group_theory.schreier | 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

8350c34a

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

c2092722

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -182,7 +182,7 @@ theorem card_commutator_dvd_index_center_pow [Finite (commutatorSet G)] :
   · simp_rw [hG, MulZeroClass.zero_mul, zero_add, pow_one, dvd_zero]
   haveI : finite_index (center G) := ⟨hG⟩
   -- Rewrite as `|Z(G) ∩ G'| * [G' : Z(G) ∩ G'] ∣ [G : Z(G)] ^ ([G : Z(G)] * n) * [G : Z(G)]`
-  rw [← ((center G).subgroupOf (commutator G)).card_mul_index, pow_succ']
+  rw [← ((center G).subgroupOf (commutator G)).card_mul_index, pow_succ]
   -- We have `h1 : [G' : Z(G) ∩ G'] ∣ [G : Z(G)]`
   have h1 := relindex_dvd_index_of_normal (center G) (commutator G)
   -- So we can reduce to proving `|Z(G) ∩ G'| ∣ [G : Z(G)] ^ ([G : Z(G)] * n)`
@@ -224,7 +224,7 @@ theorem card_commutator_le_of_finite_commutatorSet [Finite (commutatorSet G)] :
   replace h1 :=
     h1.trans (Nat.pow_le_pow_right Finite.card_pos (rank_closureCommutatorRepresentatives_le G))
   replace h2 := h2.trans (pow_dvd_pow _ (add_le_add_right (mul_le_mul_right' h1 _) 1))
-  rw [← pow_succ'] at h2
+  rw [← pow_succ] at h2
   refine' (Nat.le_of_dvd _ h2).trans (Nat.pow_le_pow_left h1 _)
   exact pow_pos (Nat.pos_of_ne_zero finite_index.finite_index) _
 #align subgroup.card_commutator_le_of_finite_commutator_set Subgroup.card_commutator_le_of_finite_commutatorSet

c2092722

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -219,12 +219,12 @@ theorem card_commutator_le_of_finite_commutatorSet [Finite (commutatorSet G)] :
   by
   have h1 := index_center_le_pow (closureCommutatorRepresentatives G)
   have h2 := card_commutator_dvd_index_center_pow (closureCommutatorRepresentatives G)
-  rw [card_commutatorSet_closureCommutatorRepresentatives] at h1 h2 
-  rw [card_commutator_closureCommutatorRepresentatives] at h2 
+  rw [card_commutatorSet_closureCommutatorRepresentatives] at h1 h2
+  rw [card_commutator_closureCommutatorRepresentatives] at h2
   replace h1 :=
     h1.trans (Nat.pow_le_pow_right Finite.card_pos (rank_closureCommutatorRepresentatives_le G))
   replace h2 := h2.trans (pow_dvd_pow _ (add_le_add_right (mul_le_mul_right' h1 _) 1))
-  rw [← pow_succ'] at h2 
+  rw [← pow_succ'] at h2
   refine' (Nat.le_of_dvd _ h2).trans (Nat.pow_le_pow_left h1 _)
   exact pow_pos (Nat.pos_of_ne_zero finite_index.finite_index) _
 #align subgroup.card_commutator_le_of_finite_commutator_set Subgroup.card_commutator_le_of_finite_commutatorSet
@@ -235,7 +235,7 @@ instance [Finite (commutatorSet G)] : Finite (commutator G) :=
   by
   have h2 := card_commutator_dvd_index_center_pow (closureCommutatorRepresentatives G)
   refine' Nat.finite_of_card_ne_zero fun h => _
-  rw [card_commutator_closureCommutatorRepresentatives, h, zero_dvd_iff] at h2 
+  rw [card_commutator_closureCommutatorRepresentatives, h, zero_dvd_iff] at h2
   exact finite_index.finite_index (pow_eq_zero h2)
 
 end Subgroup

c2092722

bump to nightly-2023-12-20-06

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

058cd493

Diff

@@ -222,11 +222,10 @@ theorem card_commutator_le_of_finite_commutatorSet [Finite (commutatorSet G)] :
   rw [card_commutatorSet_closureCommutatorRepresentatives] at h1 h2 
   rw [card_commutator_closureCommutatorRepresentatives] at h2 
   replace h1 :=
-    h1.trans
-      (Nat.pow_le_pow_of_le_right Finite.card_pos (rank_closureCommutatorRepresentatives_le G))
+    h1.trans (Nat.pow_le_pow_right Finite.card_pos (rank_closureCommutatorRepresentatives_le G))
   replace h2 := h2.trans (pow_dvd_pow _ (add_le_add_right (mul_le_mul_right' h1 _) 1))
   rw [← pow_succ'] at h2 
-  refine' (Nat.le_of_dvd _ h2).trans (Nat.pow_le_pow_of_le_left h1 _)
+  refine' (Nat.le_of_dvd _ h2).trans (Nat.pow_le_pow_left h1 _)
   exact pow_pos (Nat.pos_of_ne_zero finite_index.finite_index) _
 #align subgroup.card_commutator_le_of_finite_commutator_set Subgroup.card_commutator_le_of_finite_commutatorSet
 -/

c2092722

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) 2022 Thomas Browning. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
 -/
-import Mathbin.GroupTheory.Abelianization
-import Mathbin.GroupTheory.Exponent
-import Mathbin.GroupTheory.Transfer
+import GroupTheory.Abelianization
+import GroupTheory.Exponent
+import GroupTheory.Transfer
 
