group_theory.perm.cycle.type ⟷ Mathlib.GroupTheory.Perm.Cycle.Type

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Thomas Browning. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
 -/
-import Algebra.GcdMonoid.Multiset
-import Combinatorics.Partition
+import Algebra.GCDMonoid.Multiset
+import Combinatorics.Enumerative.Partition
 import Data.List.Rotate
 import GroupTheory.Perm.Cycle.Basic
 import RingTheory.Int.Basic

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

@@ -109,7 +109,7 @@ theorem card_cycleType_eq_zero {σ : Perm α} : σ.cycleType.card = 0 ↔ σ = 1
 theorem two_le_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType) : 2 ≤ n :=
   by
   simp only [cycle_type_def, ← Finset.mem_def, Function.comp_apply, Multiset.mem_map,
-    mem_cycle_factors_finset_iff] at h 
+    mem_cycle_factors_finset_iff] at h
   obtain ⟨_, ⟨hc, -⟩, rfl⟩ := h
   exact hc.two_le_card_support
 #align equiv.perm.two_le_of_mem_cycle_type Equiv.Perm.two_le_of_mem_cycleType
@@ -238,7 +238,7 @@ theorem dvd_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType) :
 theorem orderOf_cycleOf_dvd_orderOf (f : Perm α) (x : α) : orderOf (cycleOf f x) ∣ orderOf f :=
   by
   by_cases hx : f x = x
-  · rw [← cycle_of_eq_one_iff] at hx 
+  · rw [← cycle_of_eq_one_iff] at hx
     simp [hx]
   · refine' dvd_of_mem_cycle_type _
     rw [cycle_type, Multiset.mem_map]
@@ -270,7 +270,7 @@ theorem cycleType_prime_order {σ : Perm α} (hσ : (orderOf σ).Prime) :
   rw [tsub_add_cancel_of_le]
   rw [Nat.succ_le_iff, pos_iff_ne_zero, Ne, card_cycle_type_eq_zero]
   intro H
-  rw [H, orderOf_one] at hσ 
+  rw [H, orderOf_one] at hσ
   exact hσ.ne_one rfl
 #align equiv.perm.cycle_type_prime_order Equiv.Perm.cycleType_prime_order
 -/
@@ -281,7 +281,7 @@ theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
   by
   obtain ⟨n, hn⟩ := cycle_type_prime_order h1
   rw [← σ.sum_cycle_type, hn, Multiset.sum_replicate, nsmul_eq_mul, Nat.cast_id,
-    mul_lt_mul_right (orderOf_pos σ), Nat.succ_lt_succ_iff, Nat.lt_succ_iff, le_zero_iff] at h2 
+    mul_lt_mul_right (orderOf_pos σ), Nat.succ_lt_succ_iff, Nat.lt_succ_iff, le_zero_iff] at h2
   rw [← card_cycle_type_eq_one, hn, card_replicate, h2]
 #align equiv.perm.is_cycle_of_prime_order Equiv.Perm.isCycle_of_prime_order
 -/
@@ -290,7 +290,7 @@ theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
 theorem cycleType_le_of_mem_cycleFactorsFinset {f g : Perm α} (hf : f ∈ g.cycleFactorsFinset) :
     f.cycleType ≤ g.cycleType :=
   by
-  rw [mem_cycle_factors_finset_iff] at hf 
+  rw [mem_cycle_factors_finset_iff] at hf
   rw [cycle_type_def, cycle_type_def, hf.left.cycle_factors_finset_eq_singleton]
   refine' map_le_map _
   simpa [← Finset.mem_def, mem_cycle_factors_finset_iff] using hf
@@ -303,7 +303,7 @@ theorem cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub {f g : Perm α}
   by
   suffices (g * f⁻¹).cycleType + f.cycle_type = g.cycle_type - f.cycle_type + f.cycle_type
     by
-    rw [tsub_add_cancel_of_le (cycle_type_le_of_mem_cycle_factors_finset hf)] at this 
+    rw [tsub_add_cancel_of_le (cycle_type_le_of_mem_cycle_factors_finset hf)] at this
     simp [← this]
   simp [← (disjoint_mul_inv_of_mem_cycle_factors_finset hf).cycleType,
     tsub_add_cancel_of_le (cycle_type_le_of_mem_cycle_factors_finset hf)]
@@ -316,17 +316,17 @@ theorem isConj_of_cycleType_eq {σ τ : Perm α} (h : cycleType σ = cycleType 
   revert τ
   apply cycle_induction_on _ σ
   · intro τ h
-    rw [cycle_type_one, eq_comm, cycle_type_eq_zero] at h 
+    rw [cycle_type_one, eq_comm, cycle_type_eq_zero] at h
     rw [h]
   · intro σ hσ τ hστ
     have hτ := card_cycle_type_eq_one.2 hσ
-    rw [hστ, card_cycle_type_eq_one] at hτ 
+    rw [hστ, card_cycle_type_eq_one] at hτ
     apply hσ.is_conj hτ
-    rw [hσ.cycle_type, hτ.cycle_type, coe_eq_coe, singleton_perm] at hστ 
-    simp only [and_true_iff, eq_self_iff_true] at hστ 
+    rw [hσ.cycle_type, hτ.cycle_type, coe_eq_coe, singleton_perm] at hστ
+    simp only [and_true_iff, eq_self_iff_true] at hστ
     exact hστ
   · intro σ τ hστ hσ h1 h2 π hπ
-    rw [hστ.cycle_type] at hπ 
+    rw [hστ.cycle_type] at hπ
     · have h : σ.support.card ∈ map (Finset.card ∘ perm.support) π.cycle_factors_finset.val := by
         simp [← cycle_type_def, ← hπ, hσ.cycle_type]
       obtain ⟨σ', hσ'l, hσ'⟩ := multiset.mem_map.mp h
@@ -338,7 +338,7 @@ theorem isConj_of_cycleType_eq {σ τ : Perm α} (h : cycleType σ = cycleType 
       refine' IsConj.trans _ key
       have hs : σ.cycle_type = σ'.cycle_type :=
         by
-        rw [← Finset.mem_def, mem_cycle_factors_finset_iff] at hσ'l 
+        rw [← Finset.mem_def, mem_cycle_factors_finset_iff] at hσ'l
         rw [hσ.cycle_type, ← hσ', hσ'l.left.cycle_type]
       refine' hστ.is_conj_mul (h1 hs) (h2 _) _
       · rw [cycle_type_mul_mem_cycle_factors_finset_eq_sub, ← hπ, add_comm, hs,
@@ -385,9 +385,9 @@ theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
   constructor
   · intro h
     obtain ⟨l, rfl, hlc, hld⟩ := trunc_cycle_factors σ
-    rw [cycle_type_eq _ rfl hlc hld] at h 
+    rw [cycle_type_eq _ rfl hlc hld] at h
     obtain ⟨c, cl, rfl⟩ := List.exists_of_mem_map h
-    rw [(List.perm_cons_erase cl).pairwise_iff fun _ _ hd => _] at hld 
+    rw [(List.perm_cons_erase cl).pairwise_iff fun _ _ hd => _] at hld
     swap; · exact hd.symm
     refine' ⟨c, (l.erase c).Prod, _, _, hlc _ cl, rfl⟩
     ·
@@ -440,7 +440,7 @@ theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p 
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by
   classical
   contrapose! hα
-  simp_rw [← mem_support] at hα 
+  simp_rw [← mem_support] at hα
   exact
     nat.modeq_zero_iff_dvd.mp
       ((congr_arg _
@@ -751,14 +751,14 @@ theorem card_support_eq_three_iff : σ.support.card = 3 ↔ σ.IsThreeCycle :=
   by
   refine' ⟨fun h => _, is_three_cycle.card_support⟩
   by_cases h0 : σ.cycle_type = 0
-  · rw [← sum_cycle_type, h0, sum_zero] at h 
+  · rw [← sum_cycle_type, h0, sum_zero] at h
     exact (ne_of_lt zero_lt_three h).elim
   obtain ⟨n, hn⟩ := exists_mem_of_ne_zero h0
   by_cases h1 : σ.cycle_type.erase n = 0
-  · rw [← sum_cycle_type, ← cons_erase hn, h1, cons_zero, Multiset.sum_singleton] at h 
+  · rw [← sum_cycle_type, ← cons_erase hn, h1, cons_zero, Multiset.sum_singleton] at h
     rw [is_three_cycle, ← cons_erase hn, h1, h, ← cons_zero]
   obtain ⟨m, hm⟩ := exists_mem_of_ne_zero h1
-  rw [← sum_cycle_type, ← cons_erase hn, ← cons_erase hm, Multiset.sum_cons, Multiset.sum_cons] at h 
+  rw [← sum_cycle_type, ← cons_erase hn, ← cons_erase hm, Multiset.sum_cons, Multiset.sum_cons] at h
   -- TODO: linarith [...] should solve this directly
   have : ∀ {k}, 2 ≤ m → 2 ≤ n → n + (m + k) = 3 → False := by intros; linarith
   cases this (two_le_of_mem_cycle_type (mem_of_mem_erase hm)) (two_le_of_mem_cycle_type hn) h
@@ -822,7 +822,7 @@ theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠
     simp [ab, ac, bc]
   apply le_antisymm ((support_mul_le _ _).trans fun x => _) fun x hx => _
   · simp [ab, ac, bc]
-  · simp only [Finset.mem_insert, Finset.mem_singleton] at hx 
+  · simp only [Finset.mem_insert, Finset.mem_singleton] at hx
     rw [mem_support]
     simp only [perm.coe_mul, Function.comp_apply, Ne.def]
     obtain rfl | rfl | rfl := hx

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

@@ -437,7 +437,15 @@ theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime
 
 #print Equiv.Perm.exists_fixed_point_of_prime /-
 theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p ∣ Fintype.card α)
-    {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by classical
+    {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by
+  classical
+  contrapose! hα
+  simp_rw [← mem_support] at hα 
+  exact
+    nat.modeq_zero_iff_dvd.mp
+      ((congr_arg _
+            (finset.card_eq_zero.mpr (compl_eq_bot.mpr (finset.eq_univ_iff_forall.mpr hα)))).mp
+        (card_compl_support_modeq hσ).symm)
 #align equiv.perm.exists_fixed_point_of_prime Equiv.Perm.exists_fixed_point_of_prime
 -/
 
@@ -445,19 +453,34 @@ theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p 
 theorem exists_fixed_point_of_prime' {p n : ℕ} [hp : Fact p.Prime] (hα : p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) {a : α} (ha : σ a = a) : ∃ b : α, σ b = b ∧ b ≠ a := by
   classical
+  have h : ∀ b : α, b ∈ σ.supportᶜ ↔ σ b = b := fun b => by
+    rw [Finset.mem_compl, mem_support, Classical.not_not]
+  obtain ⟨b, hb1, hb2⟩ :=
+    Finset.exists_ne_of_one_lt_card
+      (lt_of_lt_of_le hp.out.one_lt
+        (Nat.le_of_dvd (finset.card_pos.mpr ⟨a, (h a).mpr ha⟩)
+          (nat.modeq_zero_iff_dvd.mp
+            ((card_compl_support_modeq hσ).trans (nat.modeq_zero_iff_dvd.mpr hα)))))
+      a
+  exact ⟨b, (h b).mp hb1, hb2⟩
 #align equiv.perm.exists_fixed_point_of_prime' Equiv.Perm.exists_fixed_point_of_prime'
 -/
 
 #print Equiv.Perm.isCycle_of_prime_order' /-
 theorem isCycle_of_prime_order' {σ : Perm α} (h1 : (orderOf σ).Prime)
-    (h2 : Fintype.card α < 2 * orderOf σ) : σ.IsCycle := by classical
+    (h2 : Fintype.card α < 2 * orderOf σ) : σ.IsCycle := by
+  classical exact is_cycle_of_prime_order h1 (lt_of_le_of_lt σ.support.card_le_univ h2)
 #align equiv.perm.is_cycle_of_prime_order' Equiv.Perm.isCycle_of_prime_order'
 -/
 
 #print Equiv.Perm.isCycle_of_prime_order'' /-
 theorem isCycle_of_prime_order'' {σ : Perm α} (h1 : (Fintype.card α).Prime)
     (h2 : orderOf σ = Fintype.card α) : σ.IsCycle :=
-  isCycle_of_prime_order' ((congr_arg Nat.Prime h2).mpr h1) (by classical)
+  isCycle_of_prime_order' ((congr_arg Nat.Prime h2).mpr h1)
+    (by
+      classical
+      rw [← one_mul (Fintype.card α), ← h2, mul_lt_mul_right (orderOf_pos σ)]
+      exact one_lt_two)
 #align equiv.perm.is_cycle_of_prime_order'' Equiv.Perm.isCycle_of_prime_order''
 -/
 

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

@@ -437,15 +437,7 @@ theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime
 
 #print Equiv.Perm.exists_fixed_point_of_prime /-
 theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p ∣ Fintype.card α)
-    {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by
-  classical
-  contrapose! hα
-  simp_rw [← mem_support] at hα 
-  exact
-    nat.modeq_zero_iff_dvd.mp
-      ((congr_arg _
-            (finset.card_eq_zero.mpr (compl_eq_bot.mpr (finset.eq_univ_iff_forall.mpr hα)))).mp
-        (card_compl_support_modeq hσ).symm)
+    {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by classical
 #align equiv.perm.exists_fixed_point_of_prime Equiv.Perm.exists_fixed_point_of_prime
 -/
 
@@ -453,34 +445,19 @@ theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p 
 theorem exists_fixed_point_of_prime' {p n : ℕ} [hp : Fact p.Prime] (hα : p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) {a : α} (ha : σ a = a) : ∃ b : α, σ b = b ∧ b ≠ a := by
   classical
-  have h : ∀ b : α, b ∈ σ.supportᶜ ↔ σ b = b := fun b => by
-    rw [Finset.mem_compl, mem_support, Classical.not_not]
-  obtain ⟨b, hb1, hb2⟩ :=
-    Finset.exists_ne_of_one_lt_card
-      (lt_of_lt_of_le hp.out.one_lt
-        (Nat.le_of_dvd (finset.card_pos.mpr ⟨a, (h a).mpr ha⟩)
-          (nat.modeq_zero_iff_dvd.mp
-            ((card_compl_support_modeq hσ).trans (nat.modeq_zero_iff_dvd.mpr hα)))))
-      a
-  exact ⟨b, (h b).mp hb1, hb2⟩
 #align equiv.perm.exists_fixed_point_of_prime' Equiv.Perm.exists_fixed_point_of_prime'
 -/
 
 #print Equiv.Perm.isCycle_of_prime_order' /-
 theorem isCycle_of_prime_order' {σ : Perm α} (h1 : (orderOf σ).Prime)
-    (h2 : Fintype.card α < 2 * orderOf σ) : σ.IsCycle := by
-  classical exact is_cycle_of_prime_order h1 (lt_of_le_of_lt σ.support.card_le_univ h2)
+    (h2 : Fintype.card α < 2 * orderOf σ) : σ.IsCycle := by classical
 #align equiv.perm.is_cycle_of_prime_order' Equiv.Perm.isCycle_of_prime_order'
 -/
 
 #print Equiv.Perm.isCycle_of_prime_order'' /-
 theorem isCycle_of_prime_order'' {σ : Perm α} (h1 : (Fintype.card α).Prime)
     (h2 : orderOf σ = Fintype.card α) : σ.IsCycle :=
-  isCycle_of_prime_order' ((congr_arg Nat.Prime h2).mpr h1)
-    (by
-      classical
-      rw [← one_mul (Fintype.card α), ← h2, mul_lt_mul_right (orderOf_pos σ)]
-      exact one_lt_two)
+  isCycle_of_prime_order' ((congr_arg Nat.Prime h2).mpr h1) (by classical)
 #align equiv.perm.is_cycle_of_prime_order'' Equiv.Perm.isCycle_of_prime_order''
 -/
 

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

@@ -657,7 +657,7 @@ theorem subgroup_eq_top_of_swap_mem [DecidableEq α] {H : Subgroup (Perm α)}
   by
   haveI : Fact (Fintype.card α).Prime := ⟨h0⟩
   obtain ⟨σ, hσ⟩ := exists_prime_orderOf_dvd_card (Fintype.card α) h1
-  have hσ1 : orderOf (σ : perm α) = Fintype.card α := (orderOf_subgroup σ).trans hσ
+  have hσ1 : orderOf (σ : perm α) = Fintype.card α := (Subgroup.orderOf_coe σ).trans hσ
   have hσ2 : is_cycle ↑σ := is_cycle_of_prime_order'' h0 hσ1
   have hσ3 : (σ : perm α).support = ⊤ :=
     Finset.eq_univ_of_card (σ : perm α).support (hσ2.order_of.symm.trans hσ1)

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

@@ -3,11 +3,11 @@ Copyright (c) 2020 Thomas Browning. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
 -/
-import Mathbin.Algebra.GcdMonoid.Multiset
-import Mathbin.Combinatorics.Partition
-import Mathbin.Data.List.Rotate
-import Mathbin.GroupTheory.Perm.Cycle.Basic
-import Mathbin.RingTheory.Int.Basic
+import Algebra.GcdMonoid.Multiset
+import Combinatorics.Partition
+import Data.List.Rotate
+import GroupTheory.Perm.Cycle.Basic
+import RingTheory.Int.Basic
 import Mathbin.Tactic.Linarith.Default
 
 #align_import group_theory.perm.cycle.type from "leanprover-community/mathlib"@"75be6b616681ab6ca66d798ead117e75cd64f125"

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 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.perm.cycle.type
-! leanprover-community/mathlib commit 75be6b616681ab6ca66d798ead117e75cd64f125
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.GcdMonoid.Multiset
 import Mathbin.Combinatorics.Partition
@@ -15,6 +10,8 @@ import Mathbin.GroupTheory.Perm.Cycle.Basic
 import Mathbin.RingTheory.Int.Basic
 import Mathbin.Tactic.Linarith.Default
 
+#align_import group_theory.perm.cycle.type from "leanprover-community/mathlib"@"75be6b616681ab6ca66d798ead117e75cd64f125"
+
 /-!
 # Cycle Types
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -665,7 +665,7 @@ theorem subgroup_eq_top_of_swap_mem [DecidableEq α] {H : Subgroup (Perm α)}
   have hσ3 : (σ : perm α).support = ⊤ :=
     Finset.eq_univ_of_card (σ : perm α).support (hσ2.order_of.symm.trans hσ1)
   have hσ4 : Subgroup.closure {↑σ, τ} = ⊤ := closure_prime_cycle_swap h0 hσ2 hσ3 h3
-  rw [eq_top_iff, ← hσ4, Subgroup.closure_le, Set.insert_subset, Set.singleton_subset_iff]
+  rw [eq_top_iff, ← hσ4, Subgroup.closure_le, Set.insert_subset_iff, Set.singleton_subset_iff]
   exact ⟨Subtype.mem σ, h2⟩
 #align equiv.perm.subgroup_eq_top_of_swap_mem Equiv.Perm.subgroup_eq_top_of_swap_mem
 -/

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

@@ -76,6 +76,7 @@ theorem cycleType_eq' {σ : Perm α} (s : Finset (Perm α)) (h1 : ∀ f : Perm 
 #align equiv.perm.cycle_type_eq' Equiv.Perm.cycleType_eq'
 -/
 
+#print Equiv.Perm.cycleType_eq /-
 theorem cycleType_eq {σ : Perm α} (l : List (Perm α)) (h0 : l.Prod = σ)
     (h1 : ∀ σ : Perm α, σ ∈ l → σ.IsCycle) (h2 : l.Pairwise Disjoint) :
     σ.cycleType = l.map (Finset.card ∘ support) :=
@@ -87,18 +88,25 @@ theorem cycleType_eq {σ : Perm α} (l : List (Perm α)) (h0 : l.Prod = σ)
   · simpa [hl] using h0
   · simpa [list.dedup_eq_self.mpr hl] using h2.forall disjoint.symmetric
 #align equiv.perm.cycle_type_eq Equiv.Perm.cycleType_eq
+-/
 
+#print Equiv.Perm.cycleType_one /-
 theorem cycleType_one : (1 : Perm α).cycleType = 0 :=
   cycleType_eq [] rfl (fun _ => False.elim) Pairwise.nil
 #align equiv.perm.cycle_type_one Equiv.Perm.cycleType_one
+-/
 
+#print Equiv.Perm.cycleType_eq_zero /-
 theorem cycleType_eq_zero {σ : Perm α} : σ.cycleType = 0 ↔ σ = 1 := by
   simp [cycle_type_def, cycle_factors_finset_eq_empty_iff]
 #align equiv.perm.cycle_type_eq_zero Equiv.Perm.cycleType_eq_zero
+-/
 
+#print Equiv.Perm.card_cycleType_eq_zero /-
 theorem card_cycleType_eq_zero {σ : Perm α} : σ.cycleType.card = 0 ↔ σ = 1 := by
   rw [card_eq_zero, cycle_type_eq_zero]
 #align equiv.perm.card_cycle_type_eq_zero Equiv.Perm.card_cycleType_eq_zero
+-/
 
 #print Equiv.Perm.two_le_of_mem_cycleType /-
 theorem two_le_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType) : 2 ≤ n :=
@@ -123,6 +131,7 @@ theorem IsCycle.cycleType {σ : Perm α} (hσ : IsCycle σ) : σ.cycleType = [σ
 #align equiv.perm.is_cycle.cycle_type Equiv.Perm.IsCycle.cycleType
 -/
 
+#print Equiv.Perm.card_cycleType_eq_one /-
 theorem card_cycleType_eq_one {σ : Perm α} : σ.cycleType.card = 1 ↔ σ.IsCycle :=
   by
   rw [card_eq_one]
@@ -135,7 +144,9 @@ theorem card_cycleType_eq_one {σ : Perm α} : σ.cycleType.card = 1 ↔ σ.IsCy
     use σ.support.card, σ
     simp [h]
 #align equiv.perm.card_cycle_type_eq_one Equiv.Perm.card_cycleType_eq_one
+-/
 
+#print Equiv.Perm.Disjoint.cycleType /-
 theorem Disjoint.cycleType {σ τ : Perm α} (h : Disjoint σ τ) :
     (σ * τ).cycleType = σ.cycleType + τ.cycleType :=
   by
@@ -143,7 +154,9 @@ theorem Disjoint.cycleType {σ τ : Perm α} (h : Disjoint σ τ) :
     Multiset.map_add, Finset.union_val, multiset.add_eq_union_iff_disjoint.mpr _]
   exact Finset.disjoint_val.2 h.disjoint_cycle_factors_finset
 #align equiv.perm.disjoint.cycle_type Equiv.Perm.Disjoint.cycleType
+-/
 
+#print Equiv.Perm.cycleType_inv /-
 theorem cycleType_inv (σ : Perm α) : σ⁻¹.cycleType = σ.cycleType :=
   cycle_induction_on (fun τ : Perm α => τ⁻¹.cycleType = τ.cycleType) σ rfl
     (fun σ hσ => by rw [hσ.cycle_type, hσ.inv.cycle_type, support_inv]) fun σ τ hστ hc hσ hτ => by
@@ -152,7 +165,9 @@ theorem cycleType_inv (σ : Perm α) : σ⁻¹.cycleType = σ.cycleType :=
         Or.imp (fun h : τ x = x => inv_eq_iff_eq.mpr h.symm)
           (fun h : σ x = x => inv_eq_iff_eq.mpr h.symm) (hστ x).symm]
 #align equiv.perm.cycle_type_inv Equiv.Perm.cycleType_inv
+-/
 
+#print Equiv.Perm.cycleType_conj /-
 theorem cycleType_conj {σ τ : Perm α} : (τ * σ * τ⁻¹).cycleType = σ.cycleType :=
   by
   revert τ
@@ -166,6 +181,7 @@ theorem cycleType_conj {σ τ : Perm α} : (τ * σ * τ⁻¹).cycleType = σ.cy
     intro a
     apply (hd (π⁻¹ a)).imp _ _ <;> · intro h; rw [perm.mul_apply, perm.mul_apply, h, apply_inv_self]
 #align equiv.perm.cycle_type_conj Equiv.Perm.cycleType_conj
+-/
 
 #print Equiv.Perm.sum_cycleType /-
 theorem sum_cycleType (σ : Perm α) : σ.cycleType.Sum = σ.support.card :=
@@ -176,6 +192,7 @@ theorem sum_cycleType (σ : Perm α) : σ.cycleType.Sum = σ.support.card :=
 #align equiv.perm.sum_cycle_type Equiv.Perm.sum_cycleType
 -/
 
