 +308,15 @@ theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
 
 /- warning: doset.doset_union_left_coset -> Doset.doset_union_leftCoset is a dubious translation:
 lean 3 declaration is
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+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] (H : Subgroup.{u1} G _inst_1) (K : Subgroup.{u1} G _inst_1) (a : G), Eq.{succ u1} (Set.{u1} G) (Set.iUnion.{u1, succ u1} G (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) (fun (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) => leftCoset.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (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))))) ((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) 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)))) K))) (Doset.doset.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{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)))) 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) (a : G), Eq.{succ u1} (Set.{u1} G) (Set.unionᵢ.{u1, succ u1} G (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)) (fun (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)) => leftCoset.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (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))))) (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) a) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) K))) (Doset.doset.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) a (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) (a : G), Eq.{succ u1} (Set.{u1} G) (Set.iUnion.{u1, succ u1} G (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)) (fun (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)) => leftCoset.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (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))))) (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) a) (SetLike.coe.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1) K))) (Doset.doset.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) a (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 doset.doset_union_left_coset Doset.doset_union_leftCosetₓ'. -/
 theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
     (⋃ h : H, leftCoset (h * a : G) K) = Doset.doset a H K :=
   by
   ext x
-  simp only [mem_leftCoset_iff, mul_inv_rev, Set.mem_unionᵢ, mem_doset]
+  simp only [mem_leftCoset_iff, mul_inv_rev, Set.mem_iUnion, mem_doset]
   constructor
   · rintro ⟨y, h_h⟩
     refine' ⟨y, y.2, a⁻¹ * y⁻¹ * x, h_h, _⟩

50832dae

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

4c19a16e

chore: split Subsingleton,Nontrivial off of Data.Set.Basic (#11832)

Moves definition of and lemmas related to Set.Subsingleton and Set.Nontrivial to a new file, so that Basic can be shorter.

493a947e

Diff

@@ -7,7 +7,7 @@ import Mathlib.Data.Setoid.Basic
 import Mathlib.GroupTheory.Subgroup.Basic
 import Mathlib.GroupTheory.Coset
 import Mathlib.GroupTheory.Subgroup.Pointwise
-import Mathlib.Data.Set.Basic
+import Mathlib.Data.Set.Subsingleton
 
 #align_import group_theory.double_coset from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"

4c19a16e

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

@@ -24,7 +24,7 @@ this is the usual left or right quotient of a group by a subgroup.
 * `rel`: The double coset relation defined by two subgroups `H K` of `G`.
 * `Doset.quotient`: The quotient of `G` by the double coset relation, i.e, `H \ G / K`.
 -/
--- porting note: removed import
+-- Porting note: removed import
 -- import Mathlib.Tactic.Group
 
 variable {G : Type*} [Group G] {α : Type*} [Mul α] (J : Subgroup G) (g : G)

4c19a16e

chore: replace SubgroupClass.inv by InvMemClass.inv (#9761)

b47d3300

Diff

@@ -178,7 +178,7 @@ theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
   constructor
   · rintro ⟨y, h_h⟩
     refine' ⟨x * (y⁻¹ * a⁻¹), h_h, y, y.2, _⟩
-    simp only [← mul_assoc, Subgroup.coe_mk, inv_mul_cancel_right, SubgroupClass.coe_inv]
+    simp only [← mul_assoc, Subgroup.coe_mk, inv_mul_cancel_right, InvMemClass.coe_inv]
   · rintro ⟨x, hx, y, hy, hxy⟩
     refine' ⟨⟨y, hy⟩, _⟩
     simp only [hxy, ← mul_assoc, hx, mul_inv_cancel_right, Subgroup.coe_mk]
@@ -191,7 +191,7 @@ theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
   constructor
   · rintro ⟨y, h_h⟩
     refine' ⟨y, y.2, a⁻¹ * y⁻¹ * x, h_h, _⟩
-    simp only [← mul_assoc, one_mul, mul_right_inv, mul_inv_cancel_right, SubgroupClass.coe_inv]
+    simp only [← mul_assoc, one_mul, mul_right_inv, mul_inv_cancel_right, InvMemClass.coe_inv]
   · rintro ⟨x, hx, y, hy, hxy⟩
     refine' ⟨⟨x, hx⟩, _⟩
     simp only [hxy, ← mul_assoc, hy, one_mul, mul_left_inv, Subgroup.coe_mk, inv_mul_cancel_right]

4c19a16e

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

@@ -39,9 +39,11 @@ def doset (a : α) (s t : Set α) : Set α :=
   s * {a} * t
 #align doset Doset.doset
 