 #align_import group_theory.schreier from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"

c2092722

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -49,11 +49,11 @@ theorem closure_mul_image_mul_eq_top (hR : R ∈ rightTransversals (H : Set G))
   · exact ⟨1, 1, (closure U).one_mem, hR1, one_mul 1⟩
   · rintro - s hs ⟨u, r, hu, hr, rfl⟩
     rw [show u * r * s = u * (r * s * (f (r * s))⁻¹) * f (r * s) by group]
-    refine' Set.mul_mem_mul ((closure U).mul_mem hu _) (f (r * s)).coe_prop
+    refine' Set.mul_mem_mul ((closure U).hMul_mem hu _) (f (r * s)).coe_prop
     exact subset_closure ⟨r * s, Set.mul_mem_mul hr hs, rfl⟩
   · rintro - s hs ⟨u, r, hu, hr, rfl⟩
     rw [show u * r * s⁻¹ = u * (f (r * s⁻¹) * s * r⁻¹)⁻¹ * f (r * s⁻¹) by group]
-    refine' Set.mul_mem_mul ((closure U).mul_mem hu ((closure U).inv_mem _)) (f (r * s⁻¹)).2
+    refine' Set.mul_mem_mul ((closure U).hMul_mem hu ((closure U).inv_mem _)) (f (r * s⁻¹)).2
     refine' subset_closure ⟨f (r * s⁻¹) * s, Set.mul_mem_mul (f (r * s⁻¹)).2 hs, _⟩
     rw [mul_right_inj, inv_inj, ← Subtype.coe_mk r hr, ← Subtype.ext_iff, Subtype.coe_mk]
     apply

c2092722

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) 2022 Thomas Browning. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
-
-! This file was ported from Lean 3 source module group_theory.schreier
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.Abelianization
 import Mathbin.GroupTheory.Exponent
 import Mathbin.GroupTheory.Transfer
 
+#align_import group_theory.schreier from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-!
 # Schreier's Lemma

c2092722

bump to nightly-2023-06-22-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

c99553dc

Diff

@@ -146,15 +146,15 @@ theorem exists_finset_card_le_mul [FiniteIndex H] {S : Finset G} (hS : closure (
 #align subgroup.exists_finset_card_le_mul Subgroup.exists_finset_card_le_mul
 -/
 
-#print Subgroup.fG_of_index_ne_zero /-
+#print Subgroup.fg_of_index_ne_zero /-
 /-- **Schreier's Lemma**: A finite index subgroup of a finitely generated
   group is finitely generated. -/
-instance fG_of_index_ne_zero [hG : Group.FG G] [FiniteIndex H] : Group.FG H :=
+instance fg_of_index_ne_zero [hG : Group.FG G] [FiniteIndex H] : Group.FG H :=
   by
   obtain ⟨S, hS⟩ := hG.1
   obtain ⟨T, -, hT⟩ := exists_finset_card_le_mul H hS
   exact ⟨⟨T, hT⟩⟩
-#align subgroup.fg_of_index_ne_zero Subgroup.fG_of_index_ne_zero
+#align subgroup.fg_of_index_ne_zero Subgroup.fg_of_index_ne_zero
 -/
 
 #print Subgroup.rank_le_index_mul_rank /-

c2092722

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -40,6 +40,7 @@ open MemRightTransversals
 
 variable {G : Type _} [Group G] {H : Subgroup G} {R S : Set G}
 
+#print Subgroup.closure_mul_image_mul_eq_top /-
 theorem closure_mul_image_mul_eq_top (hR : R ∈ rightTransversals (H : Set G)) (hR1 : (1 : G) ∈ R)
     (hS : closure S = ⊤) : (closure ((R * S).image fun g => g * (toFun hR g)⁻¹) : Set G) * R = ⊤ :=
   by
@@ -64,7 +65,9 @@ theorem closure_mul_image_mul_eq_top (hR : R ∈ rightTransversals (H : Set G))
     rw [mul_assoc, ← inv_inv s, ← mul_inv_rev, inv_inv]
     exact to_fun_mul_inv_mem hR (r * s⁻¹)
 #align subgroup.closure_mul_image_mul_eq_top Subgroup.closure_mul_image_mul_eq_top
+-/
 
+#print Subgroup.closure_mul_image_eq /-
 /-- **Schreier's Lemma**: If `R : set G` is a right_transversal of `H : subgroup G`
   with `1 ∈ R`, and if `G` is generated by `S : set G`, then `H` is generated by the `set`
   `(R * S).image (λ g, g * (to_fun hR g)⁻¹)`. -/
@@ -86,7 +89,9 @@ theorem closure_mul_image_eq (hR : R ∈ rightTransversals (H : Set G)) (hR1 : (
   · rw [Subtype.coe_mk, inv_one, mul_one]
     exact (H.mul_mem_cancel_left (hU hg)).mp hh
 #align subgroup.closure_mul_image_eq Subgroup.closure_mul_image_eq
+-/
 
+#print Subgroup.closure_mul_image_eq_top /-
 /-- **Schreier's Lemma**: If `R : set G` is a right_transversal of `H : subgroup G`
   with `1 ∈ R`, and if `G` is generated by `S : set G`, then `H` is generated by the `set`
   `(R * S).image (λ g, g * (to_fun hR g)⁻¹)`. -/
@@ -97,7 +102,9 @@ theorem closure_mul_image_eq_top (hR : R ∈ rightTransversals (H : Set G)) (hR1
   rw [eq_top_iff, ← map_subtype_le_map_subtype, MonoidHom.map_closure, Set.image_image]
   exact (map_subtype_le ⊤).trans (ge_of_eq (closure_mul_image_eq hR hR1 hS))
 #align subgroup.closure_mul_image_eq_top Subgroup.closure_mul_image_eq_top
+-/
 