+#print Equiv.Perm.sign_of_cycleType' /-
 theorem sign_of_cycleType' (σ : Perm α) : sign σ = (σ.cycleType.map fun n => -(-1 : ℤˣ) ^ n).Prod :=
   cycle_induction_on (fun τ : Perm α => sign τ = (τ.cycleType.map fun n => -(-1 : ℤˣ) ^ n).Prod) σ
     (by rw [sign_one, cycle_type_one, Multiset.map_zero, prod_zero])
@@ -183,7 +200,9 @@ theorem sign_of_cycleType' (σ : Perm α) : sign σ = (σ.cycleType.map fun n =>
       rw [hσ.sign, hσ.cycle_type, coe_map, coe_prod, List.map_singleton, List.prod_singleton])
     fun σ τ hστ hc hσ hτ => by rw [sign_mul, hσ, hτ, hστ.cycle_type, Multiset.map_add, prod_add]
 #align equiv.perm.sign_of_cycle_type' Equiv.Perm.sign_of_cycleType'
+-/
 
+#print Equiv.Perm.sign_of_cycleType /-
 theorem sign_of_cycleType (f : Perm α) :
     sign f = (-1 : ℤˣ) ^ (f.cycleType.Sum + f.cycleType.card) :=
   cycle_induction_on (fun f : Perm α => sign f = (-1 : ℤˣ) ^ (f.cycleType.Sum + f.cycleType.card)) f
@@ -199,13 +218,16 @@ theorem sign_of_cycleType (f : Perm α) :
       add_comm f.cycle_type.sum g.cycle_type.sum, add_assoc g.cycle_type.sum _ _,
       add_comm g.cycle_type.sum _, add_assoc, pow_add, ← Pf, ← Pg, Equiv.Perm.sign_mul]
 #align equiv.perm.sign_of_cycle_type Equiv.Perm.sign_of_cycleType
+-/
 
+#print Equiv.Perm.lcm_cycleType /-
 theorem lcm_cycleType (σ : Perm α) : σ.cycleType.lcm = orderOf σ :=
   cycle_induction_on (fun τ : Perm α => τ.cycleType.lcm = orderOf τ) σ
     (by rw [cycle_type_one, lcm_zero, orderOf_one])
     (fun σ hσ => by rw [hσ.cycle_type, coe_singleton, lcm_singleton, hσ.order_of, normalize_eq])
     fun σ τ hστ hc hσ hτ => by rw [hστ.cycle_type, lcm_add, lcm_eq_nat_lcm, hστ.order_of, hσ, hτ]
 #align equiv.perm.lcm_cycle_type Equiv.Perm.lcm_cycleType
+-/
 
 #print Equiv.Perm.dvd_of_mem_cycleType /-
 theorem dvd_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType) : n ∣ orderOf σ :=
@@ -229,6 +251,7 @@ theorem orderOf_cycleOf_dvd_orderOf (f : Perm α) (x : α) : orderOf (cycleOf f
 #align equiv.perm.order_of_cycle_of_dvd_order_of Equiv.Perm.orderOf_cycleOf_dvd_orderOf
 -/
 
+#print Equiv.Perm.two_dvd_card_support /-
 theorem two_dvd_card_support {σ : Perm α} (hσ : σ ^ 2 = 1) : 2 ∣ σ.support.card :=
   (congr_arg (Dvd.Dvd 2) σ.sum_cycleType).mp
     (Multiset.dvd_sum fun n hn => by
@@ -237,6 +260,7 @@ theorem two_dvd_card_support {σ : Perm α} (hσ : σ ^ 2 = 1) : 2 ∣ σ.suppor
             (dvd_of_mem_cycle_type hn).trans <| orderOf_dvd_of_pow_eq_one hσ)
           (two_le_of_mem_cycle_type hn)])
 #align equiv.perm.two_dvd_card_support Equiv.Perm.two_dvd_card_support
+-/
 
 #print Equiv.Perm.cycleType_prime_order /-
 theorem cycleType_prime_order {σ : Perm α} (hσ : (orderOf σ).Prime) :
@@ -265,6 +289,7 @@ theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
 #align equiv.perm.is_cycle_of_prime_order Equiv.Perm.isCycle_of_prime_order
 -/
 
+#print Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinset /-
 theorem cycleType_le_of_mem_cycleFactorsFinset {f g : Perm α} (hf : f ∈ g.cycleFactorsFinset) :
     f.cycleType ≤ g.cycleType :=
   by
@@ -273,7 +298,9 @@ theorem cycleType_le_of_mem_cycleFactorsFinset {f g : Perm α} (hf : f ∈ g.cyc
   refine' map_le_map _
   simpa [← Finset.mem_def, mem_cycle_factors_finset_iff] using hf
 #align equiv.perm.cycle_type_le_of_mem_cycle_factors_finset Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinset
+-/
 
+#print Equiv.Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub /-
 theorem cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub {f g : Perm α}
     (hf : f ∈ g.cycleFactorsFinset) : (g * f⁻¹).cycleType = g.cycleType - f.cycleType :=
   by
@@ -284,6 +311,7 @@ theorem cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub {f g : Perm α}
   simp [← (disjoint_mul_inv_of_mem_cycle_factors_finset hf).cycleType,
     tsub_add_cancel_of_le (cycle_type_le_of_mem_cycle_factors_finset hf)]
 #align equiv.perm.cycle_type_mul_mem_cycle_factors_finset_eq_sub Equiv.Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub
+-/
 
 #print Equiv.Perm.isConj_of_cycleType_eq /-
 theorem isConj_of_cycleType_eq {σ τ : Perm α} (h : cycleType σ = cycleType τ) : IsConj σ τ :=
@@ -346,11 +374,14 @@ theorem cycleType_extendDomain {β : Type _} [Fintype β] [DecidableEq β] {p :
 #align equiv.perm.cycle_type_extend_domain Equiv.Perm.cycleType_extendDomain
 -/
 
+#print Equiv.Perm.cycleType_ofSubtype /-
 theorem cycleType_ofSubtype {p : α → Prop} [DecidablePred p] {g : Perm (Subtype p)} :
     cycleType g.ofSubtype = cycleType g :=
   cycleType_extendDomain (Equiv.refl (Subtype p))
 #align equiv.perm.cycle_type_of_subtype Equiv.Perm.cycleType_ofSubtype
+-/
 
+#print Equiv.Perm.mem_cycleType_iff /-
 theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
     n ∈ cycleType σ ↔ ∃ c τ : Perm α, σ = c * τ ∧ Disjoint c τ ∧ IsCycle c ∧ c.support.card = n :=
   by
@@ -369,6 +400,7 @@ theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
   · rintro ⟨c, t, rfl, hd, hc, rfl⟩
     simp [hd.cycle_type, hc.cycle_type]
 #align equiv.perm.mem_cycle_type_iff Equiv.Perm.mem_cycleType_iff
+-/
 
 #print Equiv.Perm.le_card_support_of_mem_cycleType /-
 theorem le_card_support_of_mem_cycleType {n : ℕ} {σ : Perm α} (h : n ∈ cycleType σ) :
@@ -393,6 +425,7 @@ theorem cycleType_of_card_le_mem_cycleType_add_two {n : ℕ} {g : Perm α}
 
 end CycleType
 
+#print Equiv.Perm.card_compl_support_modEq /-
 theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime] {σ : Perm α}
     (hσ : σ ^ p ^ n = 1) : σ.supportᶜ.card ≡ Fintype.card α [MOD p] :=
   by
@@ -403,7 +436,9 @@ theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime
     (Nat.dvd_prime_pow hp.out).mp ((congr_arg _ hm).mp (dvd_of_mem_cycle_type hk))
   exact dvd_pow_self _ fun h => (one_lt_of_mem_cycle_type hk).Ne <| by rw [h, pow_zero]
 #align equiv.perm.card_compl_support_modeq Equiv.Perm.card_compl_support_modEq
+-/
 
+#print Equiv.Perm.exists_fixed_point_of_prime /-
 theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by
   classical
@@ -415,7 +450,9 @@ theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p 
             (finset.card_eq_zero.mpr (compl_eq_bot.mpr (finset.eq_univ_iff_forall.mpr hα)))).mp
         (card_compl_support_modeq hσ).symm)
 #align equiv.perm.exists_fixed_point_of_prime Equiv.Perm.exists_fixed_point_of_prime
+-/
 
+#print Equiv.Perm.exists_fixed_point_of_prime' /-
 theorem exists_fixed_point_of_prime' {p n : ℕ} [hp : Fact p.Prime] (hα : p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) {a : α} (ha : σ a = a) : ∃ b : α, σ b = b ∧ b ≠ a := by
   classical
@@ -430,6 +467,7 @@ theorem exists_fixed_point_of_prime' {p n : ℕ} [hp : Fact p.Prime] (hα : p 
       a
   exact ⟨b, (h b).mp hb1, hb2⟩
 #align equiv.perm.exists_fixed_point_of_prime' Equiv.Perm.exists_fixed_point_of_prime'
+-/
 
 #print Equiv.Perm.isCycle_of_prime_order' /-
 theorem isCycle_of_prime_order' {σ : Perm α} (h1 : (orderOf σ).Prime)
@@ -462,9 +500,11 @@ def vectorsProdEqOne : Set (Vector G n) :=
 
 namespace VectorsProdEqOne
 
+#print Equiv.Perm.VectorsProdEqOne.mem_iff /-
 theorem mem_iff {n : ℕ} (v : Vector G n) : v ∈ vectorsProdEqOne G n ↔ v.toList.Prod = 1 :=
   Iff.rfl
 #align equiv.perm.vectors_prod_eq_one.mem_iff Equiv.Perm.VectorsProdEqOne.mem_iff
+-/
 
 #print Equiv.Perm.VectorsProdEqOne.zero_eq /-
 theorem zero_eq : vectorsProdEqOne G 0 = {Vector.nil} :=
@@ -472,12 +512,14 @@ theorem zero_eq : vectorsProdEqOne G 0 = {Vector.nil} :=
 #align equiv.perm.vectors_prod_eq_one.zero_eq Equiv.Perm.VectorsProdEqOne.zero_eq
 -/
 
+#print Equiv.Perm.VectorsProdEqOne.one_eq /-
 theorem one_eq : vectorsProdEqOne G 1 = {Vector.nil.cons 1} :=
   by
   simp_rw [Set.eq_singleton_iff_unique_mem, mem_iff, Vector.toList_singleton, List.prod_singleton,
     Vector.head_cons]
   exact ⟨rfl, fun v hv => v.cons_head_tail.symm.trans (congr_arg₂ Vector.cons hv v.tail.eq_nil)⟩
 #align equiv.perm.vectors_prod_eq_one.one_eq Equiv.Perm.VectorsProdEqOne.one_eq
+-/
 
 #print Equiv.Perm.VectorsProdEqOne.zeroUnique /-
 instance zeroUnique : Unique (vectorsProdEqOne G 0) := by rw [zero_eq];
@@ -611,6 +653,7 @@ attribute [to_additive exists_prime_addOrderOf_dvd_card] exists_prime_orderOf_dv
 
 end Cauchy
 
+#print Equiv.Perm.subgroup_eq_top_of_swap_mem /-
 theorem subgroup_eq_top_of_swap_mem [DecidableEq α] {H : Subgroup (Perm α)}
     [d : DecidablePred (· ∈ H)] {τ : Perm α} (h0 : (Fintype.card α).Prime)
     (h1 : Fintype.card α ∣ Fintype.card H) (h2 : τ ∈ H) (h3 : IsSwap τ) : H = ⊤ :=
@@ -625,6 +668,7 @@ theorem subgroup_eq_top_of_swap_mem [DecidableEq α] {H : Subgroup (Perm α)}
   rw [eq_top_iff, ← hσ4, Subgroup.closure_le, Set.insert_subset, Set.singleton_subset_iff]
   exact ⟨Subtype.mem σ, h2⟩
 #align equiv.perm.subgroup_eq_top_of_swap_mem Equiv.Perm.subgroup_eq_top_of_swap_mem
+-/
 
 section Partition
 
@@ -652,6 +696,7 @@ theorem parts_partition {σ : Perm α} :
 #align equiv.perm.parts_partition Equiv.Perm.parts_partition
 -/
 
+#print Equiv.Perm.filter_parts_partition_eq_cycleType /-
 theorem filter_parts_partition_eq_cycleType {σ : Perm α} :
     ((partition σ).parts.filterₓ fun n => 2 ≤ n) = σ.cycleType :=
   by
@@ -660,6 +705,7 @@ theorem filter_parts_partition_eq_cycleType {σ : Perm α} :
   rw [Multiset.eq_of_mem_replicate h]
   decide
 #align equiv.perm.filter_parts_partition_eq_cycle_type Equiv.Perm.filter_parts_partition_eq_cycleType
+-/
 
 #print Equiv.Perm.partition_eq_of_isConj /-
 theorem partition_eq_of_isConj {σ τ : Perm α} : IsConj σ τ ↔ σ.partitionₓ = τ.partitionₓ :=
@@ -728,20 +774,26 @@ theorem isCycle (h : IsThreeCycle σ) : IsCycle σ := by
 #align equiv.perm.is_three_cycle.is_cycle Equiv.Perm.IsThreeCycle.isCycle
 -/
 
+#print Equiv.Perm.IsThreeCycle.sign /-
 theorem sign (h : IsThreeCycle σ) : sign σ = 1 :=
   by
   rw [Equiv.Perm.sign_of_cycleType, h.cycle_type]
   rfl
 #align equiv.perm.is_three_cycle.sign Equiv.Perm.IsThreeCycle.sign
+-/
 
+#print Equiv.Perm.IsThreeCycle.inv /-
 theorem inv {f : Perm α} (h : IsThreeCycle f) : IsThreeCycle f⁻¹ := by
   rwa [is_three_cycle, cycle_type_inv]
 #align equiv.perm.is_three_cycle.inv Equiv.Perm.IsThreeCycle.inv
+-/
 
+#print Equiv.Perm.IsThreeCycle.inv_iff /-
 @[simp]
 theorem inv_iff {f : Perm α} : IsThreeCycle f⁻¹ ↔ IsThreeCycle f :=
   ⟨by rw [← inv_inv f]; apply inv, inv⟩
 #align equiv.perm.is_three_cycle.inv_iff Equiv.Perm.IsThreeCycle.inv_iff
+-/
 
 #print Equiv.Perm.IsThreeCycle.orderOf /-
 theorem orderOf {g : Perm α} (ht : IsThreeCycle g) : orderOf g = 3 := by
@@ -749,12 +801,14 @@ theorem orderOf {g : Perm α} (ht : IsThreeCycle g) : orderOf g = 3 := by
 #align equiv.perm.is_three_cycle.order_of Equiv.Perm.IsThreeCycle.orderOf
 -/
 
+#print Equiv.Perm.IsThreeCycle.isThreeCycle_sq /-
 theorem isThreeCycle_sq {g : Perm α} (ht : IsThreeCycle g) : IsThreeCycle (g * g) :=
   by
   rw [← pow_two, ← card_support_eq_three_iff, support_pow_coprime, ht.card_support]
   rw [ht.order_of, Nat.coprime_iff_gcd_eq_one]
   norm_num
 #align equiv.perm.is_three_cycle.is_three_cycle_sq Equiv.Perm.IsThreeCycle.isThreeCycle_sq
+-/
 
 end IsThreeCycle
 
@@ -762,6 +816,7 @@ section
 
 variable [DecidableEq α]
 
+#print Equiv.Perm.isThreeCycle_swap_mul_swap_same /-
 theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠ c) (bc : b ≠ c) :
     IsThreeCycle (swap a b * swap a c) :=
   by
@@ -781,9 +836,11 @@ theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠
     · rw [swap_apply_right, swap_apply_left]
       exact bc
 #align equiv.perm.is_three_cycle_swap_mul_swap_same Equiv.Perm.isThreeCycle_swap_mul_swap_same
+-/
 
 open Subgroup
 
+#print Equiv.Perm.swap_mul_swap_same_mem_closure_three_cycles /-
 theorem swap_mul_swap_same_mem_closure_three_cycles {a b c : α} (ab : a ≠ b) (ac : a ≠ c) :
     swap a b * swap a c ∈ closure {σ : Perm α | IsThreeCycle σ} :=
   by
@@ -792,7 +849,9 @@ theorem swap_mul_swap_same_mem_closure_three_cycles {a b c : α} (ab : a ≠ b)
     simp [one_mem]
   exact subset_closure (is_three_cycle_swap_mul_swap_same ab ac bc)
 #align equiv.perm.swap_mul_swap_same_mem_closure_three_cycles Equiv.Perm.swap_mul_swap_same_mem_closure_three_cycles
+-/
 
+#print Equiv.Perm.IsSwap.mul_mem_closure_three_cycles /-
 theorem IsSwap.mul_mem_closure_three_cycles {σ τ : Perm α} (hσ : IsSwap σ) (hτ : IsSwap τ) :
     σ * τ ∈ closure {σ : Perm α | IsThreeCycle σ} :=
   by
@@ -808,6 +867,7 @@ theorem IsSwap.mul_mem_closure_three_cycles {σ τ : Perm α} (hσ : IsSwap σ)
     mul_mem (swap_mul_swap_same_mem_closure_three_cycles ab ac)
       (swap_mul_swap_same_mem_closure_three_cycles (Ne.symm ac) cd)
 #align equiv.perm.is_swap.mul_mem_closure_three_cycles Equiv.Perm.IsSwap.mul_mem_closure_three_cycles
+-/
 
 end
 

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

@@ -573,7 +573,6 @@ theorem exists_prime_orderOf_dvd_card {G : Type _} [Group G] [Fintype G] (p : 
     calc
       p ∣ Fintype.card G ^ (p - 1) := hdvd.trans (dvd_pow (dvd_refl _) hp')
       _ = Fintype.card (vectors_prod_eq_one G p) := (vectors_prod_eq_one.card G p).symm
-      
   let f : ℕ → vectors_prod_eq_one G p → vectors_prod_eq_one G p := fun k v =>
     vectors_prod_eq_one.rotate v k
   have hf1 : ∀ v, f 0 v = v := vectors_prod_eq_one.rotate_zero

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

@@ -407,28 +407,28 @@ theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime
 theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by
   classical
-    contrapose! hα
-    simp_rw [← mem_support] at hα 
-    exact
-      nat.modeq_zero_iff_dvd.mp
-        ((congr_arg _
-              (finset.card_eq_zero.mpr (compl_eq_bot.mpr (finset.eq_univ_iff_forall.mpr hα)))).mp
-          (card_compl_support_modeq hσ).symm)
+  contrapose! hα
+  simp_rw [← mem_support] at hα 
+  exact
+    nat.modeq_zero_iff_dvd.mp
+      ((congr_arg _
+            (finset.card_eq_zero.mpr (compl_eq_bot.mpr (finset.eq_univ_iff_forall.mpr hα)))).mp
+        (card_compl_support_modeq hσ).symm)
 #align equiv.perm.exists_fixed_point_of_prime Equiv.Perm.exists_fixed_point_of_prime
 
 theorem exists_fixed_point_of_prime' {p n : ℕ} [hp : Fact p.Prime] (hα : p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) {a : α} (ha : σ a = a) : ∃ b : α, σ b = b ∧ b ≠ a := by
   classical
-    have h : ∀ b : α, b ∈ σ.supportᶜ ↔ σ b = b := fun b => by
-      rw [Finset.mem_compl, mem_support, Classical.not_not]
-    obtain ⟨b, hb1, hb2⟩ :=
-      Finset.exists_ne_of_one_lt_card
-        (lt_of_lt_of_le hp.out.one_lt
-          (Nat.le_of_dvd (finset.card_pos.mpr ⟨a, (h a).mpr ha⟩)
-            (nat.modeq_zero_iff_dvd.mp
-              ((card_compl_support_modeq hσ).trans (nat.modeq_zero_iff_dvd.mpr hα)))))
-        a
-    exact ⟨b, (h b).mp hb1, hb2⟩
+  have h : ∀ b : α, b ∈ σ.supportᶜ ↔ σ b = b := fun b => by
+    rw [Finset.mem_compl, mem_support, Classical.not_not]
+  obtain ⟨b, hb1, hb2⟩ :=
+    Finset.exists_ne_of_one_lt_card
+      (lt_of_lt_of_le hp.out.one_lt
+        (Nat.le_of_dvd (finset.card_pos.mpr ⟨a, (h a).mpr ha⟩)
+          (nat.modeq_zero_iff_dvd.mp
+            ((card_compl_support_modeq hσ).trans (nat.modeq_zero_iff_dvd.mpr hα)))))
+      a
+  exact ⟨b, (h b).mp hb1, hb2⟩
 #align equiv.perm.exists_fixed_point_of_prime' Equiv.Perm.exists_fixed_point_of_prime'
 
 #print Equiv.Perm.isCycle_of_prime_order' /-
@@ -444,8 +444,8 @@ theorem isCycle_of_prime_order'' {σ : Perm α} (h1 : (Fintype.card α).Prime)
   isCycle_of_prime_order' ((congr_arg Nat.Prime h2).mpr h1)
     (by
       classical
-        rw [← one_mul (Fintype.card α), ← h2, mul_lt_mul_right (orderOf_pos σ)]
-        exact one_lt_two)
+      rw [← one_mul (Fintype.card α), ← h2, mul_lt_mul_right (orderOf_pos σ)]
+      exact one_lt_two)
 #align equiv.perm.is_cycle_of_prime_order'' Equiv.Perm.isCycle_of_prime_order''
 -/
 
@@ -456,7 +456,7 @@ variable (G : Type _) [Group G] (n : ℕ)
 #print Equiv.Perm.vectorsProdEqOne /-
 /-- The type of vectors with terms from `G`, length `n`, and product equal to `1:G`. -/
 def vectorsProdEqOne : Set (Vector G n) :=
-  { v | v.toList.Prod = 1 }
+  {v | v.toList.Prod = 1}
 #align equiv.perm.vectors_prod_eq_one Equiv.Perm.vectorsProdEqOne
 -/
 
@@ -786,7 +786,7 @@ theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠
 open Subgroup
 
 theorem swap_mul_swap_same_mem_closure_three_cycles {a b c : α} (ab : a ≠ b) (ac : a ≠ c) :
-    swap a b * swap a c ∈ closure { σ : Perm α | IsThreeCycle σ } :=
+    swap a b * swap a c ∈ closure {σ : Perm α | IsThreeCycle σ} :=
   by
   by_cases bc : b = c
   · subst bc
@@ -795,7 +795,7 @@ theorem swap_mul_swap_same_mem_closure_three_cycles {a b c : α} (ab : a ≠ b)
 #align equiv.perm.swap_mul_swap_same_mem_closure_three_cycles Equiv.Perm.swap_mul_swap_same_mem_closure_three_cycles
 
 theorem IsSwap.mul_mem_closure_three_cycles {σ τ : Perm α} (hσ : IsSwap σ) (hτ : IsSwap τ) :
-    σ * τ ∈ closure { σ : Perm α | IsThreeCycle σ } :=
+    σ * τ ∈ closure {σ : Perm α | IsThreeCycle σ} :=
   by
   obtain ⟨a, b, ab, rfl⟩ := hσ
   obtain ⟨c, d, cd, rfl⟩ := hτ