-theorem mem_doset {s t : Set α} {a b : α} : b ∈ doset a s t ↔ ∃ x ∈ s, ∃ y ∈ t, b = x * a * y :=
-  ⟨fun ⟨_, y, ⟨x, _, hx, rfl, rfl⟩, hy, h⟩ => ⟨x, hx, y, hy, h.symm⟩, fun ⟨x, hx, y, hy, h⟩ =>
-    ⟨x * a, y, ⟨x, a, hx, rfl, rfl⟩, hy, h.symm⟩⟩
+lemma doset_eq_image2 (a : α) (s t : Set α) : doset a s t = Set.image2 (· * a * ·) s t := by
+  simp_rw [doset, Set.mul_singleton, ← Set.image2_mul, Set.image2_image_left]
+
+theorem mem_doset {s t : Set α} {a b : α} : b ∈ doset a s t ↔ ∃ x ∈ s, ∃ y ∈ t, b = x * a * y := by
+  simp only [doset_eq_image2, Set.mem_image2, eq_comm]
 #align doset.mem_doset Doset.mem_doset
 
 theorem mem_doset_self (H K : Subgroup G) (a : G) : a ∈ doset a H K :=
@@ -50,7 +52,7 @@ theorem mem_doset_self (H K : Subgroup G) (a : G) : a ∈ doset a H K :=
 
 theorem doset_eq_of_mem {H K : Subgroup G} {a b : G} (hb : b ∈ doset a H K) :
     doset b H K = doset a H K := by
-  obtain ⟨_, k, ⟨h, a, hh, rfl : _ = _, rfl⟩, hk, rfl⟩ := hb
+  obtain ⟨h, hh, k, hk, rfl⟩ := mem_doset.1 hb
   rw [doset, doset, ← Set.singleton_mul_singleton, ← Set.singleton_mul_singleton, mul_assoc,
     mul_assoc, Subgroup.singleton_mul_subgroup hk, ← mul_assoc, ← mul_assoc,
     Subgroup.subgroup_mul_singleton hh]

4c19a16e

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

@@ -29,9 +29,10 @@ this is the usual left or right quotient of a group by a subgroup.
 
 variable {G : Type*} [Group G] {α : Type*} [Mul α] (J : Subgroup G) (g : G)
 
-namespace Doset
+open MulOpposite
+open scoped Pointwise
 
-open Pointwise
+namespace Doset
 
 /-- The double coset as an element of `Set α` corresponding to `s a t` -/
 def doset (a : α) (s t : Set α) : Set α :=
@@ -168,7 +169,7 @@ theorem union_quotToDoset (H K : Subgroup G) : ⋃ q, quotToDoset H K q = Set.un
 #align doset.union_quot_to_doset Doset.union_quotToDoset
 
 theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
-    ⋃ k : K, rightCoset (↑H) (a * k) = doset a H K := by
+    ⋃ k : K, op (a * k) • ↑H = doset a H K := by
   ext x
   simp only [mem_rightCoset_iff, exists_prop, mul_inv_rev, Set.mem_iUnion, mem_doset,
     Subgroup.mem_carrier, SetLike.mem_coe]
@@ -182,7 +183,7 @@ theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
 #align doset.doset_union_right_coset Doset.doset_union_rightCoset
 
 theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
-    ⋃ h : H, leftCoset (h * a : G) K = doset a H K := by
+    ⋃ h : H, (h * a : G) • ↑K = doset a H K := by
   ext x
   simp only [mem_leftCoset_iff, mul_inv_rev, Set.mem_iUnion, mem_doset]
   constructor

4c19a16e

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

@@ -27,7 +27,7 @@ this is the usual left or right quotient of a group by a subgroup.
 -- porting note: removed import
 -- import Mathlib.Tactic.Group
 
-variable {G : Type _} [Group G] {α : Type _} [Mul α] (J : Subgroup G) (g : G)
+variable {G : Type*} [Group G] {α : Type*} [Mul α] (J : Subgroup G) (g : G)
 
 namespace Doset

4c19a16e

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Chris Birkbeck. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Birkbeck
-
-! This file was ported from Lean 3 source module group_theory.double_coset
-! leanprover-community/mathlib commit 4c19a16e4b705bf135cf9a80ac18fcc99c438514
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Setoid.Basic
 import Mathlib.GroupTheory.Subgroup.Basic
@@ -14,6 +9,8 @@ import Mathlib.GroupTheory.Coset
 import Mathlib.GroupTheory.Subgroup.Pointwise
 import Mathlib.Data.Set.Basic
 
+#align_import group_theory.double_coset from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
+
 /-!
 # Double cosets