+#print Subgroup.closure_mul_image_eq_top' /-
 /-- **Schreier's Lemma**: If `R : finset G` is a right_transversal of `H : subgroup G`
   with `1 ∈ R`, and if `G` is generated by `S : finset G`, then `H` is generated by the `finset`
   `(R * S).image (λ g, g * (to_fun hR g)⁻¹)`. -/
@@ -109,10 +116,12 @@ theorem closure_mul_image_eq_top' [DecidableEq G] {R S : Finset G}
   rw [Finset.coe_image, Finset.coe_mul]
   exact closure_mul_image_eq_top hR hR1 hS
 #align subgroup.closure_mul_image_eq_top' Subgroup.closure_mul_image_eq_top'
+-/
 
 variable (H)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Subgroup.exists_finset_card_le_mul /-
 theorem exists_finset_card_le_mul [FiniteIndex H] {S : Finset G} (hS : closure (S : Set G) = ⊤) :
     ∃ T : Finset H, T.card ≤ H.index * S.card ∧ closure (T : Set H) = ⊤ :=
   by
@@ -135,7 +144,9 @@ theorem exists_finset_card_le_mul [FiniteIndex H] {S : Finset G} (hS : closure (
     _ = Fintype.card (G ⧸ H) := (QuotientGroup.card_quotient_rightRel H)
     _ = H.index := H.index_eq_card.symm
 #align subgroup.exists_finset_card_le_mul Subgroup.exists_finset_card_le_mul
+-/
 
+#print Subgroup.fG_of_index_ne_zero /-
 /-- **Schreier's Lemma**: A finite index subgroup of a finitely generated
   group is finitely generated. -/
 instance fG_of_index_ne_zero [hG : Group.FG G] [FiniteIndex H] : Group.FG H :=
@@ -144,7 +155,9 @@ instance fG_of_index_ne_zero [hG : Group.FG G] [FiniteIndex H] : Group.FG H :=
   obtain ⟨T, -, hT⟩ := exists_finset_card_le_mul H hS
   exact ⟨⟨T, hT⟩⟩
 #align subgroup.fg_of_index_ne_zero Subgroup.fG_of_index_ne_zero
+-/
 
+#print Subgroup.rank_le_index_mul_rank /-
 theorem rank_le_index_mul_rank [hG : Group.FG G] [FiniteIndex H] :
     Group.rank H ≤ H.index * Group.rank G :=
   by
@@ -156,9 +169,11 @@ theorem rank_le_index_mul_rank [hG : Group.FG G] [FiniteIndex H] :
     _ ≤ H.index * S.card := hT₀
     _ = H.index * Group.rank G := congr_arg ((· * ·) H.index) hS₀
 #align subgroup.rank_le_index_mul_rank Subgroup.rank_le_index_mul_rank
+-/
 
 variable (G)
 
+#print Subgroup.card_commutator_dvd_index_center_pow /-
 /-- If `G` has `n` commutators `[g₁, g₂]`, then `|G'| ∣ [G : Z(G)] ^ ([G : Z(G)] * n + 1)`,
 where `G'` denotes the commutator of `G`. -/
 theorem card_commutator_dvd_index_center_pow [Finite (commutatorSet G)] :
@@ -190,6 +205,7 @@ theorem card_commutator_dvd_index_center_pow [Finite (commutatorSet G)] :
   -- `transfer g` is defeq to `g ^ [G : Z(G)]`, so we are done
   simpa only [MonoidHom.mem_ker, Subtype.ext_iff] using this
 #align subgroup.card_commutator_dvd_index_center_pow Subgroup.card_commutator_dvd_index_center_pow
+-/
 
 #print Subgroup.cardCommutatorBound /-
 /-- A bound for the size of the commutator subgroup in terms of the number of commutators. -/
@@ -198,6 +214,7 @@ def cardCommutatorBound (n : ℕ) :=
 #align subgroup.card_commutator_bound Subgroup.cardCommutatorBound
 -/
 
+#print Subgroup.card_commutator_le_of_finite_commutatorSet /-
 /-- A theorem of Schur: The size of the commutator subgroup is bounded in terms of the number of
   commutators. -/
 theorem card_commutator_le_of_finite_commutatorSet [Finite (commutatorSet G)] :
@@ -215,6 +232,7 @@ theorem card_commutator_le_of_finite_commutatorSet [Finite (commutatorSet G)] :
   refine' (Nat.le_of_dvd _ h2).trans (Nat.pow_le_pow_of_le_left h1 _)
   exact pow_pos (Nat.pos_of_ne_zero finite_index.finite_index) _
 #align subgroup.card_commutator_le_of_finite_commutator_set Subgroup.card_commutator_le_of_finite_commutatorSet
+-/
 
 /-- A theorem of Schur: A group with finitely many commutators has finite commutator subgroup. -/
 instance [Finite (commutatorSet G)] : Finite (commutator G) :=

c2092722

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -129,13 +129,11 @@ theorem exists_finset_card_le_mul [FiniteIndex H] {S : Finset G} (hS : closure (
     _ ≤ (R ×ˢ S).card := Finset.card_image_le
     _ = R.card * S.card := (R.card_product S)
     _ = H.index * S.card := congr_arg (· * S.card) _
-    
   calc
     R.card = Fintype.card R := (Fintype.card_coe R).symm
     _ = _ := (Fintype.card_congr (mem_right_transversals.to_equiv hR)).symm
     _ = Fintype.card (G ⧸ H) := (QuotientGroup.card_quotient_rightRel H)
     _ = H.index := H.index_eq_card.symm
-    
 #align subgroup.exists_finset_card_le_mul Subgroup.exists_finset_card_le_mul
 
 /-- **Schreier's Lemma**: A finite index subgroup of a finitely generated
@@ -157,7 +155,6 @@ theorem rank_le_index_mul_rank [hG : Group.FG G] [FiniteIndex H] :
     Group.rank H ≤ T.card := Group.rank_le H hT
     _ ≤ H.index * S.card := hT₀
     _ = H.index * Group.rank G := congr_arg ((· * ·) H.index) hS₀
-    
 #align subgroup.rank_le_index_mul_rank Subgroup.rank_le_index_mul_rank
 
 variable (G)

c2092722

bump to nightly-2023-06-08-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

8f04dc2b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
 
 ! This file was ported from Lean 3 source module group_theory.schreier
-! leanprover-community/mathlib commit 8350c34a64b9bc3fc64335df8006bffcadc7baa6
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.GroupTheory.Transfer
 /-!
 # Schreier's Lemma
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove Schreier's lemma.
 