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

@@ -104,7 +104,7 @@ theorem card_cycleType_eq_zero {σ : Perm α} : σ.cycleType.card = 0 ↔ σ = 1
 theorem two_le_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType) : 2 ≤ n :=
   by
   simp only [cycle_type_def, ← Finset.mem_def, Function.comp_apply, Multiset.mem_map,
-    mem_cycle_factors_finset_iff] at h
+    mem_cycle_factors_finset_iff] at h 
   obtain ⟨_, ⟨hc, -⟩, rfl⟩ := h
   exact hc.two_le_card_support
 #align equiv.perm.two_le_of_mem_cycle_type Equiv.Perm.two_le_of_mem_cycleType
@@ -219,7 +219,7 @@ theorem dvd_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType) :
 theorem orderOf_cycleOf_dvd_orderOf (f : Perm α) (x : α) : orderOf (cycleOf f x) ∣ orderOf f :=
   by
   by_cases hx : f x = x
-  · rw [← cycle_of_eq_one_iff] at hx
+  · rw [← cycle_of_eq_one_iff] at hx 
     simp [hx]
   · refine' dvd_of_mem_cycle_type _
     rw [cycle_type, Multiset.mem_map]
@@ -249,7 +249,7 @@ theorem cycleType_prime_order {σ : Perm α} (hσ : (orderOf σ).Prime) :
   rw [tsub_add_cancel_of_le]
   rw [Nat.succ_le_iff, pos_iff_ne_zero, Ne, card_cycle_type_eq_zero]
   intro H
-  rw [H, orderOf_one] at hσ
+  rw [H, orderOf_one] at hσ 
   exact hσ.ne_one rfl
 #align equiv.perm.cycle_type_prime_order Equiv.Perm.cycleType_prime_order
 -/
@@ -260,7 +260,7 @@ theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
   by
   obtain ⟨n, hn⟩ := cycle_type_prime_order h1
   rw [← σ.sum_cycle_type, hn, Multiset.sum_replicate, nsmul_eq_mul, Nat.cast_id,
-    mul_lt_mul_right (orderOf_pos σ), Nat.succ_lt_succ_iff, Nat.lt_succ_iff, le_zero_iff] at h2
+    mul_lt_mul_right (orderOf_pos σ), Nat.succ_lt_succ_iff, Nat.lt_succ_iff, le_zero_iff] at h2 
   rw [← card_cycle_type_eq_one, hn, card_replicate, h2]
 #align equiv.perm.is_cycle_of_prime_order Equiv.Perm.isCycle_of_prime_order
 -/
@@ -268,7 +268,7 @@ theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
 theorem cycleType_le_of_mem_cycleFactorsFinset {f g : Perm α} (hf : f ∈ g.cycleFactorsFinset) :
     f.cycleType ≤ g.cycleType :=
   by
-  rw [mem_cycle_factors_finset_iff] at hf
+  rw [mem_cycle_factors_finset_iff] at hf 
   rw [cycle_type_def, cycle_type_def, hf.left.cycle_factors_finset_eq_singleton]
   refine' map_le_map _
   simpa [← Finset.mem_def, mem_cycle_factors_finset_iff] using hf
@@ -279,7 +279,7 @@ theorem cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub {f g : Perm α}
   by
   suffices (g * f⁻¹).cycleType + f.cycle_type = g.cycle_type - f.cycle_type + f.cycle_type
     by
-    rw [tsub_add_cancel_of_le (cycle_type_le_of_mem_cycle_factors_finset hf)] at this
+    rw [tsub_add_cancel_of_le (cycle_type_le_of_mem_cycle_factors_finset hf)] at this 
     simp [← this]
   simp [← (disjoint_mul_inv_of_mem_cycle_factors_finset hf).cycleType,
     tsub_add_cancel_of_le (cycle_type_le_of_mem_cycle_factors_finset hf)]
@@ -291,17 +291,17 @@ theorem isConj_of_cycleType_eq {σ τ : Perm α} (h : cycleType σ = cycleType 
   revert τ
   apply cycle_induction_on _ σ
   · intro τ h
-    rw [cycle_type_one, eq_comm, cycle_type_eq_zero] at h
+    rw [cycle_type_one, eq_comm, cycle_type_eq_zero] at h 
     rw [h]
   · intro σ hσ τ hστ
     have hτ := card_cycle_type_eq_one.2 hσ
-    rw [hστ, card_cycle_type_eq_one] at hτ
+    rw [hστ, card_cycle_type_eq_one] at hτ 
     apply hσ.is_conj hτ
-    rw [hσ.cycle_type, hτ.cycle_type, coe_eq_coe, singleton_perm] at hστ
-    simp only [and_true_iff, eq_self_iff_true] at hστ
+    rw [hσ.cycle_type, hτ.cycle_type, coe_eq_coe, singleton_perm] at hστ 
+    simp only [and_true_iff, eq_self_iff_true] at hστ 
     exact hστ
   · intro σ τ hστ hσ h1 h2 π hπ
-    rw [hστ.cycle_type] at hπ
+    rw [hστ.cycle_type] at hπ 
     · have h : σ.support.card ∈ map (Finset.card ∘ perm.support) π.cycle_factors_finset.val := by
         simp [← cycle_type_def, ← hπ, hσ.cycle_type]
       obtain ⟨σ', hσ'l, hσ'⟩ := multiset.mem_map.mp h
@@ -313,7 +313,7 @@ theorem isConj_of_cycleType_eq {σ τ : Perm α} (h : cycleType σ = cycleType 
       refine' IsConj.trans _ key
       have hs : σ.cycle_type = σ'.cycle_type :=
         by
-        rw [← Finset.mem_def, mem_cycle_factors_finset_iff] at hσ'l
+        rw [← Finset.mem_def, mem_cycle_factors_finset_iff] at hσ'l 
         rw [hσ.cycle_type, ← hσ', hσ'l.left.cycle_type]
       refine' hστ.is_conj_mul (h1 hs) (h2 _) _
       · rw [cycle_type_mul_mem_cycle_factors_finset_eq_sub, ← hπ, add_comm, hs,
@@ -357,9 +357,9 @@ theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
   constructor
   · intro h
     obtain ⟨l, rfl, hlc, hld⟩ := trunc_cycle_factors σ
-    rw [cycle_type_eq _ rfl hlc hld] at h
+    rw [cycle_type_eq _ rfl hlc hld] at h 
     obtain ⟨c, cl, rfl⟩ := List.exists_of_mem_map h
-    rw [(List.perm_cons_erase cl).pairwise_iff fun _ _ hd => _] at hld
+    rw [(List.perm_cons_erase cl).pairwise_iff fun _ _ hd => _] at hld 
     swap; · exact hd.symm
     refine' ⟨c, (l.erase c).Prod, _, _, hlc _ cl, rfl⟩
     ·
@@ -408,7 +408,7 @@ theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p 
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by
   classical
     contrapose! hα
-    simp_rw [← mem_support] at hα
+    simp_rw [← mem_support] at hα 
     exact
       nat.modeq_zero_iff_dvd.mp
         ((congr_arg _
@@ -709,16 +709,16 @@ theorem card_support_eq_three_iff : σ.support.card = 3 ↔ σ.IsThreeCycle :=
   by
   refine' ⟨fun h => _, is_three_cycle.card_support⟩
   by_cases h0 : σ.cycle_type = 0
-  · rw [← sum_cycle_type, h0, sum_zero] at h
+  · rw [← sum_cycle_type, h0, sum_zero] at h 
     exact (ne_of_lt zero_lt_three h).elim
   obtain ⟨n, hn⟩ := exists_mem_of_ne_zero h0
   by_cases h1 : σ.cycle_type.erase n = 0
-  · rw [← sum_cycle_type, ← cons_erase hn, h1, cons_zero, Multiset.sum_singleton] at h
+  · rw [← sum_cycle_type, ← cons_erase hn, h1, cons_zero, Multiset.sum_singleton] at h 
     rw [is_three_cycle, ← cons_erase hn, h1, h, ← cons_zero]
   obtain ⟨m, hm⟩ := exists_mem_of_ne_zero h1
-  rw [← sum_cycle_type, ← cons_erase hn, ← cons_erase hm, Multiset.sum_cons, Multiset.sum_cons] at h
+  rw [← sum_cycle_type, ← cons_erase hn, ← cons_erase hm, Multiset.sum_cons, Multiset.sum_cons] at h 
   -- TODO: linarith [...] should solve this directly
-  have : ∀ {k}, 2 ≤ m → 2 ≤ n → n + (m + k) = 3 → False := by intros ; linarith
+  have : ∀ {k}, 2 ≤ m → 2 ≤ n → n + (m + k) = 3 → False := by intros; linarith
   cases this (two_le_of_mem_cycle_type (mem_of_mem_erase hm)) (two_le_of_mem_cycle_type hn) h
 #align card_support_eq_three_iff card_support_eq_three_iff
 -/
@@ -771,7 +771,7 @@ theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠
     simp [ab, ac, bc]
   apply le_antisymm ((support_mul_le _ _).trans fun x => _) fun x hx => _
   · simp [ab, ac, bc]
-  · simp only [Finset.mem_insert, Finset.mem_singleton] at hx
+  · simp only [Finset.mem_insert, Finset.mem_singleton] at hx 
     rw [mem_support]
     simp only [perm.coe_mul, Function.comp_apply, Ne.def]
     obtain rfl | rfl | rfl := hx

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

@@ -76,12 +76,6 @@ theorem cycleType_eq' {σ : Perm α} (s : Finset (Perm α)) (h1 : ∀ f : Perm 
 #align equiv.perm.cycle_type_eq' Equiv.Perm.cycleType_eq'
 -/
 
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 theorem cycleType_eq {σ : Perm α} (l : List (Perm α)) (h0 : l.Prod = σ)
     (h1 : ∀ σ : Perm α, σ ∈ l → σ.IsCycle) (h2 : l.Pairwise Disjoint) :
     σ.cycleType = l.map (Finset.card ∘ support) :=
@@ -94,32 +88,14 @@ theorem cycleType_eq {σ : Perm α} (l : List (Perm α)) (h0 : l.Prod = σ)
   · simpa [list.dedup_eq_self.mpr hl] using h2.forall disjoint.symmetric
 #align equiv.perm.cycle_type_eq Equiv.Perm.cycleType_eq
 
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 theorem cycleType_one : (1 : Perm α).cycleType = 0 :=
   cycleType_eq [] rfl (fun _ => False.elim) Pairwise.nil
 #align equiv.perm.cycle_type_one Equiv.Perm.cycleType_one
 
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 theorem cycleType_eq_zero {σ : Perm α} : σ.cycleType = 0 ↔ σ = 1 := by
   simp [cycle_type_def, cycle_factors_finset_eq_empty_iff]
 #align equiv.perm.cycle_type_eq_zero Equiv.Perm.cycleType_eq_zero
 
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 theorem card_cycleType_eq_zero {σ : Perm α} : σ.cycleType.card = 0 ↔ σ = 1 := by
   rw [card_eq_zero, cycle_type_eq_zero]
 #align equiv.perm.card_cycle_type_eq_zero Equiv.Perm.card_cycleType_eq_zero
@@ -147,12 +123,6 @@ theorem IsCycle.cycleType {σ : Perm α} (hσ : IsCycle σ) : σ.cycleType = [σ
 #align equiv.perm.is_cycle.cycle_type Equiv.Perm.IsCycle.cycleType
 -/
 
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 theorem card_cycleType_eq_one {σ : Perm α} : σ.cycleType.card = 1 ↔ σ.IsCycle :=
   by
   rw [card_eq_one]
@@ -166,12 +136,6 @@ theorem card_cycleType_eq_one {σ : Perm α} : σ.cycleType.card = 1 ↔ σ.IsCy
     simp [h]
 #align equiv.perm.card_cycle_type_eq_one Equiv.Perm.card_cycleType_eq_one
 
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 theorem Disjoint.cycleType {σ τ : Perm α} (h : Disjoint σ τ) :
     (σ * τ).cycleType = σ.cycleType + τ.cycleType :=
   by
@@ -180,12 +144,6 @@ theorem Disjoint.cycleType {σ τ : Perm α} (h : Disjoint σ τ) :
   exact Finset.disjoint_val.2 h.disjoint_cycle_factors_finset
 #align equiv.perm.disjoint.cycle_type Equiv.Perm.Disjoint.cycleType
 
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 theorem cycleType_inv (σ : Perm α) : σ⁻¹.cycleType = σ.cycleType :=
   cycle_induction_on (fun τ : Perm α => τ⁻¹.cycleType = τ.cycleType) σ rfl
     (fun σ hσ => by rw [hσ.cycle_type, hσ.inv.cycle_type, support_inv]) fun σ τ hστ hc hσ hτ => by
@@ -195,12 +153,6 @@ theorem cycleType_inv (σ : Perm α) : σ⁻¹.cycleType = σ.cycleType :=
           (fun h : σ x = x => inv_eq_iff_eq.mpr h.symm) (hστ x).symm]
 #align equiv.perm.cycle_type_inv Equiv.Perm.cycleType_inv
 
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 theorem cycleType_conj {σ τ : Perm α} : (τ * σ * τ⁻¹).cycleType = σ.cycleType :=
   by
   revert τ
@@ -224,12 +176,6 @@ theorem sum_cycleType (σ : Perm α) : σ.cycleType.Sum = σ.support.card :=
 #align equiv.perm.sum_cycle_type Equiv.Perm.sum_cycleType
 -/
 
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 theorem sign_of_cycleType' (σ : Perm α) : sign σ = (σ.cycleType.map fun n => -(-1 : ℤˣ) ^ n).Prod :=
   cycle_induction_on (fun τ : Perm α => sign τ = (τ.cycleType.map fun n => -(-1 : ℤˣ) ^ n).Prod) σ
     (by rw [sign_one, cycle_type_one, Multiset.map_zero, prod_zero])
@@ -238,9 +184,6 @@ theorem sign_of_cycleType' (σ : Perm α) : sign σ = (σ.cycleType.map fun n =>
     fun σ τ hστ hc hσ hτ => by rw [sign_mul, hσ, hτ, hστ.cycle_type, Multiset.map_add, prod_add]
 #align equiv.perm.sign_of_cycle_type' Equiv.Perm.sign_of_cycleType'
 
-/- warning: equiv.perm.sign_of_cycle_type -> Equiv.Perm.sign_of_cycleType is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align equiv.perm.sign_of_cycle_type Equiv.Perm.sign_of_cycleTypeₓ'. -/
 theorem sign_of_cycleType (f : Perm α) :
     sign f = (-1 : ℤˣ) ^ (f.cycleType.Sum + f.cycleType.card) :=
   cycle_induction_on (fun f : Perm α => sign f = (-1 : ℤˣ) ^ (f.cycleType.Sum + f.cycleType.card)) f
@@ -257,12 +200,6 @@ theorem sign_of_cycleType (f : Perm α) :
       add_comm g.cycle_type.sum _, add_assoc, pow_add, ← Pf, ← Pg, Equiv.Perm.sign_mul]
 #align equiv.perm.sign_of_cycle_type Equiv.Perm.sign_of_cycleType
 
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 theorem lcm_cycleType (σ : Perm α) : σ.cycleType.lcm = orderOf σ :=
   cycle_induction_on (fun τ : Perm α => τ.cycleType.lcm = orderOf τ) σ
     (by rw [cycle_type_one, lcm_zero, orderOf_one])
@@ -292,12 +229,6 @@ theorem orderOf_cycleOf_dvd_orderOf (f : Perm α) (x : α) : orderOf (cycleOf f
 #align equiv.perm.order_of_cycle_of_dvd_order_of Equiv.Perm.orderOf_cycleOf_dvd_orderOf
 -/
 
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 theorem two_dvd_card_support {σ : Perm α} (hσ : σ ^ 2 = 1) : 2 ∣ σ.support.card :=
   (congr_arg (Dvd.Dvd 2) σ.sum_cycleType).mp
     (Multiset.dvd_sum fun n hn => by
@@ -334,12 +265,6 @@ theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
 #align equiv.perm.is_cycle_of_prime_order Equiv.Perm.isCycle_of_prime_order
 -/
 
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 theorem cycleType_le_of_mem_cycleFactorsFinset {f g : Perm α} (hf : f ∈ g.cycleFactorsFinset) :
     f.cycleType ≤ g.cycleType :=
   by
@@ -349,12 +274,6 @@ theorem cycleType_le_of_mem_cycleFactorsFinset {f g : Perm α} (hf : f ∈ g.cyc
   simpa [← Finset.mem_def, mem_cycle_factors_finset_iff] using hf
 #align equiv.perm.cycle_type_le_of_mem_cycle_factors_finset Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinset
 
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 theorem cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub {f g : Perm α}
     (hf : f ∈ g.cycleFactorsFinset) : (g * f⁻¹).cycleType = g.cycleType - f.cycleType :=
   by
@@ -427,23 +346,11 @@ theorem cycleType_extendDomain {β : Type _} [Fintype β] [DecidableEq β] {p :
 #align equiv.perm.cycle_type_extend_domain Equiv.Perm.cycleType_extendDomain
 -/
 
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 theorem cycleType_ofSubtype {p : α → Prop} [DecidablePred p] {g : Perm (Subtype p)} :
     cycleType g.ofSubtype = cycleType g :=
   cycleType_extendDomain (Equiv.refl (Subtype p))
 #align equiv.perm.cycle_type_of_subtype Equiv.Perm.cycleType_ofSubtype
 
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 theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
     n ∈ cycleType σ ↔ ∃ c τ : Perm α, σ = c * τ ∧ Disjoint c τ ∧ IsCycle c ∧ c.support.card = n :=
   by
@@ -486,12 +393,6 @@ theorem cycleType_of_card_le_mem_cycleType_add_two {n : ℕ} {g : Perm α}
 
 end CycleType
 
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 theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime] {σ : Perm α}
     (hσ : σ ^ p ^ n = 1) : σ.supportᶜ.card ≡ Fintype.card α [MOD p] :=
   by
@@ -503,12 +404,6 @@ theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime
   exact dvd_pow_self _ fun h => (one_lt_of_mem_cycle_type hk).Ne <| by rw [h, pow_zero]
 #align equiv.perm.card_compl_support_modeq Equiv.Perm.card_compl_support_modEq
 
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 theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by
   classical
@@ -521,12 +416,6 @@ theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p 
           (card_compl_support_modeq hσ).symm)
 #align equiv.perm.exists_fixed_point_of_prime Equiv.Perm.exists_fixed_point_of_prime
 
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 theorem exists_fixed_point_of_prime' {p n : ℕ} [hp : Fact p.Prime] (hα : p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) {a : α} (ha : σ a = a) : ∃ b : α, σ b = b ∧ b ≠ a := by
   classical
@@ -573,12 +462,6 @@ def vectorsProdEqOne : Set (Vector G n) :=
 
 namespace VectorsProdEqOne
 
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 theorem mem_iff {n : ℕ} (v : Vector G n) : v ∈ vectorsProdEqOne G n ↔ v.toList.Prod = 1 :=
   Iff.rfl
 #align equiv.perm.vectors_prod_eq_one.mem_iff Equiv.Perm.VectorsProdEqOne.mem_iff
@@ -589,12 +472,6 @@ theorem zero_eq : vectorsProdEqOne G 0 = {Vector.nil} :=
 #align equiv.perm.vectors_prod_eq_one.zero_eq Equiv.Perm.VectorsProdEqOne.zero_eq
 -/
 
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 theorem one_eq : vectorsProdEqOne G 1 = {Vector.nil.cons 1} :=
   by
   simp_rw [Set.eq_singleton_iff_unique_mem, mem_iff, Vector.toList_singleton, List.prod_singleton,
@@ -735,12 +612,6 @@ attribute [to_additive exists_prime_addOrderOf_dvd_card] exists_prime_orderOf_dv
 
 end Cauchy
 
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 theorem subgroup_eq_top_of_swap_mem [DecidableEq α] {H : Subgroup (Perm α)}
     [d : DecidablePred (· ∈ H)] {τ : Perm α} (h0 : (Fintype.card α).Prime)
     (h1 : Fintype.card α ∣ Fintype.card H) (h2 : τ ∈ H) (h3 : IsSwap τ) : H = ⊤ :=
@@ -782,12 +653,6 @@ theorem parts_partition {σ : Perm α} :
 #align equiv.perm.parts_partition Equiv.Perm.parts_partition
 -/
 
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 theorem filter_parts_partition_eq_cycleType {σ : Perm α} :
     ((partition σ).parts.filterₓ fun n => 2 ≤ n) = σ.cycleType :=
   by
@@ -864,34 +729,16 @@ theorem isCycle (h : IsThreeCycle σ) : IsCycle σ := by
 #align equiv.perm.is_three_cycle.is_cycle Equiv.Perm.IsThreeCycle.isCycle
 -/
 
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 theorem sign (h : IsThreeCycle σ) : sign σ = 1 :=
   by
   rw [Equiv.Perm.sign_of_cycleType, h.cycle_type]
   rfl
 #align equiv.perm.is_three_cycle.sign Equiv.Perm.IsThreeCycle.sign
 
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 theorem inv {f : Perm α} (h : IsThreeCycle f) : IsThreeCycle f⁻¹ := by
   rwa [is_three_cycle, cycle_type_inv]
 #align equiv.perm.is_three_cycle.inv Equiv.Perm.IsThreeCycle.inv
 
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 @[simp]
 theorem inv_iff {f : Perm α} : IsThreeCycle f⁻¹ ↔ IsThreeCycle f :=
   ⟨by rw [← inv_inv f]; apply inv, inv⟩
@@ -903,12 +750,6 @@ theorem orderOf {g : Perm α} (ht : IsThreeCycle g) : orderOf g = 3 := by
 #align equiv.perm.is_three_cycle.order_of Equiv.Perm.IsThreeCycle.orderOf
 -/
 
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 theorem isThreeCycle_sq {g : Perm α} (ht : IsThreeCycle g) : IsThreeCycle (g * g) :=
   by
   rw [← pow_two, ← card_support_eq_three_iff, support_pow_coprime, ht.card_support]
@@ -922,12 +763,6 @@ section
 
 variable [DecidableEq α]
 
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-Case conversion may be inaccurate. Consider using '#align equiv.perm.is_three_cycle_swap_mul_swap_same Equiv.Perm.isThreeCycle_swap_mul_swap_sameₓ'. -/
 theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠ c) (bc : b ≠ c) :
     IsThreeCycle (swap a b * swap a c) :=
   by
@@ -950,12 +785,6 @@ theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠
 
 open Subgroup
 
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-Case conversion may be inaccurate. Consider using '#align equiv.perm.swap_mul_swap_same_mem_closure_three_cycles Equiv.Perm.swap_mul_swap_same_mem_closure_three_cyclesₓ'. -/
 theorem swap_mul_swap_same_mem_closure_three_cycles {a b c : α} (ab : a ≠ b) (ac : a ≠ c) :
     swap a b * swap a c ∈ closure { σ : Perm α | IsThreeCycle σ } :=
   by
@@ -965,12 +794,6 @@ theorem swap_mul_swap_same_mem_closure_three_cycles {a b c : α} (ab : a ≠ b)
   exact subset_closure (is_three_cycle_swap_mul_swap_same ab ac bc)
 #align equiv.perm.swap_mul_swap_same_mem_closure_three_cycles Equiv.Perm.swap_mul_swap_same_mem_closure_three_cycles
 
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-Case conversion may be inaccurate. Consider using '#align equiv.perm.is_swap.mul_mem_closure_three_cycles Equiv.Perm.IsSwap.mul_mem_closure_three_cyclesₓ'. -/
 theorem IsSwap.mul_mem_closure_three_cycles {σ τ : Perm α} (hσ : IsSwap σ) (hτ : IsSwap τ) :
     σ * τ ∈ closure { σ : Perm α | IsThreeCycle σ } :=
   by

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

@@ -212,9 +212,7 @@ theorem cycleType_conj {σ τ : Perm α} : (τ * σ * τ⁻¹).cycleType = σ.cy
   · intro σ τ hd hc hσ hτ π
     rw [← conj_mul, hd.cycle_type, disjoint.cycle_type, hσ, hτ]
     intro a
-    apply (hd (π⁻¹ a)).imp _ _ <;>
-      · intro h
-        rw [perm.mul_apply, perm.mul_apply, h, apply_inv_self]
+    apply (hd (π⁻¹ a)).imp _ _ <;> · intro h; rw [perm.mul_apply, perm.mul_apply, h, apply_inv_self]
 #align equiv.perm.cycle_type_conj Equiv.Perm.cycleType_conj
 
 #print Equiv.Perm.sum_cycleType /-
@@ -455,8 +453,7 @@ theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
     rw [cycle_type_eq _ rfl hlc hld] at h
     obtain ⟨c, cl, rfl⟩ := List.exists_of_mem_map h
     rw [(List.perm_cons_erase cl).pairwise_iff fun _ _ hd => _] at hld
-    swap
-    · exact hd.symm
+    swap; · exact hd.symm
     refine' ⟨c, (l.erase c).Prod, _, _, hlc _ cl, rfl⟩
     ·
       rw [← List.prod_cons,
@@ -606,17 +603,13 @@ theorem one_eq : vectorsProdEqOne G 1 = {Vector.nil.cons 1} :=
 #align equiv.perm.vectors_prod_eq_one.one_eq Equiv.Perm.VectorsProdEqOne.one_eq
 
 #print Equiv.Perm.VectorsProdEqOne.zeroUnique /-
-instance zeroUnique : Unique (vectorsProdEqOne G 0) :=
-  by
-  rw [zero_eq]
+instance zeroUnique : Unique (vectorsProdEqOne G 0) := by rw [zero_eq];
   exact Set.uniqueSingleton Vector.nil
 #align equiv.perm.vectors_prod_eq_one.zero_unique Equiv.Perm.VectorsProdEqOne.zeroUnique
 -/
 