4c19a16e

fix: precedences of ⨆⋃⋂⨅ (#5614)

e3c8f983

Diff

@@ -160,7 +160,7 @@ theorem disjoint_out' {H K : Subgroup G} {a b : Quotient H.1 K} :
   simpa [out_eq'] using mk_eq_of_doset_eq (eq_of_not_disjoint h)
 #align doset.disjoint_out' Doset.disjoint_out'
 
-theorem union_quotToDoset (H K : Subgroup G) : (⋃ q, quotToDoset H K q) = Set.univ := by
+theorem union_quotToDoset (H K : Subgroup G) : ⋃ q, quotToDoset H K q = Set.univ := by
   ext x
   simp only [Set.mem_iUnion, quotToDoset, mem_doset, SetLike.mem_coe, exists_prop, Set.mem_univ,
     iff_true_iff]
@@ -171,7 +171,7 @@ theorem union_quotToDoset (H K : Subgroup G) : (⋃ q, quotToDoset H K q) = Set.
 #align doset.union_quot_to_doset Doset.union_quotToDoset
 
 theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
-    (⋃ k : K, rightCoset (↑H) (a * k)) = doset a H K := by
+    ⋃ k : K, rightCoset (↑H) (a * k) = doset a H K := by
   ext x
   simp only [mem_rightCoset_iff, exists_prop, mul_inv_rev, Set.mem_iUnion, mem_doset,
     Subgroup.mem_carrier, SetLike.mem_coe]
@@ -185,7 +185,7 @@ theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
 #align doset.doset_union_right_coset Doset.doset_union_rightCoset
 
 theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
-    (⋃ h : H, leftCoset (h * a : G) K) = doset a H K := by
+    ⋃ h : H, leftCoset (h * a : G) K = doset a H K := by
   ext x
   simp only [mem_leftCoset_iff, mul_inv_rev, Set.mem_iUnion, mem_doset]
   constructor

4c19a16e

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -93,7 +93,7 @@ theorem rel_iff {H K : Subgroup G} {x y : G} :
 
 theorem bot_rel_eq_leftRel (H : Subgroup G) :
     (setoid ↑(⊥ : Subgroup G) ↑H).Rel = (QuotientGroup.leftRel H).Rel := by
-  ext (a b)
+  ext a b
   rw [rel_iff, Setoid.Rel, QuotientGroup.leftRel_apply]
   constructor
   · rintro ⟨a, rfl : a = 1, b, hb, rfl⟩
@@ -105,7 +105,7 @@ theorem bot_rel_eq_leftRel (H : Subgroup G) :
 
 theorem rel_bot_eq_right_group_rel (H : Subgroup G) :
     (setoid ↑H ↑(⊥ : Subgroup G)).Rel = (QuotientGroup.rightRel H).Rel := by
-  ext (a b)
+  ext a b
   rw [rel_iff, Setoid.Rel, QuotientGroup.rightRel_apply]
   constructor
   · rintro ⟨b, hb, a, rfl : a = 1, rfl⟩

4c19a16e

chore: fix backtick in docs (#5077)

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

878d95c4

Diff

@@ -25,7 +25,7 @@ this is the usual left or right quotient of a group by a subgroup.
 ## Main definitions
 
 * `rel`: The double coset relation defined by two subgroups `H K` of `G`.
-* `Doset.quotient`: The quotient of `G` by the double coset relation, i.e, ``H \ G / K`.
+* `Doset.quotient`: The quotient of `G` by the double coset relation, i.e, `H \ G / K`.
 -/
 -- porting note: removed import
 -- import Mathlib.Tactic.Group

4c19a16e

chore: fix many typos (#4535)

Run codespell Mathlib and keep some suggestions.

92f5c622

Diff

@@ -18,7 +18,7 @@ import Mathlib.Data.Set.Basic
 # Double cosets
 
 This file defines double cosets for two subgroups `H K` of a group `G` and the quotient of `G` by
-the double coset relation, i.e. `H \ G / K`. We also prove that `G` can be writen as a disjoint
+the double coset relation, i.e. `H \ G / K`. We also prove that `G` can be written as a disjoint
 union of the double cosets and that if one of `H` or `K` is the trivial group (i.e. `⊥` ) then
 this is the usual left or right quotient of a group by a subgroup.