 ## Main results

8350c34a

bump to nightly-2023-06-06-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

152a172d

Diff

@@ -191,10 +191,12 @@ theorem card_commutator_dvd_index_center_pow [Finite (commutatorSet G)] :
   simpa only [MonoidHom.mem_ker, Subtype.ext_iff] using this
 #align subgroup.card_commutator_dvd_index_center_pow Subgroup.card_commutator_dvd_index_center_pow
 
+#print Subgroup.cardCommutatorBound /-
 /-- A bound for the size of the commutator subgroup in terms of the number of commutators. -/
 def cardCommutatorBound (n : ℕ) :=
   (n ^ (2 * n)) ^ (n ^ (2 * n + 1) + 1)
 #align subgroup.card_commutator_bound Subgroup.cardCommutatorBound
+-/
 
 /-- A theorem of Schur: The size of the commutator subgroup is bounded in terms of the number of
   commutators. -/

8350c34a

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -203,13 +203,13 @@ theorem card_commutator_le_of_finite_commutatorSet [Finite (commutatorSet G)] :
   by
   have h1 := index_center_le_pow (closureCommutatorRepresentatives G)
   have h2 := card_commutator_dvd_index_center_pow (closureCommutatorRepresentatives G)
-  rw [card_commutatorSet_closureCommutatorRepresentatives] at h1 h2
-  rw [card_commutator_closureCommutatorRepresentatives] at h2
+  rw [card_commutatorSet_closureCommutatorRepresentatives] at h1 h2 
+  rw [card_commutator_closureCommutatorRepresentatives] at h2 
   replace h1 :=
     h1.trans
       (Nat.pow_le_pow_of_le_right Finite.card_pos (rank_closureCommutatorRepresentatives_le G))
   replace h2 := h2.trans (pow_dvd_pow _ (add_le_add_right (mul_le_mul_right' h1 _) 1))
-  rw [← pow_succ'] at h2
+  rw [← pow_succ'] at h2 
   refine' (Nat.le_of_dvd _ h2).trans (Nat.pow_le_pow_of_le_left h1 _)
   exact pow_pos (Nat.pos_of_ne_zero finite_index.finite_index) _
 #align subgroup.card_commutator_le_of_finite_commutator_set Subgroup.card_commutator_le_of_finite_commutatorSet
@@ -219,7 +219,7 @@ instance [Finite (commutatorSet G)] : Finite (commutator G) :=
   by
   have h2 := card_commutator_dvd_index_center_pow (closureCommutatorRepresentatives G)
   refine' Nat.finite_of_card_ne_zero fun h => _
-  rw [card_commutator_closureCommutatorRepresentatives, h, zero_dvd_iff] at h2
+  rw [card_commutator_closureCommutatorRepresentatives, h, zero_dvd_iff] at h2 
   exact finite_index.finite_index (pow_eq_zero h2)
 
 end Subgroup

8350c34a

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -29,7 +29,7 @@ In this file we prove Schreier's lemma.
 -/
 
 
-open Pointwise
+open scoped Pointwise
 
 namespace Subgroup

8350c34a

bump to nightly-2023-05-16-10

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

7f411d29

Diff

@@ -137,14 +137,14 @@ theorem exists_finset_card_le_mul [FiniteIndex H] {S : Finset G} (hS : closure (
 
 /-- **Schreier's Lemma**: A finite index subgroup of a finitely generated
   group is finitely generated. -/
-instance fg_of_index_ne_zero [hG : Group.Fg G] [FiniteIndex H] : Group.Fg H :=
+instance fG_of_index_ne_zero [hG : Group.FG G] [FiniteIndex H] : Group.FG H :=
   by
   obtain ⟨S, hS⟩ := hG.1
   obtain ⟨T, -, hT⟩ := exists_finset_card_le_mul H hS
   exact ⟨⟨T, hT⟩⟩
-#align subgroup.fg_of_index_ne_zero Subgroup.fg_of_index_ne_zero
+#align subgroup.fg_of_index_ne_zero Subgroup.fG_of_index_ne_zero
 
-theorem rank_le_index_mul_rank [hG : Group.Fg G] [FiniteIndex H] :
+theorem rank_le_index_mul_rank [hG : Group.FG G] [FiniteIndex H] :
     Group.rank H ≤ H.index * Group.rank G :=
   by
   haveI := H.fg_of_index_ne_zero

8350c34a

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -167,7 +167,7 @@ theorem card_commutator_dvd_index_center_pow [Finite (commutatorSet G)] :
   by
   -- First handle the case when `Z(G)` has infinite index and `[G : Z(G)]` is defined to be `0`
   by_cases hG : (center G).index = 0
-  · simp_rw [hG, zero_mul, zero_add, pow_one, dvd_zero]
+  · simp_rw [hG, MulZeroClass.zero_mul, zero_add, pow_one, dvd_zero]
   haveI : finite_index (center G) := ⟨hG⟩
   -- Rewrite as `|Z(G) ∩ G'| * [G' : Z(G) ∩ G'] ∣ [G : Z(G)] ^ ([G : Z(G)] * n) * [G : Z(G)]`
   rw [← ((center G).subgroupOf (commutator G)).card_mul_index, pow_succ']