 #print Equiv.Perm.VectorsProdEqOne.oneUnique /-
-instance oneUnique : Unique (vectorsProdEqOne G 1) :=
-  by
-  rw [one_eq]
+instance oneUnique : Unique (vectorsProdEqOne G 1) := by rw [one_eq];
   exact Set.uniqueSingleton (vector.nil.cons 1)
 #align equiv.perm.vectors_prod_eq_one.one_unique Equiv.Perm.VectorsProdEqOne.oneUnique
 -/
@@ -649,10 +642,7 @@ by deleting the last entry of `v`. -/
 def equivVector : vectorsProdEqOne G n ≃ Vector G (n - 1) :=
   ((vectorEquiv G (n - 1)).trans
       (if hn : n = 0 then
-        show vectorsProdEqOne G (n - 1 + 1) ≃ vectorsProdEqOne G n
-          by
-          rw [hn]
-          apply equiv_of_unique
+        show vectorsProdEqOne G (n - 1 + 1) ≃ vectorsProdEqOne G n by rw [hn]; apply equiv_of_unique
       else by rw [tsub_add_cancel_of_le (Nat.pos_of_ne_zero hn).nat_succ_le])).symm
 #align equiv.perm.vectors_prod_eq_one.equiv_vector Equiv.Perm.VectorsProdEqOne.equivVector
 -/
@@ -863,10 +853,7 @@ theorem card_support_eq_three_iff : σ.support.card = 3 ↔ σ.IsThreeCycle :=
   obtain ⟨m, hm⟩ := exists_mem_of_ne_zero h1
   rw [← sum_cycle_type, ← cons_erase hn, ← cons_erase hm, Multiset.sum_cons, Multiset.sum_cons] at h
   -- TODO: linarith [...] should solve this directly
-  have : ∀ {k}, 2 ≤ m → 2 ≤ n → n + (m + k) = 3 → False :=
-    by
-    intros
-    linarith
+  have : ∀ {k}, 2 ≤ m → 2 ≤ n → n + (m + k) = 3 → False := by intros ; linarith
   cases this (two_le_of_mem_cycle_type (mem_of_mem_erase hm)) (two_le_of_mem_cycle_type hn) h
 #align card_support_eq_three_iff card_support_eq_three_iff
 -/
@@ -907,9 +894,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align equiv.perm.is_three_cycle.inv_iff Equiv.Perm.IsThreeCycle.inv_iffₓ'. -/
 @[simp]
 theorem inv_iff {f : Perm α} : IsThreeCycle f⁻¹ ↔ IsThreeCycle f :=
-  ⟨by
-    rw [← inv_inv f]
-    apply inv, inv⟩
+  ⟨by rw [← inv_inv f]; apply inv, inv⟩
 #align equiv.perm.is_three_cycle.inv_iff Equiv.Perm.IsThreeCycle.inv_iff
 
 #print Equiv.Perm.IsThreeCycle.orderOf /-

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

@@ -241,10 +241,7 @@ theorem sign_of_cycleType' (σ : Perm α) : sign σ = (σ.cycleType.map fun n =>
 #align equiv.perm.sign_of_cycle_type' Equiv.Perm.sign_of_cycleType'
 
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(Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1) f) (HPow.hPow.{0, 0, 0} (Units.{0} Int Int.instMonoidInt) Nat (Units.{0} Int Int.instMonoidInt) (instHPow.{0, 0} (Units.{0} Int Int.instMonoidInt) Nat (Monoid.Pow.{0} (Units.{0} Int Int.instMonoidInt) (DivInvMonoid.toMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Group.toDivInvMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instGroupUnits.{0} Int Int.instMonoidInt))))) (Neg.neg.{0} (Units.{0} Int Int.instMonoidInt) (Units.instNegUnits.{0} Int Int.instMonoidInt (NonUnitalNonAssocRing.toHasDistribNeg.{0} Int (NonAssocRing.toNonUnitalNonAssocRing.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)))) (OfNat.ofNat.{0} (Units.{0} Int Int.instMonoidInt) 1 (One.toOfNat1.{0} (Units.{0} Int Int.instMonoidInt) (InvOneClass.toOne.{0} (Units.{0} Int Int.instMonoidInt) (DivInvOneMonoid.toInvOneClass.{0} (Units.{0} Int Int.instMonoidInt) (DivisionMonoid.toDivInvOneMonoid.{0} (Units.{0} Int Int.instMonoidInt) (DivisionCommMonoid.toDivisionMonoid.{0} (Units.{0} Int Int.instMonoidInt) (CommGroup.toDivisionCommMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instCommGroupUnitsToMonoid.{0} Int Int.instCommMonoidInt))))))))) (HAdd.hAdd.{0, 0, 0} Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{0} Nat) => Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)) Nat (instHAdd.{0} Nat instAddNat) (Multiset.sum.{0} Nat Nat.addCommMonoid (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{0} Nat) (fun (_x : Multiset.{0} Nat) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{0} Nat) => Nat) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{0} Nat) Nat (AddZeroClass.toAdd.{0} (Multiset.{0} Nat) (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align equiv.perm.sign_of_cycle_type Equiv.Perm.sign_of_cycleTypeₓ'. -/
 theorem sign_of_cycleType (f : Perm α) :
     sign f = (-1 : ℤˣ) ^ (f.cycleType.Sum + f.cycleType.card) :=

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

@@ -230,7 +230,7 @@ theorem sum_cycleType (σ : Perm α) : σ.cycleType.Sum = σ.support.card :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (σ : Equiv.Perm.{succ u1} α), Eq.{1} (Units.{0} Int Int.monoid) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u1} α) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1) σ) (Multiset.prod.{0} (Units.{0} Int Int.monoid) (CommGroup.toCommMonoid.{0} (Units.{0} Int Int.monoid) (Units.instCommGroupUnitsToMonoid.{0} Int Int.commMonoid)) (Multiset.map.{0, 0} Nat (Units.{0} Int Int.monoid) (fun (n : Nat) => Neg.neg.{0} (Units.{0} Int Int.monoid) (Units.hasNeg.{0} Int Int.monoid (NonUnitalNonAssocRing.toHasDistribNeg.{0} Int (NonAssocRing.toNonUnitalNonAssocRing.{0} Int (Ring.toNonAssocRing.{0} Int Int.ring)))) (HPow.hPow.{0, 0, 0} (Units.{0} Int Int.monoid) Nat (Units.{0} Int Int.monoid) (instHPow.{0, 0} (Units.{0} Int Int.monoid) Nat (Monoid.Pow.{0} (Units.{0} Int Int.monoid) (DivInvMonoid.toMonoid.{0} (Units.{0} Int Int.monoid) (Group.toDivInvMonoid.{0} (Units.{0} Int Int.monoid) (Units.group.{0} Int Int.monoid))))) (Neg.neg.{0} (Units.{0} Int Int.monoid) (Units.hasNeg.{0} Int Int.monoid (NonUnitalNonAssocRing.toHasDistribNeg.{0} Int (NonAssocRing.toNonUnitalNonAssocRing.{0} Int (Ring.toNonAssocRing.{0} Int Int.ring)))) (OfNat.ofNat.{0} (Units.{0} Int Int.monoid) 1 (OfNat.mk.{0} (Units.{0} Int Int.monoid) 1 (One.one.{0} (Units.{0} Int Int.monoid) (MulOneClass.toHasOne.{0} (Units.{0} Int Int.monoid) (Units.mulOneClass.{0} Int Int.monoid)))))) n)) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (σ : Equiv.Perm.{succ u1} α), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1) σ) (Multiset.prod.{0} (Units.{0} Int Int.instMonoidInt) (CommGroup.toCommMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instCommGroupUnitsToMonoid.{0} Int Int.instCommMonoidInt)) (Multiset.map.{0, 0} Nat (Units.{0} Int Int.instMonoidInt) (fun (n : Nat) => Neg.neg.{0} (Units.{0} Int Int.instMonoidInt) (Units.instNegUnits.{0} Int Int.instMonoidInt (NonUnitalNonAssocRing.toHasDistribNeg.{0} Int (NonAssocRing.toNonUnitalNonAssocRing.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)))) (HPow.hPow.{0, 0, 0} (Units.{0} Int Int.instMonoidInt) Nat (Units.{0} Int Int.instMonoidInt) (instHPow.{0, 0} (Units.{0} Int Int.instMonoidInt) Nat (Monoid.Pow.{0} (Units.{0} Int Int.instMonoidInt) (DivInvMonoid.toMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Group.toDivInvMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instGroupUnits.{0} Int Int.instMonoidInt))))) (Neg.neg.{0} (Units.{0} Int Int.instMonoidInt) (Units.instNegUnits.{0} Int Int.instMonoidInt (NonUnitalNonAssocRing.toHasDistribNeg.{0} Int (NonAssocRing.toNonUnitalNonAssocRing.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)))) (OfNat.ofNat.{0} (Units.{0} Int Int.instMonoidInt) 1 (One.toOfNat1.{0} (Units.{0} Int Int.instMonoidInt) (InvOneClass.toOne.{0} (Units.{0} Int Int.instMonoidInt) (DivInvOneMonoid.toInvOneClass.{0} (Units.{0} Int Int.instMonoidInt) (DivisionMonoid.toDivInvOneMonoid.{0} (Units.{0} Int Int.instMonoidInt) (DivisionCommMonoid.toDivisionMonoid.{0} (Units.{0} Int Int.instMonoidInt) (CommGroup.toDivisionCommMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instCommGroupUnitsToMonoid.{0} Int Int.instCommMonoidInt))))))))) n)) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ)))
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (σ : Equiv.Perm.{succ u1} α), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1) σ) (Multiset.prod.{0} (Units.{0} Int Int.instMonoidInt) (CommGroup.toCommMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instCommGroupUnitsToMonoid.{0} Int Int.instCommMonoidInt)) (Multiset.map.{0, 0} Nat (Units.{0} Int Int.instMonoidInt) (fun (n : Nat) => Neg.neg.{0} (Units.{0} Int Int.instMonoidInt) (Units.instNegUnits.{0} Int Int.instMonoidInt (NonUnitalNonAssocRing.toHasDistribNeg.{0} Int (NonAssocRing.toNonUnitalNonAssocRing.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)))) (HPow.hPow.{0, 0, 0} (Units.{0} Int Int.instMonoidInt) Nat (Units.{0} Int Int.instMonoidInt) (instHPow.{0, 0} (Units.{0} Int Int.instMonoidInt) Nat (Monoid.Pow.{0} (Units.{0} Int Int.instMonoidInt) (DivInvMonoid.toMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Group.toDivInvMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instGroupUnits.{0} Int Int.instMonoidInt))))) (Neg.neg.{0} (Units.{0} Int Int.instMonoidInt) (Units.instNegUnits.{0} Int Int.instMonoidInt (NonUnitalNonAssocRing.toHasDistribNeg.{0} Int (NonAssocRing.toNonUnitalNonAssocRing.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)))) (OfNat.ofNat.{0} (Units.{0} Int Int.instMonoidInt) 1 (One.toOfNat1.{0} (Units.{0} Int Int.instMonoidInt) (InvOneClass.toOne.{0} (Units.{0} Int Int.instMonoidInt) (DivInvOneMonoid.toInvOneClass.{0} (Units.{0} Int Int.instMonoidInt) (DivisionMonoid.toDivInvOneMonoid.{0} (Units.{0} Int Int.instMonoidInt) (DivisionCommMonoid.toDivisionMonoid.{0} (Units.{0} Int Int.instMonoidInt) (CommGroup.toDivisionCommMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instCommGroupUnitsToMonoid.{0} Int Int.instCommMonoidInt))))))))) n)) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ)))
 Case conversion may be inaccurate. Consider using '#align equiv.perm.sign_of_cycle_type' Equiv.Perm.sign_of_cycleType'ₓ'. -/
 theorem sign_of_cycleType' (σ : Perm α) : sign σ = (σ.cycleType.map fun n => -(-1 : ℤˣ) ^ n).Prod :=
   cycle_induction_on (fun τ : Perm α => sign τ = (τ.cycleType.map fun n => -(-1 : ℤˣ) ^ n).Prod) σ
@@ -244,7 +244,7 @@ theorem sign_of_cycleType' (σ : Perm α) : sign σ = (σ.cycleType.map fun n =>
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : Equiv.Perm.{succ u1} α), Eq.{1} (Units.{0} Int Int.monoid) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u1} α) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1) f) (HPow.hPow.{0, 0, 0} (Units.{0} Int Int.monoid) Nat (Units.{0} Int Int.monoid) (instHPow.{0, 0} (Units.{0} Int Int.monoid) Nat (Monoid.Pow.{0} (Units.{0} Int Int.monoid) (DivInvMonoid.toMonoid.{0} (Units.{0} Int Int.monoid) (Group.toDivInvMonoid.{0} (Units.{0} Int Int.monoid) (Units.group.{0} Int Int.monoid))))) (Neg.neg.{0} (Units.{0} Int Int.monoid) (Units.hasNeg.{0} Int Int.monoid (NonUnitalNonAssocRing.toHasDistribNeg.{0} Int (NonAssocRing.toNonUnitalNonAssocRing.{0} Int (Ring.toNonAssocRing.{0} Int Int.ring)))) (OfNat.ofNat.{0} (Units.{0} Int Int.monoid) 1 (OfNat.mk.{0} (Units.{0} Int Int.monoid) 1 (One.one.{0} (Units.{0} Int Int.monoid) (MulOneClass.toHasOne.{0} (Units.{0} Int Int.monoid) (Units.mulOneClass.{0} Int Int.monoid)))))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Multiset.sum.{0} Nat Nat.addCommMonoid (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)) (coeFn.{1, 1} (AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.orderedCancelAddCommMonoid.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.orderedCancelAddCommMonoid.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{0} Nat) -> Nat) (AddMonoidHom.hasCoeToFun.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.orderedCancelAddCommMonoid.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : Equiv.Perm.{succ u1} α), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) f) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1) f) (HPow.hPow.{0, 0, 0} (Units.{0} Int Int.instMonoidInt) Nat (Units.{0} Int Int.instMonoidInt) (instHPow.{0, 0} (Units.{0} Int Int.instMonoidInt) Nat (Monoid.Pow.{0} (Units.{0} Int Int.instMonoidInt) (DivInvMonoid.toMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Group.toDivInvMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instGroupUnits.{0} Int Int.instMonoidInt))))) (Neg.neg.{0} (Units.{0} Int Int.instMonoidInt) (Units.instNegUnits.{0} Int Int.instMonoidInt (NonUnitalNonAssocRing.toHasDistribNeg.{0} Int (NonAssocRing.toNonUnitalNonAssocRing.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)))) (OfNat.ofNat.{0} (Units.{0} Int Int.instMonoidInt) 1 (One.toOfNat1.{0} (Units.{0} Int Int.instMonoidInt) (InvOneClass.toOne.{0} (Units.{0} Int Int.instMonoidInt) (DivInvOneMonoid.toInvOneClass.{0} (Units.{0} Int Int.instMonoidInt) (DivisionMonoid.toDivInvOneMonoid.{0} (Units.{0} Int Int.instMonoidInt) (DivisionCommMonoid.toDivisionMonoid.{0} (Units.{0} Int Int.instMonoidInt) (CommGroup.toDivisionCommMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instCommGroupUnitsToMonoid.{0} Int Int.instCommMonoidInt))))))))) (HAdd.hAdd.{0, 0, 0} Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{0} Nat) => Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)) Nat (instHAdd.{0} Nat instAddNat) (Multiset.sum.{0} Nat Nat.addCommMonoid (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{0} Nat) (fun (_x : Multiset.{0} Nat) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{0} Nat) => Nat) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{0} Nat) Nat (AddZeroClass.toAdd.{0} (Multiset.{0} Nat) (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f))))
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : Equiv.Perm.{succ u1} α), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) f) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1) f) (HPow.hPow.{0, 0, 0} (Units.{0} Int Int.instMonoidInt) Nat (Units.{0} Int Int.instMonoidInt) (instHPow.{0, 0} (Units.{0} Int Int.instMonoidInt) Nat (Monoid.Pow.{0} (Units.{0} Int Int.instMonoidInt) (DivInvMonoid.toMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Group.toDivInvMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instGroupUnits.{0} Int Int.instMonoidInt))))) (Neg.neg.{0} (Units.{0} Int Int.instMonoidInt) (Units.instNegUnits.{0} Int Int.instMonoidInt (NonUnitalNonAssocRing.toHasDistribNeg.{0} Int (NonAssocRing.toNonUnitalNonAssocRing.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)))) (OfNat.ofNat.{0} (Units.{0} Int Int.instMonoidInt) 1 (One.toOfNat1.{0} (Units.{0} Int Int.instMonoidInt) (InvOneClass.toOne.{0} (Units.{0} Int Int.instMonoidInt) (DivInvOneMonoid.toInvOneClass.{0} (Units.{0} Int Int.instMonoidInt) (DivisionMonoid.toDivInvOneMonoid.{0} (Units.{0} Int Int.instMonoidInt) (DivisionCommMonoid.toDivisionMonoid.{0} (Units.{0} Int Int.instMonoidInt) (CommGroup.toDivisionCommMonoid.{0} (Units.{0} Int Int.instMonoidInt) (Units.instCommGroupUnitsToMonoid.{0} Int Int.instCommMonoidInt))))))))) (HAdd.hAdd.{0, 0, 0} Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{0} Nat) => Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)) Nat (instHAdd.{0} Nat instAddNat) (Multiset.sum.{0} Nat Nat.addCommMonoid (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{0} Nat) (fun (_x : Multiset.{0} Nat) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{0} Nat) => Nat) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{0} Nat) Nat (AddZeroClass.toAdd.{0} (Multiset.{0} Nat) (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{0, 0} (Multiset.{0} Nat) Nat (AddMonoid.toAddZeroClass.{0} (Multiset.{0} Nat) (AddRightCancelMonoid.toAddMonoid.{0} (Multiset.{0} Nat) (AddCancelMonoid.toAddRightCancelMonoid.{0} (Multiset.{0} Nat) (AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f))))
 Case conversion may be inaccurate. Consider using '#align equiv.perm.sign_of_cycle_type Equiv.Perm.sign_of_cycleTypeₓ'. -/
 theorem sign_of_cycleType (f : Perm α) :
     sign f = (-1 : ℤˣ) ^ (f.cycleType.Sum + f.cycleType.card) :=
@@ -436,7 +436,7 @@ theorem cycleType_extendDomain {β : Type _} [Fintype β] [DecidableEq β] {p :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {p : α -> Prop} [_inst_3 : DecidablePred.{succ u1} α p] {g : Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)}, Eq.{1} (Multiset.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (fun (_x : MonoidHom.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) => (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) -> (Equiv.Perm.{succ u1} α)) (MonoidHom.hasCoeToFun.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (Equiv.Perm.ofSubtype.{u1} α p (fun (a : α) => _inst_3 a)) g)) (Equiv.Perm.cycleType.{u1} (Subtype.{succ u1} α p) (Subtype.fintype.{u1} α (fun (x : α) => p x) (fun (a : α) => _inst_3 a) _inst_1) (fun (a : Subtype.{succ u1} α p) (b : Subtype.{succ u1} α p) => Subtype.decidableEq.{u1} α (fun (x : α) => p x) (fun (a : α) (b : α) => _inst_2 a b) a b) g)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {p : α -> Prop} [_inst_3 : DecidablePred.{succ u1} α p] {g : Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)}, Eq.{1} (Multiset.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (fun (_x : Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) => Equiv.Perm.{succ u1} α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p)))))) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (MonoidHom.monoidHomClass.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))))) (Equiv.Perm.ofSubtype.{u1} α p (fun (a : α) => _inst_3 a)) g)) (Equiv.Perm.cycleType.{u1} (Subtype.{succ u1} α p) (Subtype.fintype.{u1} α (fun (x : α) => p x) (fun (a : α) => _inst_3 a) _inst_1) (fun (a : Subtype.{succ u1} α p) (b : Subtype.{succ u1} α p) => Subtype.instDecidableEqSubtype.{u1} α (fun (x : α) => p x) (fun (a : α) (b : α) => _inst_2 a b) a b) g)
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {p : α -> Prop} [_inst_3 : DecidablePred.{succ u1} α p] {g : Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)}, Eq.{1} (Multiset.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (fun (_x : Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) => Equiv.Perm.{succ u1} α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p)))))) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (MonoidHom.monoidHomClass.{u1, u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} (Subtype.{succ u1} α p)) (Equiv.Perm.permGroup.{u1} (Subtype.{succ u1} α p))))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))))) (Equiv.Perm.ofSubtype.{u1} α p (fun (a : α) => _inst_3 a)) g)) (Equiv.Perm.cycleType.{u1} (Subtype.{succ u1} α p) (Subtype.fintype.{u1} α (fun (x : α) => p x) (fun (a : α) => _inst_3 a) _inst_1) (fun (a : Subtype.{succ u1} α p) (b : Subtype.{succ u1} α p) => Subtype.instDecidableEqSubtype.{u1} α (fun (x : α) => p x) (fun (a : α) (b : α) => _inst_2 a b) a b) g)
 Case conversion may be inaccurate. Consider using '#align equiv.perm.cycle_type_of_subtype Equiv.Perm.cycleType_ofSubtypeₓ'. -/
 theorem cycleType_ofSubtype {p : α → Prop} [DecidablePred p] {g : Perm (Subtype p)} :
     cycleType g.ofSubtype = cycleType g :=
@@ -513,7 +513,7 @@ theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)], (Not (Dvd.Dvd.{0} Nat Nat.hasDvd p (Fintype.card.{u1} α _inst_1))) -> (forall {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (OfNat.mk.{u1} (Equiv.Perm.{succ u1} α) 1 (One.one.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasOne.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))))))) -> (Exists.{succ u1} α (fun (a : α) => Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) σ a) a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)], (Not (Dvd.dvd.{0} Nat Nat.instDvdNat p (Fintype.card.{u1} α _inst_1))) -> (forall {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (One.toOfNat1.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toOne.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))))) -> (Exists.{succ u1} α (fun (a : α) => Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α α) σ a) a)))
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)], (Not (Dvd.dvd.{0} Nat Nat.instDvdNat p (Fintype.card.{u1} α _inst_1))) -> (forall {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (One.toOfNat1.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toOne.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))))) -> (Exists.{succ u1} α (fun (a : α) => Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α α) σ a) a)))
 Case conversion may be inaccurate. Consider using '#align equiv.perm.exists_fixed_point_of_prime Equiv.Perm.exists_fixed_point_of_primeₓ'. -/
 theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by
@@ -531,7 +531,7 @@ theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p 
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)], (Dvd.Dvd.{0} Nat Nat.hasDvd p (Fintype.card.{u1} α _inst_1)) -> (forall {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (OfNat.mk.{u1} (Equiv.Perm.{succ u1} α) 1 (One.one.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasOne.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))))))) -> (forall {a : α}, (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) σ a) a) -> (Exists.{succ u1} α (fun (b : α) => And (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) σ b) b) (Ne.{succ u1} α b a)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)], (Dvd.dvd.{0} Nat Nat.instDvdNat p (Fintype.card.{u1} α _inst_1)) -> (forall {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (One.toOfNat1.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toOne.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))))) -> (forall {a : α}, (Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α α) σ a) a) -> (Exists.{succ u1} α (fun (b : α) => And (Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α α) σ b) b) (Ne.{succ u1} α b a)))))
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)], (Dvd.dvd.{0} Nat Nat.instDvdNat p (Fintype.card.{u1} α _inst_1)) -> (forall {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (One.toOfNat1.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toOne.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))))) -> (forall {a : α}, (Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α α) σ a) a) -> (Exists.{succ u1} α (fun (b : α) => And (Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α α) σ b) b) (Ne.{succ u1} α b a)))))
 Case conversion may be inaccurate. Consider using '#align equiv.perm.exists_fixed_point_of_prime' Equiv.Perm.exists_fixed_point_of_prime'ₓ'. -/
 theorem exists_fixed_point_of_prime' {p n : ℕ} [hp : Fact p.Prime] (hα : p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) {a : α} (ha : σ a = a) : ∃ b : α, σ b = b ∧ b ≠ a := by
@@ -884,7 +884,7 @@ theorem isCycle (h : IsThreeCycle σ) : IsCycle σ := by
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α}, (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ) -> (Eq.{1} (Units.{0} Int Int.monoid) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u1} α) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1) σ) (OfNat.ofNat.{0} (Units.{0} Int Int.monoid) 1 (OfNat.mk.{0} (Units.{0} Int Int.monoid) 1 (One.one.{0} (Units.{0} Int Int.monoid) (MulOneClass.toHasOne.{0} (Units.{0} Int Int.monoid) (Units.mulOneClass.{0} Int Int.monoid))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α}, (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1) σ) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (InvOneClass.toOne.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (DivInvOneMonoid.toInvOneClass.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (DivisionMonoid.toDivInvOneMonoid.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (DivisionCommMonoid.toDivisionMonoid.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (CommGroup.toDivisionCommMonoid.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (Units.instCommGroupUnitsToMonoid.{0} Int Int.instCommMonoidInt)))))))))
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α}, (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1) σ) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (InvOneClass.toOne.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (DivInvOneMonoid.toInvOneClass.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (DivisionMonoid.toDivInvOneMonoid.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (DivisionCommMonoid.toDivisionMonoid.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (CommGroup.toDivisionCommMonoid.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Units.{0} Int Int.instMonoidInt) σ) (Units.instCommGroupUnitsToMonoid.{0} Int Int.instCommMonoidInt)))))))))
 Case conversion may be inaccurate. Consider using '#align equiv.perm.is_three_cycle.sign Equiv.Perm.IsThreeCycle.signₓ'. -/
 theorem sign (h : IsThreeCycle σ) : sign σ = 1 :=
   by

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

@@ -341,7 +341,7 @@ theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
 
 /- warning: equiv.perm.cycle_type_le_of_mem_cycle_factors_finset -> Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {f : Equiv.Perm.{succ u1} α} {g : Equiv.Perm.{succ u1} α}, (Membership.Mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Finset.{u1} (Equiv.Perm.{succ u1} α)) (Finset.hasMem.{u1} (Equiv.Perm.{succ u1} α)) f (Equiv.Perm.cycleFactorsFinset.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1 g)) -> (LE.le.{0} (Multiset.{0} Nat) (Preorder.toLE.{0} (Multiset.{0} Nat) (PartialOrder.toPreorder.{0} (Multiset.{0} Nat) (Multiset.partialOrder.{0} Nat))) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) g))
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {f : Equiv.Perm.{succ u1} α} {g : Equiv.Perm.{succ u1} α}, (Membership.Mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Finset.{u1} (Equiv.Perm.{succ u1} α)) (Finset.hasMem.{u1} (Equiv.Perm.{succ u1} α)) f (Equiv.Perm.cycleFactorsFinset.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1 g)) -> (LE.le.{0} (Multiset.{0} Nat) (Preorder.toHasLe.{0} (Multiset.{0} Nat) (PartialOrder.toPreorder.{0} (Multiset.{0} Nat) (Multiset.partialOrder.{0} Nat))) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) g))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {f : Equiv.Perm.{succ u1} α} {g : Equiv.Perm.{succ u1} α}, (Membership.mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Finset.{u1} (Equiv.Perm.{succ u1} α)) (Finset.instMembershipFinset.{u1} (Equiv.Perm.{succ u1} α)) f (Equiv.Perm.cycleFactorsFinset.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1 g)) -> (LE.le.{0} (Multiset.{0} Nat) (Preorder.toLE.{0} (Multiset.{0} Nat) (PartialOrder.toPreorder.{0} (Multiset.{0} Nat) (Multiset.instPartialOrderMultiset.{0} Nat))) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) g))
 Case conversion may be inaccurate. Consider using '#align equiv.perm.cycle_type_le_of_mem_cycle_factors_finset Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinsetₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

@@ -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.perm.cycle.type
-! leanprover-community/mathlib commit 47adfab39a11a072db552f47594bf8ed2cf8a722
+! leanprover-community/mathlib commit 75be6b616681ab6ca66d798ead117e75cd64f125
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Tactic.Linarith.Default
 /-!
 # Cycle Types
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define the cycle type of a permutation.
 