4c19a16e

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

@@ -162,7 +162,7 @@ theorem disjoint_out' {H K : Subgroup G} {a b : Quotient H.1 K} :
 
 theorem union_quotToDoset (H K : Subgroup G) : (⋃ q, quotToDoset H K q) = Set.univ := by
   ext x
-  simp only [Set.mem_unionᵢ, quotToDoset, mem_doset, SetLike.mem_coe, exists_prop, Set.mem_univ,
+  simp only [Set.mem_iUnion, quotToDoset, mem_doset, SetLike.mem_coe, exists_prop, Set.mem_univ,
     iff_true_iff]
   use mk H K x
   obtain ⟨h, k, h3, h4, h5⟩ := mk_out'_eq_mul H K x
@@ -173,7 +173,7 @@ theorem union_quotToDoset (H K : Subgroup G) : (⋃ q, quotToDoset H K q) = Set.
 theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
     (⋃ k : K, rightCoset (↑H) (a * k)) = doset a H K := by
   ext x
-  simp only [mem_rightCoset_iff, exists_prop, mul_inv_rev, Set.mem_unionᵢ, mem_doset,
+  simp only [mem_rightCoset_iff, exists_prop, mul_inv_rev, Set.mem_iUnion, mem_doset,
     Subgroup.mem_carrier, SetLike.mem_coe]
   constructor
   · rintro ⟨y, h_h⟩
@@ -187,7 +187,7 @@ theorem doset_union_rightCoset (H K : Subgroup G) (a : G) :
 theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
     (⋃ h : H, leftCoset (h * a : G) K) = doset a H K := by
   ext x
-  simp only [mem_leftCoset_iff, mul_inv_rev, Set.mem_unionᵢ, mem_doset]
+  simp only [mem_leftCoset_iff, mul_inv_rev, Set.mem_iUnion, mem_doset]
   constructor
   · rintro ⟨y, h_h⟩
     refine' ⟨y, y.2, a⁻¹ * y⁻¹ * x, h_h, _⟩

4c19a16e

chore: bye-bye, solo bys! (#3825)

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

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

14167e48

Diff

@@ -128,8 +128,8 @@ abbrev mk (H K : Subgroup G) (a : G) : Quotient (H : Set G) K :=
 instance (H K : Subgroup G) : Inhabited (Quotient (H : Set G) K) :=
   ⟨mk H K (1 : G)⟩
 
-theorem eq (H K : Subgroup G) (a b : G) : mk H K a = mk H K b ↔ ∃ h ∈ H, ∃ k ∈ K, b = h * a * k :=
-  by
+theorem eq (H K : Subgroup G) (a b : G) :
+    mk H K a = mk H K b ↔ ∃ h ∈ H, ∃ k ∈ K, b = h * a * k := by
   rw [Quotient.eq'']
   apply rel_iff
 #align doset.eq Doset.eq
@@ -197,8 +197,8 @@ theorem doset_union_leftCoset (H K : Subgroup G) (a : G) :
     simp only [hxy, ← mul_assoc, hy, one_mul, mul_left_inv, Subgroup.coe_mk, inv_mul_cancel_right]
 #align doset.doset_union_left_coset Doset.doset_union_leftCoset
 
-theorem left_bot_eq_left_quot (H : Subgroup G) : Quotient (⊥ : Subgroup G).1 (H : Set G) = (G ⧸ H):=
-  by
+theorem left_bot_eq_left_quot (H : Subgroup G) :
+    Quotient (⊥ : Subgroup G).1 (H : Set G) = (G ⧸ H) := by
   unfold Quotient
   congr
   ext

4c19a16e

chore: tidy various files (#2236)

a2ebfa0b

Diff

@@ -25,7 +25,7 @@ this is the usual left or right quotient of a group by a subgroup.
 ## Main definitions
 
 * `rel`: The double coset relation defined by two subgroups `H K` of `G`.
-* `double_coset.quotient`: The quotient of `G` by the double coset relation, i.e, ``H \ G / K`.
+* `Doset.quotient`: The quotient of `G` by the double coset relation, i.e, ``H \ G / K`.
 -/
 -- porting note: removed import
 -- import Mathlib.Tactic.Group
@@ -36,7 +36,7 @@ namespace Doset
 
 open Pointwise
 
-/-- The double coset as an element of `set α` corresponding to `s a t` -/
+/-- The double coset as an element of `Set α` corresponding to `s a t` -/
 def doset (a : α) (s t : Set α) : Set α :=
   s * {a} * t
 #align doset Doset.doset

4c19a16e

feat: port GroupTheory.DoubleCoset (#2076)

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

1c7f1a46

`group_theory.double_coset` ⟷ `Mathlib.GroupTheory.DoubleCoset`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 299

group_theory.double_coset ⟷ Mathlib.GroupTheory.DoubleCoset

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 299

`group_theory.double_coset` ⟷ `Mathlib.GroupTheory.DoubleCoset`