8350c34a

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -124,13 +124,13 @@ theorem exists_finset_card_le_mul [FiniteIndex H] {S : Finset G} (hS : closure (
   calc
     _ ≤ (R * S).card := Finset.card_image_le
     _ ≤ (R ×ˢ S).card := Finset.card_image_le
-    _ = R.card * S.card := R.card_product S
+    _ = R.card * S.card := (R.card_product S)
     _ = H.index * S.card := congr_arg (· * S.card) _
     
   calc
     R.card = Fintype.card R := (Fintype.card_coe R).symm
     _ = _ := (Fintype.card_congr (mem_right_transversals.to_equiv hR)).symm
-    _ = Fintype.card (G ⧸ H) := QuotientGroup.card_quotient_rightRel H
+    _ = Fintype.card (G ⧸ H) := (QuotientGroup.card_quotient_rightRel H)
     _ = H.index := H.index_eq_card.symm
     
 #align subgroup.exists_finset_card_le_mul Subgroup.exists_finset_card_le_mul

8350c34a

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

8350c34a

chore: superfluous parentheses part 2 (#12131)

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

d48d30ac

Diff

@@ -115,12 +115,12 @@ theorem exists_finset_card_le_mul [FiniteIndex H] {S : Finset G} (hS : closure (
   calc
     _ ≤ (R * S).card := Finset.card_image_le
     _ ≤ (R ×ˢ S).card := Finset.card_image_le
-    _ = R.card * S.card := (R.card_product S)
+    _ = R.card * S.card := R.card_product S
     _ = H.index * S.card := congr_arg (· * S.card) ?_
   calc
     R.card = Fintype.card R := (Fintype.card_coe R).symm
     _ = _ := (Fintype.card_congr (toEquiv hR)).symm
-    _ = Fintype.card (G ⧸ H) := (QuotientGroup.card_quotient_rightRel H)
+    _ = Fintype.card (G ⧸ H) := QuotientGroup.card_quotient_rightRel H
     _ = H.index := H.index_eq_card.symm
 #align subgroup.exists_finset_card_le_mul Subgroup.exists_finset_card_le_mul

8350c34a

change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -155,7 +155,7 @@ theorem card_commutator_dvd_index_center_pow [Finite (commutatorSet G)] :
   · simp_rw [hG, zero_mul, zero_add, pow_one, dvd_zero]
   haveI : FiniteIndex (center G) := ⟨hG⟩
   -- Rewrite as `|Z(G) ∩ G'| * [G' : Z(G) ∩ G'] ∣ [G : Z(G)] ^ ([G : Z(G)] * n) * [G : Z(G)]`
-  rw [← ((center G).subgroupOf (_root_.commutator G)).card_mul_index, pow_succ']
+  rw [← ((center G).subgroupOf (_root_.commutator G)).card_mul_index, pow_succ]
   -- We have `h1 : [G' : Z(G) ∩ G'] ∣ [G : Z(G)]`
   have h1 := relindex_dvd_index_of_normal (center G) (_root_.commutator G)
   -- So we can reduce to proving `|Z(G) ∩ G'| ∣ [G : Z(G)] ^ ([G : Z(G)] * n)`
@@ -195,7 +195,7 @@ theorem card_commutator_le_of_finite_commutatorSet [Finite (commutatorSet G)] :
     h1.trans
       (Nat.pow_le_pow_of_le_right Finite.card_pos (rank_closureCommutatorRepresentatives_le G))
   replace h2 := h2.trans (pow_dvd_pow _ (add_le_add_right (mul_le_mul_right' h1 _) 1))
-  rw [← pow_succ'] at h2
+  rw [← pow_succ] at h2
   refine' (Nat.le_of_dvd _ h2).trans (Nat.pow_le_pow_left h1 _)
   exact pow_pos (Nat.pos_of_ne_zero FiniteIndex.finiteIndex) _
 #align subgroup.card_commutator_le_of_finite_commutator_set Subgroup.card_commutator_le_of_finite_commutatorSet

8350c34a

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

@@ -41,13 +41,13 @@ theorem closure_mul_image_mul_eq_top
   let U : Set G := (R * S).image fun g => g * (f g : G)⁻¹
   change (closure U : Set G) * R = ⊤
   refine' top_le_iff.mp fun g _ => _
-  apply closure_induction_right (eq_top_iff.mp hS (mem_top g))
+  refine closure_induction_right ?_ ?_ ?_ (eq_top_iff.mp hS (mem_top g))
   · exact ⟨1, (closure U).one_mem, 1, hR1, one_mul 1⟩
-  · rintro - s hs ⟨u, hu, r, hr, rfl⟩
+  · rintro - - s hs ⟨u, hu, r, hr, rfl⟩
     rw [show u * r * s = u * (r * s * (f (r * s) : G)⁻¹) * f (r * s) by group]
     refine' Set.mul_mem_mul ((closure U).mul_mem hu _) (f (r * s)).coe_prop
     exact subset_closure ⟨r * s, Set.mul_mem_mul hr hs, rfl⟩
-  · rintro - s hs ⟨u, hu, r, hr, rfl⟩
+  · rintro - - s hs ⟨u, hu, r, hr, rfl⟩
     rw [show u * r * s⁻¹ = u * (f (r * s⁻¹) * s * r⁻¹)⁻¹ * f (r * s⁻¹) by group]
     refine' Set.mul_mem_mul ((closure U).mul_mem hu ((closure U).inv_mem _)) (f (r * s⁻¹)).2
     refine' subset_closure ⟨f (r * s⁻¹) * s, Set.mul_mem_mul (f (r * s⁻¹)).2 hs, _⟩