 ## Main definitions

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

@@ -46,16 +46,21 @@ section CycleType
 
 variable [DecidableEq α]
 
+#print Equiv.Perm.cycleType /-
 /-- The cycle type of a permutation -/
 def cycleType (σ : Perm α) : Multiset ℕ :=
   σ.cycleFactorsFinset.1.map (Finset.card ∘ support)
 #align equiv.perm.cycle_type Equiv.Perm.cycleType
+-/
 
+#print Equiv.Perm.cycleType_def /-
 theorem cycleType_def (σ : Perm α) :
     σ.cycleType = σ.cycleFactorsFinset.1.map (Finset.card ∘ support) :=
   rfl
 #align equiv.perm.cycle_type_def Equiv.Perm.cycleType_def
+-/
 
+#print Equiv.Perm.cycleType_eq' /-
 theorem cycleType_eq' {σ : Perm α} (s : Finset (Perm α)) (h1 : ∀ f : Perm α, f ∈ s → f.IsCycle)
     (h2 : (s : Set (Perm α)).Pairwise Disjoint)
     (h0 : s.noncommProd id (h2.imp fun _ _ => Disjoint.commute) = σ) :
@@ -66,7 +71,14 @@ theorem cycleType_eq' {σ : Perm α} (s : Finset (Perm α)) (h1 : ∀ f : Perm 
   rw [cycle_factors_finset_eq_finset]
   exact ⟨h1, h2, h0⟩
 #align equiv.perm.cycle_type_eq' Equiv.Perm.cycleType_eq'
+-/
 
+/- warning: equiv.perm.cycle_type_eq -> Equiv.Perm.cycleType_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α} (l : List.{u1} (Equiv.Perm.{succ u1} α)), (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (List.prod.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toHasOne.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) l) σ) -> (forall (σ : Equiv.Perm.{succ u1} α), (Membership.Mem.{u1, u1} (Equiv.Perm.{succ u1} α) (List.{u1} (Equiv.Perm.{succ u1} α)) (List.hasMem.{u1} (Equiv.Perm.{succ u1} α)) σ l) -> (Equiv.Perm.IsCycle.{u1} α σ)) -> (List.Pairwise.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.Disjoint.{u1} α) l) -> (Eq.{1} (Multiset.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (List.{0} Nat) (Multiset.{0} Nat) (HasLiftT.mk.{1, 1} (List.{0} Nat) (Multiset.{0} Nat) (CoeTCₓ.coe.{1, 1} (List.{0} Nat) (Multiset.{0} Nat) (coeBase.{1, 1} (List.{0} Nat) (Multiset.{0} Nat) (Multiset.hasCoe.{0} Nat)))) (List.map.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Function.comp.{succ u1, succ u1, 1} (Equiv.Perm.{succ u1} α) (Finset.{u1} α) Nat (Finset.card.{u1} α) (Equiv.Perm.support.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1)) l)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α} (l : List.{u1} (Equiv.Perm.{succ u1} α)), (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (List.prod.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (InvOneClass.toOne.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) l) σ) -> (forall (σ : Equiv.Perm.{succ u1} α), (Membership.mem.{u1, u1} (Equiv.Perm.{succ u1} α) (List.{u1} (Equiv.Perm.{succ u1} α)) (List.instMembershipList.{u1} (Equiv.Perm.{succ u1} α)) σ l) -> (Equiv.Perm.IsCycle.{u1} α σ)) -> (List.Pairwise.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.Disjoint.{u1} α) l) -> (Eq.{1} (Multiset.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ) (Multiset.ofList.{0} Nat (List.map.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Function.comp.{succ u1, succ u1, 1} (Equiv.Perm.{succ u1} α) (Finset.{u1} α) Nat (Finset.card.{u1} α) (Equiv.Perm.support.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1)) l)))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.cycle_type_eq Equiv.Perm.cycleType_eqₓ'. -/
 theorem cycleType_eq {σ : Perm α} (l : List (Perm α)) (h0 : l.Prod = σ)
     (h1 : ∀ σ : Perm α, σ ∈ l → σ.IsCycle) (h2 : l.Pairwise Disjoint) :
     σ.cycleType = l.map (Finset.card ∘ support) :=
@@ -79,18 +91,37 @@ theorem cycleType_eq {σ : Perm α} (l : List (Perm α)) (h0 : l.Prod = σ)
   · simpa [list.dedup_eq_self.mpr hl] using h2.forall disjoint.symmetric
 #align equiv.perm.cycle_type_eq Equiv.Perm.cycleType_eq
 
+/- warning: equiv.perm.cycle_type_one -> Equiv.Perm.cycleType_one is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α], Eq.{1} (Multiset.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (One.toOfNat1.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toOne.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))))) (OfNat.ofNat.{0} (Multiset.{0} Nat) 0 (Zero.toOfNat0.{0} (Multiset.{0} Nat) (Multiset.instZeroMultiset.{0} Nat)))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.cycle_type_one Equiv.Perm.cycleType_oneₓ'. -/
 theorem cycleType_one : (1 : Perm α).cycleType = 0 :=
   cycleType_eq [] rfl (fun _ => False.elim) Pairwise.nil
 #align equiv.perm.cycle_type_one Equiv.Perm.cycleType_one
 
+/- warning: equiv.perm.cycle_type_eq_zero -> Equiv.Perm.cycleType_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α}, Iff (Eq.{1} (Multiset.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ) (OfNat.ofNat.{0} (Multiset.{0} Nat) 0 (OfNat.mk.{0} (Multiset.{0} Nat) 0 (Zero.zero.{0} (Multiset.{0} Nat) (Multiset.hasZero.{0} Nat))))) (Eq.{succ u1} (Equiv.Perm.{succ u1} α) σ (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (OfNat.mk.{u1} (Equiv.Perm.{succ u1} α) 1 (One.one.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasOne.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))))))
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.cycle_type_eq_zero Equiv.Perm.cycleType_eq_zeroₓ'. -/
 theorem cycleType_eq_zero {σ : Perm α} : σ.cycleType = 0 ↔ σ = 1 := by
   simp [cycle_type_def, cycle_factors_finset_eq_empty_iff]
 #align equiv.perm.cycle_type_eq_zero Equiv.Perm.cycleType_eq_zero
 
+/- warning: equiv.perm.card_cycle_type_eq_zero -> Equiv.Perm.card_cycleType_eq_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.card_cycle_type_eq_zero Equiv.Perm.card_cycleType_eq_zeroₓ'. -/
 theorem card_cycleType_eq_zero {σ : Perm α} : σ.cycleType.card = 0 ↔ σ = 1 := by
   rw [card_eq_zero, cycle_type_eq_zero]
 #align equiv.perm.card_cycle_type_eq_zero Equiv.Perm.card_cycleType_eq_zero
 
+#print Equiv.Perm.two_le_of_mem_cycleType /-
 theorem two_le_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType) : 2 ≤ n :=
   by
   simp only [cycle_type_def, ← Finset.mem_def, Function.comp_apply, Multiset.mem_map,
@@ -98,16 +129,27 @@ theorem two_le_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType
   obtain ⟨_, ⟨hc, -⟩, rfl⟩ := h
   exact hc.two_le_card_support
 #align equiv.perm.two_le_of_mem_cycle_type Equiv.Perm.two_le_of_mem_cycleType
+-/
 
+#print Equiv.Perm.one_lt_of_mem_cycleType /-
 theorem one_lt_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType) : 1 < n :=
   two_le_of_mem_cycleType h
 #align equiv.perm.one_lt_of_mem_cycle_type Equiv.Perm.one_lt_of_mem_cycleType
+-/
 
+#print Equiv.Perm.IsCycle.cycleType /-
 theorem IsCycle.cycleType {σ : Perm α} (hσ : IsCycle σ) : σ.cycleType = [σ.support.card] :=
   cycleType_eq [σ] (mul_one σ) (fun τ hτ => (congr_arg IsCycle (List.mem_singleton.mp hτ)).mpr hσ)
     (pairwise_singleton Disjoint σ)
 #align equiv.perm.is_cycle.cycle_type Equiv.Perm.IsCycle.cycleType
+-/
 
+/- warning: equiv.perm.card_cycle_type_eq_one -> Equiv.Perm.card_cycleType_eq_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.card_cycle_type_eq_one Equiv.Perm.card_cycleType_eq_oneₓ'. -/
 theorem card_cycleType_eq_one {σ : Perm α} : σ.cycleType.card = 1 ↔ σ.IsCycle :=
   by
   rw [card_eq_one]
@@ -121,6 +163,12 @@ theorem card_cycleType_eq_one {σ : Perm α} : σ.cycleType.card = 1 ↔ σ.IsCy
     simp [h]
 #align equiv.perm.card_cycle_type_eq_one Equiv.Perm.card_cycleType_eq_one
 
+/- warning: equiv.perm.disjoint.cycle_type -> Equiv.Perm.Disjoint.cycleType is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.disjoint.cycle_type Equiv.Perm.Disjoint.cycleTypeₓ'. -/
 theorem Disjoint.cycleType {σ τ : Perm α} (h : Disjoint σ τ) :
     (σ * τ).cycleType = σ.cycleType + τ.cycleType :=
   by
@@ -129,6 +177,12 @@ theorem Disjoint.cycleType {σ τ : Perm α} (h : Disjoint σ τ) :
   exact Finset.disjoint_val.2 h.disjoint_cycle_factors_finset
 #align equiv.perm.disjoint.cycle_type Equiv.Perm.Disjoint.cycleType
 
+/- warning: equiv.perm.cycle_type_inv -> Equiv.Perm.cycleType_inv is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.cycle_type_inv Equiv.Perm.cycleType_invₓ'. -/
 theorem cycleType_inv (σ : Perm α) : σ⁻¹.cycleType = σ.cycleType :=
   cycle_induction_on (fun τ : Perm α => τ⁻¹.cycleType = τ.cycleType) σ rfl
     (fun σ hσ => by rw [hσ.cycle_type, hσ.inv.cycle_type, support_inv]) fun σ τ hστ hc hσ hτ => by
@@ -138,6 +192,12 @@ theorem cycleType_inv (σ : Perm α) : σ⁻¹.cycleType = σ.cycleType :=
           (fun h : σ x = x => inv_eq_iff_eq.mpr h.symm) (hστ x).symm]
 #align equiv.perm.cycle_type_inv Equiv.Perm.cycleType_inv
 
+/- warning: equiv.perm.cycle_type_conj -> Equiv.Perm.cycleType_conj is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.cycle_type_conj Equiv.Perm.cycleType_conjₓ'. -/
 theorem cycleType_conj {σ τ : Perm α} : (τ * σ * τ⁻¹).cycleType = σ.cycleType :=
   by
   revert τ
@@ -154,22 +214,35 @@ theorem cycleType_conj {σ τ : Perm α} : (τ * σ * τ⁻¹).cycleType = σ.cy
         rw [perm.mul_apply, perm.mul_apply, h, apply_inv_self]
 #align equiv.perm.cycle_type_conj Equiv.Perm.cycleType_conj
 
+#print Equiv.Perm.sum_cycleType /-
 theorem sum_cycleType (σ : Perm α) : σ.cycleType.Sum = σ.support.card :=
   cycle_induction_on (fun τ : Perm α => τ.cycleType.Sum = τ.support.card) σ
     (by rw [cycle_type_one, sum_zero, support_one, Finset.card_empty])
     (fun σ hσ => by rw [hσ.cycle_type, coe_sum, List.sum_singleton]) fun σ τ hστ hc hσ hτ => by
     rw [hστ.cycle_type, sum_add, hσ, hτ, hστ.card_support_mul]
 #align equiv.perm.sum_cycle_type Equiv.Perm.sum_cycleType
+-/
 
-theorem sign_of_cycle_type' (σ : Perm α) :
-    sign σ = (σ.cycleType.map fun n => -(-1 : ℤˣ) ^ n).Prod :=
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.sign_of_cycle_type' Equiv.Perm.sign_of_cycleType'ₓ'. -/
+theorem sign_of_cycleType' (σ : Perm α) : sign σ = (σ.cycleType.map fun n => -(-1 : ℤˣ) ^ n).Prod :=
   cycle_induction_on (fun τ : Perm α => sign τ = (τ.cycleType.map fun n => -(-1 : ℤˣ) ^ n).Prod) σ
     (by rw [sign_one, cycle_type_one, Multiset.map_zero, prod_zero])
     (fun σ hσ => by
       rw [hσ.sign, hσ.cycle_type, coe_map, coe_prod, List.map_singleton, List.prod_singleton])
     fun σ τ hστ hc hσ hτ => by rw [sign_mul, hσ, hτ, hστ.cycle_type, Multiset.map_add, prod_add]
-#align equiv.perm.sign_of_cycle_type' Equiv.Perm.sign_of_cycle_type'
-
+#align equiv.perm.sign_of_cycle_type' Equiv.Perm.sign_of_cycleType'
+
+/- warning: equiv.perm.sign_of_cycle_type -> Equiv.Perm.sign_of_cycleType is a dubious translation:
+lean 3 declaration is
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(AddCancelCommMonoid.toAddCancelMonoid.{0} (Multiset.{0} Nat) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} (Multiset.{0} Nat) (Multiset.instOrderedCancelAddCommMonoidMultiset.{0} Nat)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f))))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.sign_of_cycle_type Equiv.Perm.sign_of_cycleTypeₓ'. -/
 theorem sign_of_cycleType (f : Perm α) :
     sign f = (-1 : ℤˣ) ^ (f.cycleType.Sum + f.cycleType.card) :=
   cycle_induction_on (fun f : Perm α => sign f = (-1 : ℤˣ) ^ (f.cycleType.Sum + f.cycleType.card)) f
@@ -186,6 +259,12 @@ theorem sign_of_cycleType (f : Perm α) :
       add_comm g.cycle_type.sum _, add_assoc, pow_add, ← Pf, ← Pg, Equiv.Perm.sign_mul]
 #align equiv.perm.sign_of_cycle_type Equiv.Perm.sign_of_cycleType
 
+/- warning: equiv.perm.lcm_cycle_type -> Equiv.Perm.lcm_cycleType is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (σ : Equiv.Perm.{succ u1} α), Eq.{1} Nat (Multiset.lcm.{0} Nat Nat.cancelCommMonoidWithZero Nat.normalizedGcdMonoid (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ)) (orderOf.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))) σ)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (σ : Equiv.Perm.{succ u1} α), Eq.{1} Nat (Multiset.lcm.{0} Nat Nat.cancelCommMonoidWithZero instNormalizedGCDMonoidNatCancelCommMonoidWithZero (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ)) (orderOf.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))) σ)
+Case conversion may be inaccurate. Consider using '#align equiv.perm.lcm_cycle_type Equiv.Perm.lcm_cycleTypeₓ'. -/
 theorem lcm_cycleType (σ : Perm α) : σ.cycleType.lcm = orderOf σ :=
   cycle_induction_on (fun τ : Perm α => τ.cycleType.lcm = orderOf τ) σ
     (by rw [cycle_type_one, lcm_zero, orderOf_one])
@@ -193,12 +272,15 @@ theorem lcm_cycleType (σ : Perm α) : σ.cycleType.lcm = orderOf σ :=
     fun σ τ hστ hc hσ hτ => by rw [hστ.cycle_type, lcm_add, lcm_eq_nat_lcm, hστ.order_of, hσ, hτ]
 #align equiv.perm.lcm_cycle_type Equiv.Perm.lcm_cycleType
 
+#print Equiv.Perm.dvd_of_mem_cycleType /-
 theorem dvd_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType) : n ∣ orderOf σ :=
   by
   rw [← lcm_cycle_type]
   exact dvd_lcm h
 #align equiv.perm.dvd_of_mem_cycle_type Equiv.Perm.dvd_of_mem_cycleType
+-/
 
+#print Equiv.Perm.orderOf_cycleOf_dvd_orderOf /-
 theorem orderOf_cycleOf_dvd_orderOf (f : Perm α) (x : α) : orderOf (cycleOf f x) ∣ orderOf f :=
   by
   by_cases hx : f x = x
@@ -210,7 +292,14 @@ theorem orderOf_cycleOf_dvd_orderOf (f : Perm α) (x : α) : orderOf (cycleOf f
     · rwa [← Finset.mem_def, cycle_of_mem_cycle_factors_finset_iff, mem_support]
     · simp [(is_cycle_cycle_of _ hx).orderOf]
 #align equiv.perm.order_of_cycle_of_dvd_order_of Equiv.Perm.orderOf_cycleOf_dvd_orderOf
+-/
 
+/- warning: equiv.perm.two_dvd_card_support -> Equiv.Perm.two_dvd_card_support is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (OfNat.mk.{u1} (Equiv.Perm.{succ u1} α) 1 (One.one.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasOne.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))))))) -> (Dvd.Dvd.{0} Nat Nat.hasDvd (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Finset.card.{u1} α (Equiv.Perm.support.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1 σ)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (One.toOfNat1.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toOne.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))))) -> (Dvd.dvd.{0} Nat Nat.instDvdNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Finset.card.{u1} α (Equiv.Perm.support.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1 σ)))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.two_dvd_card_support Equiv.Perm.two_dvd_card_supportₓ'. -/
 theorem two_dvd_card_support {σ : Perm α} (hσ : σ ^ 2 = 1) : 2 ∣ σ.support.card :=
   (congr_arg (Dvd.Dvd 2) σ.sum_cycleType).mp
     (Multiset.dvd_sum fun n hn => by
@@ -220,6 +309,7 @@ theorem two_dvd_card_support {σ : Perm α} (hσ : σ ^ 2 = 1) : 2 ∣ σ.suppor
           (two_le_of_mem_cycle_type hn)])
 #align equiv.perm.two_dvd_card_support Equiv.Perm.two_dvd_card_support
 
+#print Equiv.Perm.cycleType_prime_order /-
 theorem cycleType_prime_order {σ : Perm α} (hσ : (orderOf σ).Prime) :
     ∃ n : ℕ, σ.cycleType = replicate (n + 1) (orderOf σ) :=
   by
@@ -233,7 +323,9 @@ theorem cycleType_prime_order {σ : Perm α} (hσ : (orderOf σ).Prime) :
   rw [H, orderOf_one] at hσ
   exact hσ.ne_one rfl
 #align equiv.perm.cycle_type_prime_order Equiv.Perm.cycleType_prime_order
+-/
 
+#print Equiv.Perm.isCycle_of_prime_order /-
 theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
     (h2 : σ.support.card < 2 * orderOf σ) : σ.IsCycle :=
   by
@@ -242,7 +334,14 @@ theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
     mul_lt_mul_right (orderOf_pos σ), Nat.succ_lt_succ_iff, Nat.lt_succ_iff, le_zero_iff] at h2
   rw [← card_cycle_type_eq_one, hn, card_replicate, h2]
 #align equiv.perm.is_cycle_of_prime_order Equiv.Perm.isCycle_of_prime_order
+-/
 
+/- warning: equiv.perm.cycle_type_le_of_mem_cycle_factors_finset -> Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {f : Equiv.Perm.{succ u1} α} {g : Equiv.Perm.{succ u1} α}, (Membership.Mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Finset.{u1} (Equiv.Perm.{succ u1} α)) (Finset.hasMem.{u1} (Equiv.Perm.{succ u1} α)) f (Equiv.Perm.cycleFactorsFinset.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1 g)) -> (LE.le.{0} (Multiset.{0} Nat) (Preorder.toLE.{0} (Multiset.{0} Nat) (PartialOrder.toPreorder.{0} (Multiset.{0} Nat) (Multiset.partialOrder.{0} Nat))) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) g))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {f : Equiv.Perm.{succ u1} α} {g : Equiv.Perm.{succ u1} α}, (Membership.mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Finset.{u1} (Equiv.Perm.{succ u1} α)) (Finset.instMembershipFinset.{u1} (Equiv.Perm.{succ u1} α)) f (Equiv.Perm.cycleFactorsFinset.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1 g)) -> (LE.le.{0} (Multiset.{0} Nat) (Preorder.toLE.{0} (Multiset.{0} Nat) (PartialOrder.toPreorder.{0} (Multiset.{0} Nat) (Multiset.instPartialOrderMultiset.{0} Nat))) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) g))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.cycle_type_le_of_mem_cycle_factors_finset Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinsetₓ'. -/
 theorem cycleType_le_of_mem_cycleFactorsFinset {f g : Perm α} (hf : f ∈ g.cycleFactorsFinset) :
     f.cycleType ≤ g.cycleType :=
   by
@@ -252,8 +351,14 @@ theorem cycleType_le_of_mem_cycleFactorsFinset {f g : Perm α} (hf : f ∈ g.cyc
   simpa [← Finset.mem_def, mem_cycle_factors_finset_iff] using hf
 #align equiv.perm.cycle_type_le_of_mem_cycle_factors_finset Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinset
 
-theorem cycleType_mul_mem_cycleFactorsFinset_eq_sub {f g : Perm α} (hf : f ∈ g.cycleFactorsFinset) :
-    (g * f⁻¹).cycleType = g.cycleType - f.cycleType :=
+/- warning: equiv.perm.cycle_type_mul_mem_cycle_factors_finset_eq_sub -> Equiv.Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {f : Equiv.Perm.{succ u1} α} {g : Equiv.Perm.{succ u1} α}, (Membership.Mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Finset.{u1} (Equiv.Perm.{succ u1} α)) (Finset.hasMem.{u1} (Equiv.Perm.{succ u1} α)) f (Equiv.Perm.cycleFactorsFinset.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1 g)) -> (Eq.{1} (Multiset.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) g (Inv.inv.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toHasInv.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))) f))) (HSub.hSub.{0, 0, 0} (Multiset.{0} Nat) (Multiset.{0} Nat) (Multiset.{0} Nat) (instHSub.{0} (Multiset.{0} Nat) (Multiset.hasSub.{0} Nat (fun (a : Nat) (b : Nat) => Nat.decidableEq a b))) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) g) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {f : Equiv.Perm.{succ u1} α} {g : Equiv.Perm.{succ u1} α}, (Membership.mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Finset.{u1} (Equiv.Perm.{succ u1} α)) (Finset.instMembershipFinset.{u1} (Equiv.Perm.{succ u1} α)) f (Equiv.Perm.cycleFactorsFinset.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1 g)) -> (Eq.{1} (Multiset.{0} Nat) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) g (Inv.inv.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toInv.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) f))) (HSub.hSub.{0, 0, 0} (Multiset.{0} Nat) (Multiset.{0} Nat) (Multiset.{0} Nat) (instHSub.{0} (Multiset.{0} Nat) (Multiset.instSubMultiset.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b))) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) g) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.cycle_type_mul_mem_cycle_factors_finset_eq_sub Equiv.Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_subₓ'. -/
+theorem cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub {f g : Perm α}
+    (hf : f ∈ g.cycleFactorsFinset) : (g * f⁻¹).cycleType = g.cycleType - f.cycleType :=
   by
   suffices (g * f⁻¹).cycleType + f.cycle_type = g.cycle_type - f.cycle_type + f.cycle_type
     by
@@ -261,8 +366,9 @@ theorem cycleType_mul_mem_cycleFactorsFinset_eq_sub {f g : Perm α} (hf : f ∈
     simp [← this]
   simp [← (disjoint_mul_inv_of_mem_cycle_factors_finset hf).cycleType,
     tsub_add_cancel_of_le (cycle_type_le_of_mem_cycle_factors_finset hf)]
-#align equiv.perm.cycle_type_mul_mem_cycle_factors_finset_eq_sub Equiv.Perm.cycleType_mul_mem_cycleFactorsFinset_eq_sub
+#align equiv.perm.cycle_type_mul_mem_cycle_factors_finset_eq_sub Equiv.Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub
 
+#print Equiv.Perm.isConj_of_cycleType_eq /-
 theorem isConj_of_cycleType_eq {σ τ : Perm α} (h : cycleType σ = cycleType τ) : IsConj σ τ :=
   by
   revert τ
@@ -298,13 +404,17 @@ theorem isConj_of_cycleType_eq {σ τ : Perm α} (h : cycleType σ = cycleType 
         rwa [Finset.mem_def]
       · exact (disjoint_mul_inv_of_mem_cycle_factors_finset hσ'l).symm
 #align equiv.perm.is_conj_of_cycle_type_eq Equiv.Perm.isConj_of_cycleType_eq
+-/
 
+#print Equiv.Perm.isConj_iff_cycleType_eq /-
 theorem isConj_iff_cycleType_eq {σ τ : Perm α} : IsConj σ τ ↔ σ.cycleType = τ.cycleType :=
   ⟨fun h => by
     obtain ⟨π, rfl⟩ := isConj_iff.1 h
     rw [cycle_type_conj], isConj_of_cycleType_eq⟩
 #align equiv.perm.is_conj_iff_cycle_type_eq Equiv.Perm.isConj_iff_cycleType_eq
+-/
 
+#print Equiv.Perm.cycleType_extendDomain /-
 @[simp]
 theorem cycleType_extendDomain {β : Type _} [Fintype β] [DecidableEq β] {p : β → Prop}
     [DecidablePred p] (f : α ≃ Subtype p) {g : Perm α} :
@@ -317,12 +427,25 @@ theorem cycleType_extendDomain {β : Type _} [Fintype β] [DecidableEq β] {p :
   · intro σ τ hd hc hσ hτ
     rw [hd.cycle_type, ← extend_domain_mul, (hd.extend_domain f).cycleType, hσ, hτ]
 #align equiv.perm.cycle_type_extend_domain Equiv.Perm.cycleType_extendDomain
+-/
 
+/- warning: equiv.perm.cycle_type_of_subtype -> Equiv.Perm.cycleType_ofSubtype is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.cycle_type_of_subtype Equiv.Perm.cycleType_ofSubtypeₓ'. -/
 theorem cycleType_ofSubtype {p : α → Prop} [DecidablePred p] {g : Perm (Subtype p)} :
     cycleType g.ofSubtype = cycleType g :=
   cycleType_extendDomain (Equiv.refl (Subtype p))
 #align equiv.perm.cycle_type_of_subtype Equiv.Perm.cycleType_ofSubtype
 
+/- warning: equiv.perm.mem_cycle_type_iff -> Equiv.Perm.mem_cycleType_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {n : Nat} {σ : Equiv.Perm.{succ u1} α}, Iff (Membership.Mem.{0, 0} Nat (Multiset.{0} Nat) (Multiset.hasMem.{0} Nat) n (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ)) (Exists.{succ u1} (Equiv.Perm.{succ u1} α) (fun (c : Equiv.Perm.{succ u1} α) => Exists.{succ u1} (Equiv.Perm.{succ u1} α) (fun (τ : Equiv.Perm.{succ u1} α) => And (Eq.{succ u1} (Equiv.Perm.{succ u1} α) σ (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) c τ)) (And (Equiv.Perm.Disjoint.{u1} α c τ) (And (Equiv.Perm.IsCycle.{u1} α c) (Eq.{1} Nat (Finset.card.{u1} α (Equiv.Perm.support.{u1} α (fun (a : α) (b : α) => _inst_2 a b) _inst_1 c)) n))))))
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.mem_cycle_type_iff Equiv.Perm.mem_cycleType_iffₓ'. -/
 theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
     n ∈ cycleType σ ↔ ∃ c τ : Perm α, σ = c * τ ∧ Disjoint c τ ∧ IsCycle c ∧ c.support.card = n :=
   by
@@ -343,11 +466,14 @@ theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
     simp [hd.cycle_type, hc.cycle_type]
 #align equiv.perm.mem_cycle_type_iff Equiv.Perm.mem_cycleType_iff
 
+#print Equiv.Perm.le_card_support_of_mem_cycleType /-
 theorem le_card_support_of_mem_cycleType {n : ℕ} {σ : Perm α} (h : n ∈ cycleType σ) :
     n ≤ σ.support.card :=
   (le_sum_of_mem h).trans (le_of_eq σ.sum_cycleType)
 #align equiv.perm.le_card_support_of_mem_cycle_type Equiv.Perm.le_card_support_of_mem_cycleType
+-/
 
+#print Equiv.Perm.cycleType_of_card_le_mem_cycleType_add_two /-
 theorem cycleType_of_card_le_mem_cycleType_add_two {n : ℕ} {g : Perm α}
     (hn2 : Fintype.card α < n + 2) (hng : n ∈ g.cycleType) : g.cycleType = {n} :=
   by
@@ -359,9 +485,16 @@ theorem cycleType_of_card_le_mem_cycleType_add_two {n : ℕ} {g : Perm α}
   rw [hd.card_support_mul]
   exact add_le_add_left (two_le_card_support_of_ne_one g'1) _
 #align equiv.perm.cycle_type_of_card_le_mem_cycle_type_add_two Equiv.Perm.cycleType_of_card_le_mem_cycleType_add_two
+-/
 
 end CycleType
 
+/- warning: equiv.perm.card_compl_support_modeq -> Equiv.Perm.card_compl_support_modEq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.card_compl_support_modeq Equiv.Perm.card_compl_support_modEqₓ'. -/
 theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime] {σ : Perm α}
     (hσ : σ ^ p ^ n = 1) : σ.supportᶜ.card ≡ Fintype.card α [MOD p] :=
   by
@@ -373,6 +506,12 @@ theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime
   exact dvd_pow_self _ fun h => (one_lt_of_mem_cycle_type hk).Ne <| by rw [h, pow_zero]
 #align equiv.perm.card_compl_support_modeq Equiv.Perm.card_compl_support_modEq
 
+/- warning: equiv.perm.exists_fixed_point_of_prime -> Equiv.Perm.exists_fixed_point_of_prime is a dubious translation:
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+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)], (Not (Dvd.Dvd.{0} Nat Nat.hasDvd p (Fintype.card.{u1} α _inst_1))) -> (forall {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (OfNat.mk.{u1} (Equiv.Perm.{succ u1} α) 1 (One.one.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasOne.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))))))) -> (Exists.{succ u1} α (fun (a : α) => Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) σ a) a)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)], (Not (Dvd.dvd.{0} Nat Nat.instDvdNat p (Fintype.card.{u1} α _inst_1))) -> (forall {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (One.toOfNat1.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toOne.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))))) -> (Exists.{succ u1} α (fun (a : α) => Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α α) σ a) a)))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.exists_fixed_point_of_prime Equiv.Perm.exists_fixed_point_of_primeₓ'. -/
 theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by
   classical
@@ -385,6 +524,12 @@ theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p 
           (card_compl_support_modeq hσ).symm)
 #align equiv.perm.exists_fixed_point_of_prime Equiv.Perm.exists_fixed_point_of_prime
 
+/- warning: equiv.perm.exists_fixed_point_of_prime' -> Equiv.Perm.exists_fixed_point_of_prime' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)], (Dvd.Dvd.{0} Nat Nat.hasDvd p (Fintype.card.{u1} α _inst_1)) -> (forall {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (OfNat.mk.{u1} (Equiv.Perm.{succ u1} α) 1 (One.one.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasOne.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))))))) -> (forall {a : α}, (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) σ a) a) -> (Exists.{succ u1} α (fun (b : α) => And (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) σ b) b) (Ne.{succ u1} α b a)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] {p : Nat} {n : Nat} [hp : Fact (Nat.Prime p)], (Dvd.dvd.{0} Nat Nat.instDvdNat p (Fintype.card.{u1} α _inst_1)) -> (forall {σ : Equiv.Perm.{succ u1} α}, (Eq.{succ u1} (Equiv.Perm.{succ u1} α) (HPow.hPow.{u1, 0, u1} (Equiv.Perm.{succ u1} α) Nat (Equiv.Perm.{succ u1} α) (instHPow.{u1, 0} (Equiv.Perm.{succ u1} α) Nat (Monoid.Pow.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) σ (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) (OfNat.ofNat.{u1} (Equiv.Perm.{succ u1} α) 1 (One.toOfNat1.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toOne.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))))) -> (forall {a : α}, (Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α α) σ a) a) -> (Exists.{succ u1} α (fun (b : α) => And (Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α α) σ b) b) (Ne.{succ u1} α b a)))))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.exists_fixed_point_of_prime' Equiv.Perm.exists_fixed_point_of_prime'ₓ'. -/
 theorem exists_fixed_point_of_prime' {p n : ℕ} [hp : Fact p.Prime] (hα : p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) {a : α} (ha : σ a = a) : ∃ b : α, σ b = b ∧ b ≠ a := by
   classical
@@ -400,11 +545,14 @@ theorem exists_fixed_point_of_prime' {p n : ℕ} [hp : Fact p.Prime] (hα : p 
     exact ⟨b, (h b).mp hb1, hb2⟩
 #align equiv.perm.exists_fixed_point_of_prime' Equiv.Perm.exists_fixed_point_of_prime'
 
+#print Equiv.Perm.isCycle_of_prime_order' /-
 theorem isCycle_of_prime_order' {σ : Perm α} (h1 : (orderOf σ).Prime)
     (h2 : Fintype.card α < 2 * orderOf σ) : σ.IsCycle := by
   classical exact is_cycle_of_prime_order h1 (lt_of_le_of_lt σ.support.card_le_univ h2)
 #align equiv.perm.is_cycle_of_prime_order' Equiv.Perm.isCycle_of_prime_order'
+-/
 
+#print Equiv.Perm.isCycle_of_prime_order'' /-
 theorem isCycle_of_prime_order'' {σ : Perm α} (h1 : (Fintype.card α).Prime)
     (h2 : orderOf σ = Fintype.card α) : σ.IsCycle :=
   isCycle_of_prime_order' ((congr_arg Nat.Prime h2).mpr h1)
@@ -413,45 +561,67 @@ theorem isCycle_of_prime_order'' {σ : Perm α} (h1 : (Fintype.card α).Prime)
         rw [← one_mul (Fintype.card α), ← h2, mul_lt_mul_right (orderOf_pos σ)]
         exact one_lt_two)
 #align equiv.perm.is_cycle_of_prime_order'' Equiv.Perm.isCycle_of_prime_order''
+-/
 
 section Cauchy
 
 variable (G : Type _) [Group G] (n : ℕ)
 
+#print Equiv.Perm.vectorsProdEqOne /-
 /-- The type of vectors with terms from `G`, length `n`, and product equal to `1:G`. -/
 def vectorsProdEqOne : Set (Vector G n) :=
   { v | v.toList.Prod = 1 }
 #align equiv.perm.vectors_prod_eq_one Equiv.Perm.vectorsProdEqOne
+-/
 
 namespace VectorsProdEqOne
 
+/- warning: equiv.perm.vectors_prod_eq_one.mem_iff -> Equiv.Perm.VectorsProdEqOne.mem_iff is a dubious translation:
+lean 3 declaration is
+  forall (G : Type.{u1}) [_inst_2 : Group.{u1} G] {n : Nat} (v : Vector.{u1} G n), Iff (Membership.Mem.{u1, u1} (Vector.{u1} G n) (Set.{u1} (Vector.{u1} G n)) (Set.hasMem.{u1} (Vector.{u1} G n)) v (Equiv.Perm.vectorsProdEqOne.{u1} G _inst_2 n)) (Eq.{succ u1} G (List.prod.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (Vector.toList.{u1} G n v)) (OfNat.ofNat.{u1} G 1 (OfNat.mk.{u1} G 1 (One.one.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))))))))
+but is expected to have type
+  forall (G : Type.{u1}) [_inst_2 : Group.{u1} G] {n : Nat} (v : Vector.{u1} G n), Iff (Membership.mem.{u1, u1} (Vector.{u1} G n) (Set.{u1} (Vector.{u1} G n)) (Set.instMembershipSet.{u1} (Vector.{u1} G n)) v (Equiv.Perm.vectorsProdEqOne.{u1} G _inst_2 n)) (Eq.{succ u1} G (List.prod.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (Vector.toList.{u1} G n v)) (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))))))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.vectors_prod_eq_one.mem_iff Equiv.Perm.VectorsProdEqOne.mem_iffₓ'. -/
 theorem mem_iff {n : ℕ} (v : Vector G n) : v ∈ vectorsProdEqOne G n ↔ v.toList.Prod = 1 :=
   Iff.rfl
-#align equiv.perm.vectors_prod_eq_one.mem_iff Equiv.Perm.vectorsProdEqOne.mem_iff
+#align equiv.perm.vectors_prod_eq_one.mem_iff Equiv.Perm.VectorsProdEqOne.mem_iff
 
+#print Equiv.Perm.VectorsProdEqOne.zero_eq /-
 theorem zero_eq : vectorsProdEqOne G 0 = {Vector.nil} :=
   Set.eq_singleton_iff_unique_mem.mpr ⟨Eq.refl (1 : G), fun v hv => v.eq_nil⟩
-#align equiv.perm.vectors_prod_eq_one.zero_eq Equiv.Perm.vectorsProdEqOne.zero_eq
+#align equiv.perm.vectors_prod_eq_one.zero_eq Equiv.Perm.VectorsProdEqOne.zero_eq
+-/
 
+/- warning: equiv.perm.vectors_prod_eq_one.one_eq -> Equiv.Perm.VectorsProdEqOne.one_eq is a dubious translation:
+lean 3 declaration is
+  forall (G : Type.{u1}) [_inst_2 : Group.{u1} G], Eq.{succ u1} (Set.{u1} (Vector.{u1} G (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Equiv.Perm.vectorsProdEqOne.{u1} G _inst_2 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Singleton.singleton.{u1, u1} (Vector.{u1} G (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Set.{u1} (Vector.{u1} G (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Set.hasSingleton.{u1} (Vector.{u1} G (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Vector.cons.{u1} G (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (OfNat.ofNat.{u1} G 1 (OfNat.mk.{u1} G 1 (One.one.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))))))) (Vector.nil.{u1} G)))
+but is expected to have type
+  forall (G : Type.{u1}) [_inst_2 : Group.{u1} G], Eq.{succ u1} (Set.{u1} (Vector.{u1} G (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Equiv.Perm.vectorsProdEqOne.{u1} G _inst_2 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Singleton.singleton.{u1, u1} (Vector.{u1} G (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Set.{u1} (Vector.{u1} G (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Set.instSingletonSet.{u1} (Vector.{u1} G (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Vector.cons.{u1} G (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))))) (Vector.nil.{u1} G)))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.vectors_prod_eq_one.one_eq Equiv.Perm.VectorsProdEqOne.one_eqₓ'. -/
 theorem one_eq : vectorsProdEqOne G 1 = {Vector.nil.cons 1} :=
   by
   simp_rw [Set.eq_singleton_iff_unique_mem, mem_iff, Vector.toList_singleton, List.prod_singleton,
     Vector.head_cons]
   exact ⟨rfl, fun v hv => v.cons_head_tail.symm.trans (congr_arg₂ Vector.cons hv v.tail.eq_nil)⟩
-#align equiv.perm.vectors_prod_eq_one.one_eq Equiv.Perm.vectorsProdEqOne.one_eq
+#align equiv.perm.vectors_prod_eq_one.one_eq Equiv.Perm.VectorsProdEqOne.one_eq
 
+#print Equiv.Perm.VectorsProdEqOne.zeroUnique /-
 instance zeroUnique : Unique (vectorsProdEqOne G 0) :=
   by
   rw [zero_eq]
   exact Set.uniqueSingleton Vector.nil
-#align equiv.perm.vectors_prod_eq_one.zero_unique Equiv.Perm.vectorsProdEqOne.zeroUnique
+#align equiv.perm.vectors_prod_eq_one.zero_unique Equiv.Perm.VectorsProdEqOne.zeroUnique
+-/
 
+#print Equiv.Perm.VectorsProdEqOne.oneUnique /-
 instance oneUnique : Unique (vectorsProdEqOne G 1) :=
   by
   rw [one_eq]
   exact Set.uniqueSingleton (vector.nil.cons 1)
-#align equiv.perm.vectors_prod_eq_one.one_unique Equiv.Perm.vectorsProdEqOne.oneUnique
+#align equiv.perm.vectors_prod_eq_one.one_unique Equiv.Perm.VectorsProdEqOne.oneUnique
+-/
 
+#print Equiv.Perm.VectorsProdEqOne.vectorEquiv /-
 /-- Given a vector `v` of length `n`, make a vector of length `n + 1` whose product is `1`,
 by appending the inverse of the product of `v`. -/
 @[simps]
@@ -470,8 +640,10 @@ def vectorEquiv : Vector G n ≃ vectorsProdEqOne G (n + 1)
                   exact v.2)).symm
             rfl).trans
         v.1.cons_head!_tail)
-#align equiv.perm.vectors_prod_eq_one.vector_equiv Equiv.Perm.vectorsProdEqOne.vectorEquiv
+#align equiv.perm.vectors_prod_eq_one.vector_equiv Equiv.Perm.VectorsProdEqOne.vectorEquiv
+-/
 
+#print Equiv.Perm.VectorsProdEqOne.equivVector /-
 /-- Given a vector `v` of length `n` whose product is 1, make a vector of length `n - 1`,
 by deleting the last entry of `v`. -/
 def equivVector : vectorsProdEqOne G n ≃ Vector G (n - 1) :=
@@ -482,36 +654,48 @@ def equivVector : vectorsProdEqOne G n ≃ Vector G (n - 1) :=
           rw [hn]
           apply equiv_of_unique
       else by rw [tsub_add_cancel_of_le (Nat.pos_of_ne_zero hn).nat_succ_le])).symm
-#align equiv.perm.vectors_prod_eq_one.equiv_vector Equiv.Perm.vectorsProdEqOne.equivVector
+#align equiv.perm.vectors_prod_eq_one.equiv_vector Equiv.Perm.VectorsProdEqOne.equivVector
+-/
 
 instance [Fintype G] : Fintype (vectorsProdEqOne G n) :=
   Fintype.ofEquiv (Vector G (n - 1)) (equivVector G n).symm
 
+#print Equiv.Perm.VectorsProdEqOne.card /-
 theorem card [Fintype G] : Fintype.card (vectorsProdEqOne G n) = Fintype.card G ^ (n - 1) :=
   (Fintype.card_congr (equivVector G n)).trans (card_vector (n - 1))
-#align equiv.perm.vectors_prod_eq_one.card Equiv.Perm.vectorsProdEqOne.card
+#align equiv.perm.vectors_prod_eq_one.card Equiv.Perm.VectorsProdEqOne.card
+-/
 
 variable {G n} {g : G} (v : vectorsProdEqOne G n) (j k : ℕ)
 
+#print Equiv.Perm.VectorsProdEqOne.rotate /-
 /-- Rotate a vector whose product is 1. -/
 def rotate : vectorsProdEqOne G n :=
   ⟨⟨_, (v.1.1.length_rotate k).trans v.1.2⟩, List.prod_rotate_eq_one_of_prod_eq_one v.2 k⟩
-#align equiv.perm.vectors_prod_eq_one.rotate Equiv.Perm.vectorsProdEqOne.rotate
+#align equiv.perm.vectors_prod_eq_one.rotate Equiv.Perm.VectorsProdEqOne.rotate
+-/
 
+#print Equiv.Perm.VectorsProdEqOne.rotate_zero /-
 theorem rotate_zero : rotate v 0 = v :=
   Subtype.ext (Subtype.ext v.1.1.rotate_zero)
-#align equiv.perm.vectors_prod_eq_one.rotate_zero Equiv.Perm.vectorsProdEqOne.rotate_zero
+#align equiv.perm.vectors_prod_eq_one.rotate_zero Equiv.Perm.VectorsProdEqOne.rotate_zero
+-/
 
+#print Equiv.Perm.VectorsProdEqOne.rotate_rotate /-
 theorem rotate_rotate : rotate (rotate v j) k = rotate v (j + k) :=
   Subtype.ext (Subtype.ext (v.1.1.rotate_rotate j k))
-#align equiv.perm.vectors_prod_eq_one.rotate_rotate Equiv.Perm.vectorsProdEqOne.rotate_rotate
+#align equiv.perm.vectors_prod_eq_one.rotate_rotate Equiv.Perm.VectorsProdEqOne.rotate_rotate
+-/
 
+#print Equiv.Perm.VectorsProdEqOne.rotate_length /-
 theorem rotate_length : rotate v n = v :=
   Subtype.ext (Subtype.ext ((congr_arg _ v.1.2.symm).trans v.1.1.rotate_length))
-#align equiv.perm.vectors_prod_eq_one.rotate_length Equiv.Perm.vectorsProdEqOne.rotate_length
+#align equiv.perm.vectors_prod_eq_one.rotate_length Equiv.Perm.VectorsProdEqOne.rotate_length
+-/
 
 end VectorsProdEqOne
 
+#print exists_prime_orderOf_dvd_card /-
 /-- For every prime `p` dividing the order of a finite group `G` there exists an element of order
 `p` in `G`. This is known as Cauchy's theorem. -/
 theorem exists_prime_orderOf_dvd_card {G : Type _} [Group G] [Fintype G] (p : ℕ) [hp : Fact p.Prime]
@@ -546,18 +730,27 @@ theorem exists_prime_orderOf_dvd_card {G : Type _} [Group G] [Fintype G] (p : 
   · rw [Subtype.ext_iff_val, Subtype.ext_iff_val, hg, hg', v.1.2]
     rfl
 #align exists_prime_order_of_dvd_card exists_prime_orderOf_dvd_card
+-/
 
+#print exists_prime_addOrderOf_dvd_card /-
 /-- For every prime `p` dividing the order of a finite additive group `G` there exists an element of
 order `p` in `G`. This is the additive version of Cauchy's theorem. -/
 theorem exists_prime_addOrderOf_dvd_card {G : Type _} [AddGroup G] [Fintype G] (p : ℕ)
     [hp : Fact p.Prime] (hdvd : p ∣ Fintype.card G) : ∃ x : G, addOrderOf x = p :=
   @exists_prime_orderOf_dvd_card (Multiplicative G) _ _ _ _ hdvd
 #align exists_prime_add_order_of_dvd_card exists_prime_addOrderOf_dvd_card
+-/
 
 attribute [to_additive exists_prime_addOrderOf_dvd_card] exists_prime_orderOf_dvd_card
 
 end Cauchy
 
+/- warning: equiv.perm.subgroup_eq_top_of_swap_mem -> Equiv.Perm.subgroup_eq_top_of_swap_mem is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.subgroup_eq_top_of_swap_mem Equiv.Perm.subgroup_eq_top_of_swap_memₓ'. -/
 theorem subgroup_eq_top_of_swap_mem [DecidableEq α] {H : Subgroup (Perm α)}
     [d : DecidablePred (· ∈ H)] {τ : Perm α} (h0 : (Fintype.card α).Prime)
     (h1 : Fintype.card α ∣ Fintype.card H) (h2 : τ ∈ H) (h3 : IsSwap τ) : H = ⊤ :=
@@ -577,6 +770,7 @@ section Partition
 
 variable [DecidableEq α]
 