8350c34a

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

@@ -42,12 +42,12 @@ theorem closure_mul_image_mul_eq_top
   change (closure U : Set G) * R = ⊤
   refine' top_le_iff.mp fun g _ => _
   apply closure_induction_right (eq_top_iff.mp hS (mem_top g))
-  · exact ⟨1, 1, (closure U).one_mem, hR1, one_mul 1⟩
-  · rintro - s hs ⟨u, r, hu, hr, rfl⟩
+  · exact ⟨1, (closure U).one_mem, 1, hR1, one_mul 1⟩
+  · rintro - s hs ⟨u, hu, r, hr, rfl⟩
     rw [show u * r * s = u * (r * s * (f (r * s) : G)⁻¹) * f (r * s) by group]
     refine' Set.mul_mem_mul ((closure U).mul_mem hu _) (f (r * s)).coe_prop
     exact subset_closure ⟨r * s, Set.mul_mem_mul hr hs, rfl⟩
-  · rintro - s hs ⟨u, r, hu, hr, rfl⟩
+  · rintro - s hs ⟨u, hu, r, hr, rfl⟩
     rw [show u * r * s⁻¹ = u * (f (r * s⁻¹) * s * r⁻¹)⁻¹ * f (r * s⁻¹) by group]
     refine' Set.mul_mem_mul ((closure U).mul_mem hu ((closure U).inv_mem _)) (f (r * s⁻¹)).2
     refine' subset_closure ⟨f (r * s⁻¹) * s, Set.mul_mem_mul (f (r * s⁻¹)).2 hs, _⟩
@@ -58,7 +58,7 @@ theorem closure_mul_image_mul_eq_top
     exact toFun_mul_inv_mem hR (r * s⁻¹)
 #align subgroup.closure_mul_image_mul_eq_top Subgroup.closure_mul_image_mul_eq_top
 
-/-- **Schreier's Lemma**: If `R : Set G` is a `rightTransversal of` `H : Subgroup G`
+/-- **Schreier's Lemma**: If `R : Set G` is a `rightTransversal` of `H : Subgroup G`
   with `1 ∈ R`, and if `G` is generated by `S : Set G`, then `H` is generated by the `Set`
   `(R * S).image (fun g ↦ g * (toFun hR g)⁻¹)`. -/
 theorem closure_mul_image_eq (hR : R ∈ rightTransversals (H : Set G)) (hR1 : (1 : G) ∈ R)
@@ -68,7 +68,7 @@ theorem closure_mul_image_eq (hR : R ∈ rightTransversals (H : Set G)) (hR1 : (
     rintro - ⟨g, -, rfl⟩
     exact mul_inv_toFun_mem hR g
   refine' le_antisymm hU fun h hh => _
-  obtain ⟨g, r, hg, hr, rfl⟩ :=
+  obtain ⟨g, hg, r, hr, rfl⟩ :=
     show h ∈ _ from eq_top_iff.mp (closure_mul_image_mul_eq_top hR hR1 hS) (mem_top h)
   suffices (⟨r, hr⟩ : R) = (⟨1, hR1⟩ : R) by
     simpa only [show r = 1 from Subtype.ext_iff.mp this, mul_one]

8350c34a

chore: Rename pow monotonicity lemmas (#9095)

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

`Algebra.GroupPower.Order`

pow_mono → pow_right_mono
pow_le_pow → pow_le_pow_right
pow_le_pow_of_le_left → pow_le_pow_left
pow_lt_pow_of_lt_left → pow_lt_pow_left
strictMonoOn_pow → pow_left_strictMonoOn
pow_strictMono_right → pow_right_strictMono
pow_lt_pow → pow_lt_pow_right
pow_lt_pow_iff → pow_lt_pow_iff_right
pow_le_pow_iff → pow_le_pow_iff_right
self_lt_pow → lt_self_pow
strictAnti_pow → pow_right_strictAnti
pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
le_of_pow_le_pow → le_of_pow_le_pow_left
pow_lt_pow₀ → pow_lt_pow_right₀

`Algebra.GroupPower.CovariantClass`

pow_le_pow_of_le_left' → pow_le_pow_left'
nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
pow_lt_pow' → pow_lt_pow_right'
nsmul_lt_nsmul → nsmul_lt_nsmul_left
pow_strictMono_left → pow_right_strictMono'
nsmul_strictMono_right → nsmul_left_strictMono
StrictMono.pow_right' → StrictMono.pow_const
StrictMono.nsmul_left → StrictMono.const_nsmul
pow_strictMono_right' → pow_left_strictMono
nsmul_strictMono_left → nsmul_right_strictMono
Monotone.pow_right → Monotone.pow_const
Monotone.nsmul_left → Monotone.const_nsmul
lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
pow_le_pow' → pow_le_pow_right'
nsmul_le_nsmul → nsmul_le_nsmul_left
pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
le_of_pow_le_pow' → le_of_pow_le_pow_left'
le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
pow_le_pow_iff' → pow_le_pow_iff_right'
nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
pow_lt_pow_iff' → pow_lt_pow_iff_right'
nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

`Data.Nat.Pow`

Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

pow_le_pow_iff_left
pow_lt_pow_iff_left
pow_right_injective
pow_right_inj
Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

self_le_pow was a duplicate of le_self_pow.
Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
Nat.pow_right_strictMono is defeq to pow_right_strictMono.
Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

A bunch of proofs have been golfed.
Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
A few Nat lemmas have been protected.
One docstring has been fixed.

d61c95e1

Diff

@@ -196,7 +196,7 @@ theorem card_commutator_le_of_finite_commutatorSet [Finite (commutatorSet G)] :
       (Nat.pow_le_pow_of_le_right Finite.card_pos (rank_closureCommutatorRepresentatives_le G))
   replace h2 := h2.trans (pow_dvd_pow _ (add_le_add_right (mul_le_mul_right' h1 _) 1))
   rw [← pow_succ'] at h2
-  refine' (Nat.le_of_dvd _ h2).trans (Nat.pow_le_pow_of_le_left h1 _)
+  refine' (Nat.le_of_dvd _ h2).trans (Nat.pow_le_pow_left h1 _)
   exact pow_pos (Nat.pos_of_ne_zero FiniteIndex.finiteIndex) _
 #align subgroup.card_commutator_le_of_finite_commutator_set Subgroup.card_commutator_le_of_finite_commutatorSet

8350c34a

feat: Existence of tranversals of a subgroup (#8932)

Specialises the existence of tranversals to the case where one subgroup is contained in another.