+#print Equiv.Perm.partition /-
 /-- The partition corresponding to a permutation -/
 def partition (σ : Perm α) : (Fintype.card α).partitionₓ
     where
@@ -589,12 +783,21 @@ def partition (σ : Perm α) : (Fintype.card α).partitionₓ
     rw [sum_add, sum_cycle_type, Multiset.sum_replicate, nsmul_eq_mul, Nat.cast_id, mul_one,
       add_tsub_cancel_of_le σ.support.card_le_univ]
 #align equiv.perm.partition Equiv.Perm.partition
+-/
 
+#print Equiv.Perm.parts_partition /-
 theorem parts_partition {σ : Perm α} :
     σ.partitionₓ.parts = σ.cycleType + replicate (Fintype.card α - σ.support.card) 1 :=
   rfl
 #align equiv.perm.parts_partition Equiv.Perm.parts_partition
+-/
 
+/- warning: equiv.perm.filter_parts_partition_eq_cycle_type -> Equiv.Perm.filter_parts_partition_eq_cycleType is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α}, Eq.{1} (Multiset.{0} Nat) (Multiset.filter.{0} Nat (fun (n : Nat) => LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) (fun (a : Nat) => Nat.decidableLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) a) (Nat.Partition.parts (Fintype.card.{u1} α _inst_1) (Equiv.Perm.partition.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ))) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α}, Eq.{1} (Multiset.{0} Nat) (Multiset.filter.{0} Nat (fun (n : Nat) => LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) (fun (a : Nat) => Nat.decLe (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) a) (Nat.Partition.parts (Fintype.card.{u1} α _inst_1) (Equiv.Perm.partition.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ))) (Equiv.Perm.cycleType.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ)
+Case conversion may be inaccurate. Consider using '#align equiv.perm.filter_parts_partition_eq_cycle_type Equiv.Perm.filter_parts_partition_eq_cycleTypeₓ'. -/
 theorem filter_parts_partition_eq_cycleType {σ : Perm α} :
     ((partition σ).parts.filterₓ fun n => 2 ≤ n) = σ.cycleType :=
   by
@@ -604,6 +807,7 @@ theorem filter_parts_partition_eq_cycleType {σ : Perm α} :
   decide
 #align equiv.perm.filter_parts_partition_eq_cycle_type Equiv.Perm.filter_parts_partition_eq_cycleType
 
+#print Equiv.Perm.partition_eq_of_isConj /-
 theorem partition_eq_of_isConj {σ τ : Perm α} : IsConj σ τ ↔ σ.partitionₓ = τ.partitionₓ :=
   by
   rw [is_conj_iff_cycle_type_eq]
@@ -613,6 +817,7 @@ theorem partition_eq_of_isConj {σ τ : Perm α} : IsConj σ τ ↔ σ.partition
       h]
   · rw [← filter_parts_partition_eq_cycle_type, ← filter_parts_partition_eq_cycle_type, h]
 #align equiv.perm.partition_eq_of_is_conj Equiv.Perm.partition_eq_of_isConj
+-/
 
 end Partition
 
@@ -621,23 +826,30 @@ end Partition
 -/
 
 
+#print Equiv.Perm.IsThreeCycle /-
 /-- A three-cycle is a cycle of length 3. -/
 def IsThreeCycle [DecidableEq α] (σ : Perm α) : Prop :=
   σ.cycleType = {3}
 #align equiv.perm.is_three_cycle Equiv.Perm.IsThreeCycle
+-/
 
 namespace IsThreeCycle
 
 variable [DecidableEq α] {σ : Perm α}
 
+#print Equiv.Perm.IsThreeCycle.cycleType /-
 theorem cycleType (h : IsThreeCycle σ) : σ.cycleType = {3} :=
   h
 #align equiv.perm.is_three_cycle.cycle_type Equiv.Perm.IsThreeCycle.cycleType
+-/
 
+#print Equiv.Perm.IsThreeCycle.card_support /-
 theorem card_support (h : IsThreeCycle σ) : σ.support.card = 3 := by
   rw [← sum_cycle_type, h.cycle_type, Multiset.sum_singleton]
 #align equiv.perm.is_three_cycle.card_support Equiv.Perm.IsThreeCycle.card_support
+-/
 
+#print card_support_eq_three_iff /-
 theorem card_support_eq_three_iff : σ.support.card = 3 ↔ σ.IsThreeCycle :=
   by
   refine' ⟨fun h => _, is_three_cycle.card_support⟩
@@ -657,21 +869,42 @@ theorem card_support_eq_three_iff : σ.support.card = 3 ↔ σ.IsThreeCycle :=
     linarith
   cases this (two_le_of_mem_cycle_type (mem_of_mem_erase hm)) (two_le_of_mem_cycle_type hn) h
 #align card_support_eq_three_iff card_support_eq_three_iff
+-/
 
+#print Equiv.Perm.IsThreeCycle.isCycle /-
 theorem isCycle (h : IsThreeCycle σ) : IsCycle σ := by
   rw [← card_cycle_type_eq_one, h.cycle_type, card_singleton]
 #align equiv.perm.is_three_cycle.is_cycle Equiv.Perm.IsThreeCycle.isCycle
+-/
 
+/- warning: equiv.perm.is_three_cycle.sign -> Equiv.Perm.IsThreeCycle.sign is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align equiv.perm.is_three_cycle.sign Equiv.Perm.IsThreeCycle.signₓ'. -/
 theorem sign (h : IsThreeCycle σ) : sign σ = 1 :=
   by
   rw [Equiv.Perm.sign_of_cycleType, h.cycle_type]
   rfl
 #align equiv.perm.is_three_cycle.sign Equiv.Perm.IsThreeCycle.sign
 
+/- warning: equiv.perm.is_three_cycle.inv -> Equiv.Perm.IsThreeCycle.inv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {f : Equiv.Perm.{succ u1} α}, (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f) -> (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (Inv.inv.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toInv.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) f))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.is_three_cycle.inv Equiv.Perm.IsThreeCycle.invₓ'. -/
 theorem inv {f : Perm α} (h : IsThreeCycle f) : IsThreeCycle f⁻¹ := by
   rwa [is_three_cycle, cycle_type_inv]
 #align equiv.perm.is_three_cycle.inv Equiv.Perm.IsThreeCycle.inv
 
+/- warning: equiv.perm.is_three_cycle.inv_iff -> Equiv.Perm.IsThreeCycle.inv_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {f : Equiv.Perm.{succ u1} α}, Iff (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (Inv.inv.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toHasInv.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))) f)) (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {f : Equiv.Perm.{succ u1} α}, Iff (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (Inv.inv.{u1} (Equiv.Perm.{succ u1} α) (InvOneClass.toInv.{u1} (Equiv.Perm.{succ u1} α) (DivInvOneMonoid.toInvOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivisionMonoid.toDivInvOneMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivisionMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) f)) (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) f)
+Case conversion may be inaccurate. Consider using '#align equiv.perm.is_three_cycle.inv_iff Equiv.Perm.IsThreeCycle.inv_iffₓ'. -/
 @[simp]
 theorem inv_iff {f : Perm α} : IsThreeCycle f⁻¹ ↔ IsThreeCycle f :=
   ⟨by
@@ -679,10 +912,18 @@ theorem inv_iff {f : Perm α} : IsThreeCycle f⁻¹ ↔ IsThreeCycle f :=
     apply inv, inv⟩
 #align equiv.perm.is_three_cycle.inv_iff Equiv.Perm.IsThreeCycle.inv_iff
 
+#print Equiv.Perm.IsThreeCycle.orderOf /-
 theorem orderOf {g : Perm α} (ht : IsThreeCycle g) : orderOf g = 3 := by
   rw [← lcm_cycle_type, ht.cycle_type, Multiset.lcm_singleton, normalize_eq]
 #align equiv.perm.is_three_cycle.order_of Equiv.Perm.IsThreeCycle.orderOf
+-/
 
+/- warning: equiv.perm.is_three_cycle.is_three_cycle_sq -> Equiv.Perm.IsThreeCycle.isThreeCycle_sq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {g : Equiv.Perm.{succ u1} α}, (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) g) -> (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) g g))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {g : Equiv.Perm.{succ u1} α}, (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) g) -> (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) g g))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.is_three_cycle.is_three_cycle_sq Equiv.Perm.IsThreeCycle.isThreeCycle_sqₓ'. -/
 theorem isThreeCycle_sq {g : Perm α} (ht : IsThreeCycle g) : IsThreeCycle (g * g) :=
   by
   rw [← pow_two, ← card_support_eq_three_iff, support_pow_coprime, ht.card_support]
@@ -696,6 +937,12 @@ section
 
 variable [DecidableEq α]
 
+/- warning: equiv.perm.is_three_cycle_swap_mul_swap_same -> Equiv.Perm.isThreeCycle_swap_mul_swap_same is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {a : α} {b : α} {c : α}, (Ne.{succ u1} α a b) -> (Ne.{succ u1} α a c) -> (Ne.{succ u1} α b c) -> (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) (Equiv.swap.{succ u1} α (fun (a : α) (b : α) => _inst_2 a b) a b) (Equiv.swap.{succ u1} α (fun (a : α) (b : α) => _inst_2 a b) a c)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {a : α} {b : α} {c : α}, (Ne.{succ u1} α a b) -> (Ne.{succ u1} α a c) -> (Ne.{succ u1} α b c) -> (Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) (Equiv.swap.{succ u1} α (fun (a : α) (b : α) => _inst_2 a b) a b) (Equiv.swap.{succ u1} α (fun (a : α) (b : α) => _inst_2 a b) a c)))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.is_three_cycle_swap_mul_swap_same Equiv.Perm.isThreeCycle_swap_mul_swap_sameₓ'. -/
 theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠ c) (bc : b ≠ c) :
     IsThreeCycle (swap a b * swap a c) :=
   by
@@ -718,6 +965,12 @@ theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠
 
 open Subgroup
 
+/- warning: equiv.perm.swap_mul_swap_same_mem_closure_three_cycles -> Equiv.Perm.swap_mul_swap_same_mem_closure_three_cycles is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {a : α} {b : α} {c : α}, (Ne.{succ u1} α a b) -> (Ne.{succ u1} α a c) -> (Membership.Mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Subgroup.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)) (Equiv.Perm.{succ u1} α) (Subgroup.setLike.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))) (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) (Equiv.swap.{succ u1} α (fun (a : α) (b : α) => _inst_2 a b) a b) (Equiv.swap.{succ u1} α (fun (a : α) (b : α) => _inst_2 a b) a c)) (Subgroup.closure.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α) (setOf.{u1} (Equiv.Perm.{succ u1} α) (fun (σ : Equiv.Perm.{succ u1} α) => Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {a : α} {b : α} {c : α}, (Ne.{succ u1} α a b) -> (Ne.{succ u1} α a c) -> (Membership.mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Subgroup.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)) (Equiv.Perm.{succ u1} α) (Subgroup.instSetLikeSubgroup.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))) (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) (Equiv.swap.{succ u1} α (fun (a : α) (b : α) => _inst_2 a b) a b) (Equiv.swap.{succ u1} α (fun (a : α) (b : α) => _inst_2 a b) a c)) (Subgroup.closure.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α) (setOf.{u1} (Equiv.Perm.{succ u1} α) (fun (σ : Equiv.Perm.{succ u1} α) => Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ))))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.swap_mul_swap_same_mem_closure_three_cycles Equiv.Perm.swap_mul_swap_same_mem_closure_three_cyclesₓ'. -/
 theorem swap_mul_swap_same_mem_closure_three_cycles {a b c : α} (ab : a ≠ b) (ac : a ≠ c) :
     swap a b * swap a c ∈ closure { σ : Perm α | IsThreeCycle σ } :=
   by
@@ -727,6 +980,12 @@ theorem swap_mul_swap_same_mem_closure_three_cycles {a b c : α} (ab : a ≠ b)
   exact subset_closure (is_three_cycle_swap_mul_swap_same ab ac bc)
 #align equiv.perm.swap_mul_swap_same_mem_closure_three_cycles Equiv.Perm.swap_mul_swap_same_mem_closure_three_cycles
 
+/- warning: equiv.perm.is_swap.mul_mem_closure_three_cycles -> Equiv.Perm.IsSwap.mul_mem_closure_three_cycles is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α} {τ : Equiv.Perm.{succ u1} α}, (Equiv.Perm.IsSwap.{u1} α (fun (a : α) (b : α) => _inst_2 a b) σ) -> (Equiv.Perm.IsSwap.{u1} α (fun (a : α) (b : α) => _inst_2 a b) τ) -> (Membership.Mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Subgroup.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)) (Equiv.Perm.{succ u1} α) (Subgroup.setLike.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))) (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toHasMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) σ τ) (Subgroup.closure.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α) (setOf.{u1} (Equiv.Perm.{succ u1} α) (fun (σ : Equiv.Perm.{succ u1} α) => Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {σ : Equiv.Perm.{succ u1} α} {τ : Equiv.Perm.{succ u1} α}, (Equiv.Perm.IsSwap.{u1} α (fun (a : α) (b : α) => _inst_2 a b) σ) -> (Equiv.Perm.IsSwap.{u1} α (fun (a : α) (b : α) => _inst_2 a b) τ) -> (Membership.mem.{u1, u1} (Equiv.Perm.{succ u1} α) (Subgroup.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)) (Equiv.Perm.{succ u1} α) (Subgroup.instSetLikeSubgroup.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))) (HMul.hMul.{u1, u1, u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u1} α) (instHMul.{u1} (Equiv.Perm.{succ u1} α) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))))) σ τ) (Subgroup.closure.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α) (setOf.{u1} (Equiv.Perm.{succ u1} α) (fun (σ : Equiv.Perm.{succ u1} α) => Equiv.Perm.IsThreeCycle.{u1} α _inst_1 (fun (a : α) (b : α) => _inst_2 a b) σ))))
+Case conversion may be inaccurate. Consider using '#align equiv.perm.is_swap.mul_mem_closure_three_cycles Equiv.Perm.IsSwap.mul_mem_closure_three_cyclesₓ'. -/
 theorem IsSwap.mul_mem_closure_three_cycles {σ τ : Perm α} (hσ : IsSwap σ) (hτ : IsSwap τ) :
     σ * τ ∈ closure { σ : Perm α | IsThreeCycle σ } :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

@@ -330,7 +330,7 @@ theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
   · intro h
     obtain ⟨l, rfl, hlc, hld⟩ := trunc_cycle_factors σ
     rw [cycle_type_eq _ rfl hlc hld] at h
-    obtain ⟨c, cl, rfl⟩ := List.exists_of_mem_map' h
+    obtain ⟨c, cl, rfl⟩ := List.exists_of_mem_map h
     rw [(List.perm_cons_erase cl).pairwise_iff fun _ _ hd => _] at hld
     swap
     · exact hd.symm

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

@@ -48,18 +48,18 @@ variable [DecidableEq α]
 
 /-- The cycle type of a permutation -/
 def cycleType (σ : Perm α) : Multiset ℕ :=
-  σ.cycleFactorsFinset.1.map (Finset.card ∘ Support)
+  σ.cycleFactorsFinset.1.map (Finset.card ∘ support)
 #align equiv.perm.cycle_type Equiv.Perm.cycleType
 
 theorem cycleType_def (σ : Perm α) :
-    σ.cycleType = σ.cycleFactorsFinset.1.map (Finset.card ∘ Support) :=
+    σ.cycleType = σ.cycleFactorsFinset.1.map (Finset.card ∘ support) :=
   rfl
 #align equiv.perm.cycle_type_def Equiv.Perm.cycleType_def
 
 theorem cycleType_eq' {σ : Perm α} (s : Finset (Perm α)) (h1 : ∀ f : Perm α, f ∈ s → f.IsCycle)
     (h2 : (s : Set (Perm α)).Pairwise Disjoint)
     (h0 : s.noncommProd id (h2.imp fun _ _ => Disjoint.commute) = σ) :
-    σ.cycleType = s.1.map (Finset.card ∘ Support) :=
+    σ.cycleType = s.1.map (Finset.card ∘ support) :=
   by
   rw [cycle_type_def]
   congr
@@ -69,7 +69,7 @@ theorem cycleType_eq' {σ : Perm α} (s : Finset (Perm α)) (h1 : ∀ f : Perm 
 
 theorem cycleType_eq {σ : Perm α} (l : List (Perm α)) (h0 : l.Prod = σ)
     (h1 : ∀ σ : Perm α, σ ∈ l → σ.IsCycle) (h2 : l.Pairwise Disjoint) :
-    σ.cycleType = l.map (Finset.card ∘ Support) :=
+    σ.cycleType = l.map (Finset.card ∘ support) :=
   by
   have hl : l.nodup := nodup_of_pairwise_disjoint_cycles h1 h2
   rw [cycle_type_eq' l.to_finset]
@@ -103,7 +103,7 @@ theorem one_lt_of_mem_cycleType {σ : Perm α} {n : ℕ} (h : n ∈ σ.cycleType
   two_le_of_mem_cycleType h
 #align equiv.perm.one_lt_of_mem_cycle_type Equiv.Perm.one_lt_of_mem_cycleType
 
-theorem IsCycle.cycleType {σ : Perm α} (hσ : IsCycle σ) : σ.cycleType = [σ.Support.card] :=
+theorem IsCycle.cycleType {σ : Perm α} (hσ : IsCycle σ) : σ.cycleType = [σ.support.card] :=
   cycleType_eq [σ] (mul_one σ) (fun τ hτ => (congr_arg IsCycle (List.mem_singleton.mp hτ)).mpr hσ)
     (pairwise_singleton Disjoint σ)
 #align equiv.perm.is_cycle.cycle_type Equiv.Perm.IsCycle.cycleType
@@ -154,8 +154,8 @@ theorem cycleType_conj {σ τ : Perm α} : (τ * σ * τ⁻¹).cycleType = σ.cy
         rw [perm.mul_apply, perm.mul_apply, h, apply_inv_self]
 #align equiv.perm.cycle_type_conj Equiv.Perm.cycleType_conj
 
-theorem sum_cycleType (σ : Perm α) : σ.cycleType.Sum = σ.Support.card :=
-  cycle_induction_on (fun τ : Perm α => τ.cycleType.Sum = τ.Support.card) σ
+theorem sum_cycleType (σ : Perm α) : σ.cycleType.Sum = σ.support.card :=
+  cycle_induction_on (fun τ : Perm α => τ.cycleType.Sum = τ.support.card) σ
     (by rw [cycle_type_one, sum_zero, support_one, Finset.card_empty])
     (fun σ hσ => by rw [hσ.cycle_type, coe_sum, List.sum_singleton]) fun σ τ hστ hc hσ hτ => by
     rw [hστ.cycle_type, sum_add, hσ, hτ, hστ.card_support_mul]
@@ -211,7 +211,7 @@ theorem orderOf_cycleOf_dvd_orderOf (f : Perm α) (x : α) : orderOf (cycleOf f
     · simp [(is_cycle_cycle_of _ hx).orderOf]
 #align equiv.perm.order_of_cycle_of_dvd_order_of Equiv.Perm.orderOf_cycleOf_dvd_orderOf
 
-theorem two_dvd_card_support {σ : Perm α} (hσ : σ ^ 2 = 1) : 2 ∣ σ.Support.card :=
+theorem two_dvd_card_support {σ : Perm α} (hσ : σ ^ 2 = 1) : 2 ∣ σ.support.card :=
   (congr_arg (Dvd.Dvd 2) σ.sum_cycleType).mp
     (Multiset.dvd_sum fun n hn => by
       rw [le_antisymm
@@ -235,7 +235,7 @@ theorem cycleType_prime_order {σ : Perm α} (hσ : (orderOf σ).Prime) :
 #align equiv.perm.cycle_type_prime_order Equiv.Perm.cycleType_prime_order
 
 theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
-    (h2 : σ.Support.card < 2 * orderOf σ) : σ.IsCycle :=
+    (h2 : σ.support.card < 2 * orderOf σ) : σ.IsCycle :=
   by
   obtain ⟨n, hn⟩ := cycle_type_prime_order h1
   rw [← σ.sum_cycle_type, hn, Multiset.sum_replicate, nsmul_eq_mul, Nat.cast_id,
@@ -324,7 +324,7 @@ theorem cycleType_ofSubtype {p : α → Prop} [DecidablePred p] {g : Perm (Subty
 #align equiv.perm.cycle_type_of_subtype Equiv.Perm.cycleType_ofSubtype
 
 theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
-    n ∈ cycleType σ ↔ ∃ c τ : Perm α, σ = c * τ ∧ Disjoint c τ ∧ IsCycle c ∧ c.Support.card = n :=
+    n ∈ cycleType σ ↔ ∃ c τ : Perm α, σ = c * τ ∧ Disjoint c τ ∧ IsCycle c ∧ c.support.card = n :=
   by
   constructor
   · intro h
@@ -344,7 +344,7 @@ theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
 #align equiv.perm.mem_cycle_type_iff Equiv.Perm.mem_cycleType_iff
 
 theorem le_card_support_of_mem_cycleType {n : ℕ} {σ : Perm α} (h : n ∈ cycleType σ) :
-    n ≤ σ.Support.card :=
+    n ≤ σ.support.card :=
   (le_sum_of_mem h).trans (le_of_eq σ.sum_cycleType)
 #align equiv.perm.le_card_support_of_mem_cycle_type Equiv.Perm.le_card_support_of_mem_cycleType
 
@@ -355,7 +355,7 @@ theorem cycleType_of_card_le_mem_cycleType_add_two {n : ℕ} {g : Perm α}
   by_cases g'1 : g' = 1
   · rw [hd.cycle_type, hc.cycle_type, coe_singleton, g'1, cycle_type_one, add_zero]
   contrapose! hn2
-  apply le_trans _ (c * g').Support.card_le_univ
+  apply le_trans _ (c * g').support.card_le_univ
   rw [hd.card_support_mul]
   exact add_le_add_left (two_le_card_support_of_ne_one g'1) _
 #align equiv.perm.cycle_type_of_card_le_mem_cycle_type_add_two Equiv.Perm.cycleType_of_card_le_mem_cycleType_add_two
@@ -363,7 +363,7 @@ theorem cycleType_of_card_le_mem_cycleType_add_two {n : ℕ} {g : Perm α}
 end CycleType
 
 theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime] {σ : Perm α}
-    (hσ : σ ^ p ^ n = 1) : σ.Supportᶜ.card ≡ Fintype.card α [MOD p] :=
+    (hσ : σ ^ p ^ n = 1) : σ.supportᶜ.card ≡ Fintype.card α [MOD p] :=
   by
   rw [Nat.modEq_iff_dvd' σ.supportᶜ.card_le_univ, ← Finset.card_compl, compl_compl]
   refine' (congr_arg _ σ.sum_cycle_type).mp (Multiset.dvd_sum fun k hk => _)
@@ -566,8 +566,8 @@ theorem subgroup_eq_top_of_swap_mem [DecidableEq α] {H : Subgroup (Perm α)}
   obtain ⟨σ, hσ⟩ := exists_prime_orderOf_dvd_card (Fintype.card α) h1
   have hσ1 : orderOf (σ : perm α) = Fintype.card α := (orderOf_subgroup σ).trans hσ
   have hσ2 : is_cycle ↑σ := is_cycle_of_prime_order'' h0 hσ1
-  have hσ3 : (σ : perm α).Support = ⊤ :=
-    Finset.eq_univ_of_card (σ : perm α).Support (hσ2.order_of.symm.trans hσ1)
+  have hσ3 : (σ : perm α).support = ⊤ :=
+    Finset.eq_univ_of_card (σ : perm α).support (hσ2.order_of.symm.trans hσ1)
   have hσ4 : Subgroup.closure {↑σ, τ} = ⊤ := closure_prime_cycle_swap h0 hσ2 hσ3 h3
   rw [eq_top_iff, ← hσ4, Subgroup.closure_le, Set.insert_subset, Set.singleton_subset_iff]
   exact ⟨Subtype.mem σ, h2⟩
@@ -580,7 +580,7 @@ variable [DecidableEq α]
 /-- The partition corresponding to a permutation -/
 def partition (σ : Perm α) : (Fintype.card α).partitionₓ
     where
-  parts := σ.cycleType + replicate (Fintype.card α - σ.Support.card) 1
+  parts := σ.cycleType + replicate (Fintype.card α - σ.support.card) 1
   parts_pos n hn := by
     cases' mem_add.mp hn with hn hn
     · exact zero_lt_one.trans (one_lt_of_mem_cycle_type hn)
@@ -591,7 +591,7 @@ def partition (σ : Perm α) : (Fintype.card α).partitionₓ
 #align equiv.perm.partition Equiv.Perm.partition
 
 theorem parts_partition {σ : Perm α} :
-    σ.partitionₓ.parts = σ.cycleType + replicate (Fintype.card α - σ.Support.card) 1 :=
+    σ.partitionₓ.parts = σ.cycleType + replicate (Fintype.card α - σ.support.card) 1 :=
   rfl
 #align equiv.perm.parts_partition Equiv.Perm.parts_partition
 