Also replace ⊤ : Set G by Set.univ and modify the lemma names accordingly.

From PFR

759a69c8

Diff

@@ -106,7 +106,7 @@ theorem exists_finset_card_le_mul [FiniteIndex H] {S : Finset G} (hS : closure (
     ∃ T : Finset H, T.card ≤ H.index * S.card ∧ closure (T : Set H) = ⊤ := by
   letI := H.fintypeQuotientOfFiniteIndex
   haveI : DecidableEq G := Classical.decEq G
-  obtain ⟨R₀, hR : R₀ ∈ rightTransversals (H : Set G), hR1⟩ := exists_right_transversal (1 : G)
+  obtain ⟨R₀, hR, hR1⟩ := H.exists_right_transversal 1
   haveI : Fintype R₀ := Fintype.ofEquiv _ (toEquiv hR)
   let R : Finset G := Set.toFinset R₀
   replace hR : (R : Set G) ∈ rightTransversals (H : Set G) := by rwa [Set.coe_toFinset]

8350c34a

chore: Replace (· op ·) a by (a op ·) (#8843)

I used the regex $\(· (.) ·$ (.)\), replacing with ($2 $1 ·).

d14658b4

Diff

@@ -140,7 +140,7 @@ theorem rank_le_index_mul_rank [hG : Group.FG G] [FiniteIndex H] :
   calc
     Group.rank H ≤ T.card := Group.rank_le H hT
     _ ≤ H.index * S.card := hT₀
-    _ = H.index * Group.rank G := congr_arg ((· * ·) H.index) hS₀
+    _ = H.index * Group.rank G := congr_arg (H.index * ·) hS₀
 #align subgroup.rank_le_index_mul_rank Subgroup.rank_le_index_mul_rank
 
 variable (G)

8350c34a

chore: make sure all #align's are on a single line (#8215)

We'll need to do this step anyway when it is time to remove them all.

(See #8214 where I'm benchmarking the removal.)

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

3dc73bd8

Diff

@@ -198,8 +198,7 @@ theorem card_commutator_le_of_finite_commutatorSet [Finite (commutatorSet G)] :
   rw [← pow_succ'] at h2
   refine' (Nat.le_of_dvd _ h2).trans (Nat.pow_le_pow_of_le_left h1 _)
   exact pow_pos (Nat.pos_of_ne_zero FiniteIndex.finiteIndex) _
-#align subgroup.card_commutator_le_of_finite_commutator_set
-  Subgroup.card_commutator_le_of_finite_commutatorSet
+#align subgroup.card_commutator_le_of_finite_commutator_set Subgroup.card_commutator_le_of_finite_commutatorSet
 
 /-- A theorem of Schur: A group with finitely many commutators has finite commutator subgroup. -/
 instance [Finite (commutatorSet G)] : Finite (_root_.commutator G) := by

8350c34a

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -152,7 +152,7 @@ theorem card_commutator_dvd_index_center_pow [Finite (commutatorSet G)] :
       (center G).index ^ ((center G).index * Nat.card (commutatorSet G) + 1) := by
   -- First handle the case when `Z(G)` has infinite index and `[G : Z(G)]` is defined to be `0`
   by_cases hG : (center G).index = 0
-  · simp_rw [hG, MulZeroClass.zero_mul, zero_add, pow_one, dvd_zero]
+  · simp_rw [hG, zero_mul, zero_add, pow_one, dvd_zero]
   haveI : FiniteIndex (center G) := ⟨hG⟩
   -- Rewrite as `|Z(G) ∩ G'| * [G' : Z(G) ∩ G'] ∣ [G : Z(G)] ^ ([G : Z(G)] * n) * [G : Z(G)]`
   rw [← ((center G).subgroupOf (_root_.commutator G)).card_mul_index, pow_succ']

8350c34a

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

@@ -32,7 +32,7 @@ namespace Subgroup
 
 open MemRightTransversals
 
-variable {G : Type _} [Group G] {H : Subgroup G} {R S : Set G}
+variable {G : Type*} [Group G] {H : Subgroup G} {R S : Set G}
 
 theorem closure_mul_image_mul_eq_top
     (hR : R ∈ rightTransversals (H : Set G)) (hR1 : (1 : G) ∈ R) (hS : closure S = ⊤) :

8350c34a

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) 2022 Thomas Browning. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
-
-! This file was ported from Lean 3 source module group_theory.schreier
-! leanprover-community/mathlib commit 8350c34a64b9bc3fc64335df8006bffcadc7baa6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.Abelianization
 import Mathlib.GroupTheory.Exponent
 import Mathlib.GroupTheory.Transfer
 
+#align_import group_theory.schreier from "leanprover-community/mathlib"@"8350c34a64b9bc3fc64335df8006bffcadc7baa6"
+
 /-!
 # Schreier's Lemma

8350c34a

chore: tidy various files (#5355)

0d584e40

Diff

@@ -22,7 +22,7 @@ In this file we prove Schreier's lemma.
 - `closure_mul_image_eq` : **Schreier's Lemma**: If `R : Set G` is a right_transversal
   of `H : Subgroup G` with `1 ∈ R`, and if `G` is generated by `S : Set G`,
   then `H` is generated by the `Set` `(R * S).image (fun g ↦ g * (toFun hR g)⁻¹)`.
-- `fG_of_index_ne_zero` : **Schreier's Lemma**: A finite index subgroup of a finitely generated
+- `fg_of_index_ne_zero` : **Schreier's Lemma**: A finite index subgroup of a finitely generated
   group is finitely generated.
 - `card_commutator_le_of_finite_commutatorSet`: A theorem of Schur: The size of the commutator
   subgroup is bounded in terms of the number of commutators.
@@ -129,15 +129,15 @@ theorem exists_finset_card_le_mul [FiniteIndex H] {S : Finset G} (hS : closure (
 
 /-- **Schreier's Lemma**: A finite index subgroup of a finitely generated
   group is finitely generated. -/
-instance fG_of_index_ne_zero [hG : Group.FG G] [FiniteIndex H] : Group.FG H := by
+instance fg_of_index_ne_zero [hG : Group.FG G] [FiniteIndex H] : Group.FG H := by
   obtain ⟨S, hS⟩ := hG.1
   obtain ⟨T, -, hT⟩ := exists_finset_card_le_mul H hS
   exact ⟨⟨T, hT⟩⟩
-#align subgroup.fg_of_index_ne_zero Subgroup.fG_of_index_ne_zero
+#align subgroup.fg_of_index_ne_zero Subgroup.fg_of_index_ne_zero
 
 theorem rank_le_index_mul_rank [hG : Group.FG G] [FiniteIndex H] :
     Group.rank H ≤ H.index * Group.rank G := by
-  haveI := H.fG_of_index_ne_zero
+  haveI := H.fg_of_index_ne_zero
   obtain ⟨S, hS₀, hS⟩ := Group.rank_spec G
   obtain ⟨T, hT₀, hT⟩ := exists_finset_card_le_mul H hS
   calc

8350c34a

chore: convert lambda in docs to fun (#5045)

Found with git grep -n "λ [a-zA-Z_ ]*,"

1164cf04

Diff

@@ -21,7 +21,7 @@ In this file we prove Schreier's lemma.
 
 - `closure_mul_image_eq` : **Schreier's Lemma**: If `R : Set G` is a right_transversal
   of `H : Subgroup G` with `1 ∈ R`, and if `G` is generated by `S : Set G`,
-  then `H` is generated by the `Set` `(R * S).image (λ g, g * (toFun hR g)⁻¹)`.
+  then `H` is generated by the `Set` `(R * S).image (fun g ↦ g * (toFun hR g)⁻¹)`.
 - `fG_of_index_ne_zero` : **Schreier's Lemma**: A finite index subgroup of a finitely generated
   group is finitely generated.
 - `card_commutator_le_of_finite_commutatorSet`: A theorem of Schur: The size of the commutator
@@ -63,7 +63,7 @@ theorem closure_mul_image_mul_eq_top
 
 /-- **Schreier's Lemma**: If `R : Set G` is a `rightTransversal of` `H : Subgroup G`
   with `1 ∈ R`, and if `G` is generated by `S : Set G`, then `H` is generated by the `Set`
-  `(R * S).image (λ g, g * (toFun hR g)⁻¹)`. -/
+  `(R * S).image (fun g ↦ g * (toFun hR g)⁻¹)`. -/
 theorem closure_mul_image_eq (hR : R ∈ rightTransversals (H : Set G)) (hR1 : (1 : G) ∈ R)
     (hS : closure S = ⊤) : closure ((R * S).image fun g => g * (toFun hR g : G)⁻¹) = H := by
   have hU : closure ((R * S).image fun g => g * (toFun hR g : G)⁻¹) ≤ H := by
@@ -84,7 +84,7 @@ theorem closure_mul_image_eq (hR : R ∈ rightTransversals (H : Set G)) (hR1 : (
 
 /-- **Schreier's Lemma**: If `R : Set G` is a `rightTransversal` of `H : Subgroup G`
   with `1 ∈ R`, and if `G` is generated by `S : Set G`, then `H` is generated by the `Set`
-  `(R * S).image (λ g, g * (toFun hR g)⁻¹)`. -/
+  `(R * S).image (fun g ↦ g * (toFun hR g)⁻¹)`. -/
 theorem closure_mul_image_eq_top (hR : R ∈ rightTransversals (H : Set G)) (hR1 : (1 : G) ∈ R)
     (hS : closure S = ⊤) : closure ((R * S).image fun g =>
       ⟨g * (toFun hR g : G)⁻¹, mul_inv_toFun_mem hR g⟩ : Set H) = ⊤ := by
@@ -94,7 +94,7 @@ theorem closure_mul_image_eq_top (hR : R ∈ rightTransversals (H : Set G)) (hR1
 
 /-- **Schreier's Lemma**: If `R : Finset G` is a `rightTransversal` of `H : Subgroup G`
   with `1 ∈ R`, and if `G` is generated by `S : Finset G`, then `H` is generated by the `Finset`
-  `(R * S).image (λ g, g * (toFun hR g)⁻¹)`. -/
+  `(R * S).image (fun g ↦ g * (toFun hR g)⁻¹)`. -/
 theorem closure_mul_image_eq_top' [DecidableEq G] {R S : Finset G}
     (hR : (R : Set G) ∈ rightTransversals (H : Set G)) (hR1 : (1 : G) ∈ R)
     (hS : closure (S : Set G) = ⊤) :

8350c34a

feat: port GroupTheory.Schreier (#4706)

aee19255

`group_theory.schreier` ⟷ `Mathlib.GroupTheory.Schreier`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`

Lemmas added

Lemmas removed

Other changes

Dependencies 8 + 542

group_theory.schreier ⟷ Mathlib.GroupTheory.Schreier

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Algebra.GroupPower.Order

Algebra.GroupPower.CovariantClass

Data.Nat.Pow

Lemmas added

Lemmas removed

Other changes

Dependencies 8 + 542

`group_theory.schreier` ⟷ `Mathlib.GroupTheory.Schreier`

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`