@@ -634,11 +634,11 @@ theorem cycleType (h : IsThreeCycle σ) : σ.cycleType = {3} :=
   h
 #align equiv.perm.is_three_cycle.cycle_type Equiv.Perm.IsThreeCycle.cycleType
 
-theorem card_support (h : IsThreeCycle σ) : σ.Support.card = 3 := by
+theorem card_support (h : IsThreeCycle σ) : σ.support.card = 3 := by
   rw [← sum_cycle_type, h.cycle_type, Multiset.sum_singleton]
 #align equiv.perm.is_three_cycle.card_support Equiv.Perm.IsThreeCycle.card_support
 
-theorem card_support_eq_three_iff : σ.Support.card = 3 ↔ σ.IsThreeCycle :=
+theorem card_support_eq_three_iff : σ.support.card = 3 ↔ σ.IsThreeCycle :=
   by
   refine' ⟨fun h => _, is_three_cycle.card_support⟩
   by_cases h0 : σ.cycle_type = 0

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

@@ -490,7 +490,7 @@ theorem _root_.exists_prime_orderOf_dvd_card {G : Type*} [Group G] [Fintype G] (
   have hσ : ∀ k v, (σ ^ k) v = f k v := fun k =>
     Nat.rec (fun v => (hf1 v).symm) (fun k hk v => by
       rw [pow_succ, Perm.mul_apply, hk (σ v), Nat.succ_eq_one_add, ← hf2 1 k]
-      rfl) k
+      simp only [σ, coe_fn_mk]) k
   replace hσ : σ ^ p ^ 1 = 1 := Perm.ext fun v => by rw [pow_one, hσ, hf3, one_apply]
   let v₀ : vectorsProdEqOne G p :=
     ⟨Vector.replicate p 1, (List.prod_replicate p 1).trans (one_pow p)⟩
@@ -501,7 +501,7 @@ theorem _root_.exists_prime_orderOf_dvd_card {G : Type*} [Group G] [Fintype G] (
       (List.rotate_one_eq_self_iff_eq_replicate.mp (Subtype.ext_iff.mp (Subtype.ext_iff.mp hv1)))
   · rw [← List.prod_replicate, ← v.1.2, ← hg, show v.val.val.prod = 1 from v.2]
   · rw [Subtype.ext_iff_val, Subtype.ext_iff_val, hg, hg', v.1.2]
-    rfl
+    simp only [v₀, Vector.replicate]
 #align exists_prime_order_of_dvd_card exists_prime_orderOf_dvd_card
 
 /-- For every prime `p` dividing the order of a finite additive group `G` there exists an element of

Previously Mathlib.GroupTheory.Perm.Fin knew about LinearMap for no good reason, because it relied on Mathlib.RingTheory.Int.Basic for some basic things, but that file also has heavy imports.

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

@@ -8,7 +8,7 @@ import Mathlib.Combinatorics.Enumerative.Partition
 import Mathlib.Data.List.Rotate
 import Mathlib.GroupTheory.Perm.Cycle.Factors
 import Mathlib.GroupTheory.Perm.Closure
-import Mathlib.RingTheory.Int.Basic
+import Mathlib.Algebra.GCDMonoid.Nat
 import Mathlib.Tactic.NormNum.GCD
 
 #align_import group_theory.perm.cycle.type from "leanprover-community/mathlib"@"47adfab39a11a072db552f47594bf8ed2cf8a722"

@@ -205,7 +205,7 @@ theorem cycleType_prime_order {σ : Perm α} (hσ : (orderOf σ).Prime) :
     ∃ n : ℕ, σ.cycleType = Multiset.replicate (n + 1) (orderOf σ) := by
   refine ⟨Multiset.card σ.cycleType - 1, eq_replicate.2 ⟨?_, fun n hn ↦ ?_⟩⟩
   · rw [tsub_add_cancel_of_le]
-    rw [Nat.succ_le_iff, card_cycleType_pos, Ne.def, ← orderOf_eq_one_iff]
+    rw [Nat.succ_le_iff, card_cycleType_pos, Ne, ← orderOf_eq_one_iff]
     exact hσ.ne_one
   · exact (hσ.eq_one_or_self_of_dvd n (dvd_of_mem_cycleType hn)).resolve_left
       (one_lt_of_mem_cycleType hn).ne'
@@ -650,7 +650,7 @@ theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠
   · simp [ab, ac, bc]
   · simp only [Finset.mem_insert, Finset.mem_singleton] at hx
     rw [mem_support]
-    simp only [Perm.coe_mul, Function.comp_apply, Ne.def]
+    simp only [Perm.coe_mul, Function.comp_apply, Ne]
     obtain rfl | rfl | rfl := hx
     · rw [swap_apply_left, swap_apply_of_ne_of_ne ac.symm bc.symm]
       exact ac.symm

Reconstitute the file Algebra.Order.Monoid.WithZero from three files:

• Algebra.Order.Monoid.WithZero.Defs
• Algebra.Order.Monoid.WithZero.Basic
• Algebra.Order.WithZero

Avoid importing it in many files. Most uses were just to get le_zero_iff to work on Nat.

Before

After

@@ -215,7 +215,7 @@ theorem isCycle_of_prime_order {σ : Perm α} (h1 : (orderOf σ).Prime)
     (h2 : σ.support.card < 2 * orderOf σ) : σ.IsCycle := by
   obtain ⟨n, hn⟩ := cycleType_prime_order h1
   rw [← σ.sum_cycleType, hn, Multiset.sum_replicate, nsmul_eq_mul, Nat.cast_id,
-    mul_lt_mul_right (orderOf_pos σ), Nat.succ_lt_succ_iff, Nat.lt_succ_iff, le_zero_iff] at h2
+    mul_lt_mul_right (orderOf_pos σ), Nat.succ_lt_succ_iff, Nat.lt_succ_iff, Nat.le_zero] at h2
   rw [← card_cycleType_eq_one, hn, card_replicate, h2]
 #align equiv.perm.is_cycle_of_prime_order Equiv.Perm.isCycle_of_prime_order
 

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.

@@ -487,8 +487,10 @@ theorem _root_.exists_prime_orderOf_dvd_card {G : Type*} [Group G] [Fintype G] (
   let σ :=
     Equiv.mk (f 1) (f (p - 1)) (fun s => by rw [hf2, add_tsub_cancel_of_le hp.out.one_lt.le, hf3])
       fun s => by rw [hf2, tsub_add_cancel_of_le hp.out.one_lt.le, hf3]
-  have hσ : ∀ k v, (σ ^ k) v = f k v := fun k v =>
-    Nat.rec (hf1 v).symm (fun k hk => Eq.trans (congr_arg σ hk) (hf2 k 1 v)) k
+  have hσ : ∀ k v, (σ ^ k) v = f k v := fun k =>
+    Nat.rec (fun v => (hf1 v).symm) (fun k hk v => by
+      rw [pow_succ, Perm.mul_apply, hk (σ v), Nat.succ_eq_one_add, ← hf2 1 k]
+      rfl) k
   replace hσ : σ ^ p ^ 1 = 1 := Perm.ext fun v => by rw [pow_one, hσ, hf3, one_apply]
   let v₀ : vectorsProdEqOne G p :=
     ⟨Vector.replicate p 1, (List.prod_replicate p 1).trans (one_pow p)⟩

Move Catalan, Composition, DoubleCounting, Partition to a new folder Combinatorics.Enumerative.

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Thomas Browning
 -/
 import Mathlib.Algebra.GCDMonoid.Multiset
-import Mathlib.Combinatorics.Partition
+import Mathlib.Combinatorics.Enumerative.Partition
 import Mathlib.Data.List.Rotate
 import Mathlib.GroupTheory.Perm.Cycle.Factors
 import Mathlib.GroupTheory.Perm.Closure

These will be caught by the linter in a future lean version.

@@ -310,9 +310,9 @@ theorem le_card_support_of_mem_cycleType {n : ℕ} {σ : Perm α} (h : n ∈ cyc
 theorem cycleType_of_card_le_mem_cycleType_add_two {n : ℕ} {g : Perm α}
     (hn2 : Fintype.card α < n + 2) (hng : n ∈ g.cycleType) : g.cycleType = {n} := by
   obtain ⟨c, g', rfl, hd, hc, rfl⟩ := mem_cycleType_iff.1 hng
-  by_cases g'1 : g' = 1
-  · rw [hd.cycleType, hc.cycleType, coe_singleton, g'1, cycleType_one, add_zero]
-  contrapose! hn2
+  suffices g'1 : g' = 1 by
+    rw [hd.cycleType, hc.cycleType, coe_singleton, g'1, cycleType_one, add_zero]
+  contrapose! hn2 with g'1
   apply le_trans _ (c * g').support.card_le_univ
   rw [hd.card_support_mul]
   exact add_le_add_left (two_le_card_support_of_ne_one g'1) _

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".

@@ -75,12 +75,12 @@ theorem cycleType_eq {σ : Perm α} (l : List (Perm α)) (h0 : l.prod = σ)
   · simp [hl, h0]
 #align equiv.perm.cycle_type_eq Equiv.Perm.cycleType_eq
 
-@[simp] -- porting note: new attr
+@[simp] -- Porting note: new attr
 theorem cycleType_eq_zero {σ : Perm α} : σ.cycleType = 0 ↔ σ = 1 := by
   simp [cycleType_def, cycleFactorsFinset_eq_empty_iff]
 #align equiv.perm.cycle_type_eq_zero Equiv.Perm.cycleType_eq_zero
 
-@[simp] -- porting note: new attr
+@[simp] -- Porting note: new attr
 theorem cycleType_one : (1 : Perm α).cycleType = 0 := cycleType_eq_zero.2 rfl
 #align equiv.perm.cycle_type_one Equiv.Perm.cycleType_one
 
@@ -126,7 +126,7 @@ theorem Disjoint.cycleType {σ τ : Perm α} (h : Disjoint σ τ) :
   exact Finset.disjoint_val.2 h.disjoint_cycleFactorsFinset
 #align equiv.perm.disjoint.cycle_type Equiv.Perm.Disjoint.cycleType
 
-@[simp] -- porting note: new attr
+@[simp] -- Porting note: new attr
 theorem cycleType_inv (σ : Perm α) : σ⁻¹.cycleType = σ.cycleType :=
   cycle_induction_on (P := fun τ : Perm α => τ⁻¹.cycleType = τ.cycleType) σ rfl
     (fun σ hσ => by simp only [hσ.cycleType, hσ.inv.cycleType, support_inv])
@@ -135,7 +135,7 @@ theorem cycleType_inv (σ : Perm α) : σ⁻¹.cycleType = σ.cycleType :=
         add_comm]
 #align equiv.perm.cycle_type_inv Equiv.Perm.cycleType_inv
 
-@[simp] -- porting note: new attr
+@[simp] -- Porting note: new attr
 theorem cycleType_conj {σ τ : Perm α} : (τ * σ * τ⁻¹).cycleType = σ.cycleType := by
   induction σ using cycle_induction_on with
   | base_one => simp
@@ -168,7 +168,7 @@ theorem sign_of_cycleType (f : Perm α) :
     simp only [pow_add, pow_one, mul_neg_one, neg_mul, mul_neg, mul_assoc, mul_one]
 #align equiv.perm.sign_of_cycle_type Equiv.Perm.sign_of_cycleType
 
-@[simp] -- porting note: new attr
+@[simp] -- Porting note: new attr
 theorem lcm_cycleType (σ : Perm α) : σ.cycleType.lcm = orderOf σ := by
   induction σ using cycle_induction_on with
   | base_one => simp

The file Mathlib.GroupTheory.Perm.Cycle.Basic was too big and this PR splits it in several components:

• Mathlib.GroupTheory.Perm.Cycle.Basic contains everything related to a permutation being a cycle,
• Mathlib.GroupTheory.Perm.Cycle.Factors is about the cycles of a permutation and the decomposition of a permutation into disjoint cycles
• Mathlib.GroupTheory.Perm.Closure contains generation results for the permutation groups
• Mathlib.GroupTheory.Perm.Finite contains general results specific to permutation of finite types

I moved some results to Mathlib.GroupTheory.Perm.Support

I also moved some results from Mathlib.GroupTheory.Perm.Sign to Mathlib.GroupTheory.Perm.Finite

Some imports could be reduced, and the shake linter required a few adjustments in some other.

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>

@@ -6,7 +6,8 @@ Authors: Thomas Browning
 import Mathlib.Algebra.GCDMonoid.Multiset
 import Mathlib.Combinatorics.Partition
 import Mathlib.Data.List.Rotate
-import Mathlib.GroupTheory.Perm.Cycle.Basic
+import Mathlib.GroupTheory.Perm.Cycle.Factors
+import Mathlib.GroupTheory.Perm.Closure
 import Mathlib.RingTheory.Int.Basic
 import Mathlib.Tactic.NormNum.GCD
 
@@ -194,14 +195,14 @@ theorem orderOf_cycleOf_dvd_orderOf (f : Perm α) (x : α) : orderOf (cycleOf f
 theorem two_dvd_card_support {σ : Perm α} (hσ : σ ^ 2 = 1) : 2 ∣ σ.support.card :=
   (congr_arg (Dvd.dvd 2) σ.sum_cycleType).mp
     (Multiset.dvd_sum fun n hn => by
-      rw [le_antisymm
+      rw [_root_.le_antisymm
           (Nat.le_of_dvd zero_lt_two <|
             (dvd_of_mem_cycleType hn).trans <| orderOf_dvd_of_pow_eq_one hσ)
           (two_le_of_mem_cycleType hn)])
 #align equiv.perm.two_dvd_card_support Equiv.Perm.two_dvd_card_support
 
 theorem cycleType_prime_order {σ : Perm α} (hσ : (orderOf σ).Prime) :
-    ∃ n : ℕ, σ.cycleType = replicate (n + 1) (orderOf σ) := by
+    ∃ n : ℕ, σ.cycleType = Multiset.replicate (n + 1) (orderOf σ) := by
   refine ⟨Multiset.card σ.cycleType - 1, eq_replicate.2 ⟨?_, fun n hn ↦ ?_⟩⟩
   · rw [tsub_add_cancel_of_le]
     rw [Nat.succ_le_iff, card_cycleType_pos, Ne.def, ← orderOf_eq_one_iff]
@@ -532,7 +533,7 @@ variable [DecidableEq α]
 
 /-- The partition corresponding to a permutation -/
 def partition (σ : Perm α) : (Fintype.card α).Partition where
-  parts := σ.cycleType + replicate (Fintype.card α - σ.support.card) 1
+  parts := σ.cycleType + Multiset.replicate (Fintype.card α - σ.support.card) 1
   parts_pos {n hn} := by
     cases' mem_add.mp hn with hn hn
     · exact zero_lt_one.trans (one_lt_of_mem_cycleType hn)
@@ -543,7 +544,7 @@ def partition (σ : Perm α) : (Fintype.card α).Partition where
 #align equiv.perm.partition Equiv.Perm.partition
 
 theorem parts_partition {σ : Perm α} :
-    σ.partition.parts = σ.cycleType + replicate (Fintype.card α - σ.support.card) 1 :=
+    σ.partition.parts = σ.cycleType + Multiset.replicate (Fintype.card α - σ.support.card) 1 :=
   rfl
 #align equiv.perm.parts_partition Equiv.Perm.parts_partition
 

These did not respect the naming convention by having the coe as a prefix instead of a suffix, or vice-versa. Also add a bunch of norm_cast

@@ -146,7 +146,7 @@ theorem cycleType_conj {σ τ : Perm α} : (τ * σ * τ⁻¹).cycleType = σ.cy
 theorem sum_cycleType (σ : Perm α) : σ.cycleType.sum = σ.support.card := by
   induction σ using cycle_induction_on with
   | base_one => simp
-  | base_cycles σ hσ => rw [hσ.cycleType, coe_sum, List.sum_singleton]
+  | base_cycles σ hσ => rw [hσ.cycleType, sum_coe, List.sum_singleton]
   | induction_disjoint σ τ hd _ hσ hτ => rw [hd.cycleType, sum_add, hσ, hτ, hd.card_support_mul]
 #align equiv.perm.sum_cycle_type Equiv.Perm.sum_cycleType
 

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -598,10 +598,7 @@ theorem _root_.card_support_eq_three_iff : σ.support.card = 3 ↔ σ.IsThreeCyc
     rw [IsThreeCycle, ← cons_erase hn, h1, h, ← cons_zero]
   obtain ⟨m, hm⟩ := exists_mem_of_ne_zero h1
   rw [← sum_cycleType, ← cons_erase hn, ← cons_erase hm, Multiset.sum_cons, Multiset.sum_cons] at h
-  -- TODO: linarith [...] should solve this directly
-  have : ∀ {k}, 2 ≤ m → 2 ≤ n → n + (m + k) = 3 → False := by
-    intros
-    linarith
+  have : ∀ {k}, 2 ≤ m → 2 ≤ n → n + (m + k) = 3 → False := by omega
   cases this (two_le_of_mem_cycleType (mem_of_mem_erase hm)) (two_le_of_mem_cycleType hn) h
 #align card_support_eq_three_iff card_support_eq_three_iff
 

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

@@ -346,7 +346,7 @@ theorem card_fixedPoints_modEq [DecidableEq α] {f : Function.End α} {p n : ℕ
     this ▸ (card_compl_support_modEq hσ).symm
   suffices f.fixedPoints = (support σ)ᶜ by
     simp only [this]; apply Fintype.card_coe
-  simp [Set.ext_iff, IsFixedPt]
+  simp [σ, Set.ext_iff, IsFixedPt]
 
 theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by

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

This follows on from #6964.

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

@@ -339,13 +339,13 @@ theorem card_fixedPoints_modEq [DecidableEq α] {f : Function.End α} {p n : ℕ
   let σ : α ≃ α := ⟨f, f ^ (p ^ n - 1),
     leftInverse_iff_comp.mpr ((pow_sub_mul_pow f (Nat.one_le_pow n p hp.out.pos)).trans hf),
     leftInverse_iff_comp.mpr ((pow_mul_pow_sub f (Nat.one_le_pow n p hp.out.pos)).trans hf)⟩
-  have hσ : σ ^ p ^ n = 1
-  · rw [DFunLike.ext'_iff, coe_pow]
+  have hσ : σ ^ p ^ n = 1 := by
+    rw [DFunLike.ext'_iff, coe_pow]
     exact (hom_coe_pow (fun g : Function.End α ↦ g) rfl (fun g h ↦ rfl) f (p ^ n)).symm.trans hf
-  suffices : Fintype.card f.fixedPoints = (support σ)ᶜ.card
-  · exact this ▸ (card_compl_support_modEq hσ).symm
-  suffices : f.fixedPoints = (support σ)ᶜ
-  · simp only [this]; apply Fintype.card_coe
+  suffices Fintype.card f.fixedPoints = (support σ)ᶜ.card from
+    this ▸ (card_compl_support_modEq hσ).symm
+  suffices f.fixedPoints = (support σ)ᶜ by
+    simp only [this]; apply Fintype.card_coe
   simp [Set.ext_iff, IsFixedPt]
 
 theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p ∣ Fintype.card α)
@@ -643,8 +643,8 @@ variable [DecidableEq α]
 
 theorem isThreeCycle_swap_mul_swap_same {a b c : α} (ab : a ≠ b) (ac : a ≠ c) (bc : b ≠ c) :
     IsThreeCycle (swap a b * swap a c) := by
-  suffices h : support (swap a b * swap a c) = {a, b, c}
-  · rw [← card_support_eq_three_iff, h]
+  suffices h : support (swap a b * swap a c) = {a, b, c} by
+    rw [← card_support_eq_three_iff, h]
     simp [ab, ac, bc]
   apply le_antisymm ((support_mul_le _ _).trans fun x => _) fun x hx => ?_
   · simp [ab, ac, bc]

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -340,7 +340,7 @@ theorem card_fixedPoints_modEq [DecidableEq α] {f : Function.End α} {p n : ℕ
     leftInverse_iff_comp.mpr ((pow_sub_mul_pow f (Nat.one_le_pow n p hp.out.pos)).trans hf),
     leftInverse_iff_comp.mpr ((pow_mul_pow_sub f (Nat.one_le_pow n p hp.out.pos)).trans hf)⟩
   have hσ : σ ^ p ^ n = 1
-  · rw [FunLike.ext'_iff, coe_pow]
+  · rw [DFunLike.ext'_iff, coe_pow]
     exact (hom_coe_pow (fun g : Function.End α ↦ g) rfl (fun g h ↦ rfl) f (p ^ n)).symm.trans hf
   suffices : Fintype.card f.fixedPoints = (support σ)ᶜ.card
   · exact this ▸ (card_compl_support_modEq hσ).symm

Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Tobias Grosser <tobias@grosser.es> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -293,7 +293,7 @@ theorem mem_cycleType_iff {n : ℕ} {σ : Perm α} :
     obtain ⟨l, rfl, hlc, hld⟩ := truncCycleFactors σ
     rw [cycleType_eq _ rfl hlc hld, Multiset.mem_coe, List.mem_map] at h
     obtain ⟨c, cl, rfl⟩ := h
-    rw [(List.perm_cons_erase cl).pairwise_iff Disjoint.symmetric] at hld
+    rw [(List.perm_cons_erase cl).pairwise_iff @(Disjoint.symmetric)] at hld
     refine' ⟨c, (l.erase c).prod, _, _, hlc _ cl, rfl⟩
     · rw [← List.prod_cons, (List.perm_cons_erase cl).symm.prod_eq' (hld.imp Disjoint.commute)]
     · exact disjoint_prod_right _ fun g => List.rel_of_pairwise_cons hld

The cardinality of a subgroup is greater than the order of any of its elements.

Rename

• order_eq_card_zpowers → Fintype.card_zpowers
• order_eq_card_zpowers' → Nat.card_zpowers (and turn it around to match Nat.card_subgroupPowers)
• Submonoid.powers_subset → Submonoid.powers_le
• orderOf_dvd_card_univ → orderOf_dvd_card
• orderOf_subgroup → Subgroup.orderOf
• Subgroup.nonempty → Subgroup.coe_nonempty

@@ -517,7 +517,7 @@ theorem subgroup_eq_top_of_swap_mem [DecidableEq α] {H : Subgroup (Perm α)}
     (h1 : Fintype.card α ∣ Fintype.card H) (h2 : τ ∈ H) (h3 : IsSwap τ) : H = ⊤ := by
   haveI : Fact (Fintype.card α).Prime := ⟨h0⟩
   obtain ⟨σ, hσ⟩ := exists_prime_orderOf_dvd_card (Fintype.card α) h1
-  have hσ1 : orderOf (σ : Perm α) = Fintype.card α := (orderOf_subgroup σ).trans hσ
+  have hσ1 : orderOf (σ : Perm α) = Fintype.card α := (Subgroup.orderOf_coe σ).trans hσ
   have hσ2 : IsCycle ↑σ := isCycle_of_prime_order'' h0 hσ1
   have hσ3 : (σ : Perm α).support = ⊤ :=
     Finset.eq_univ_of_card (σ : Perm α).support (hσ2.orderOf.symm.trans hσ1)

@@ -330,6 +330,24 @@ theorem card_compl_support_modEq [DecidableEq α] {p n : ℕ} [hp : Fact p.Prime
   · exact Finset.card_le_univ _
 #align equiv.perm.card_compl_support_modeq Equiv.Perm.card_compl_support_modEq
 
+open Function in
+/-- The number of fixed points of a `p ^ n`-th root of the identity function over a finite set
+and the set's cardinality have the same residue modulo `p`, where `p` is a prime. -/
+theorem card_fixedPoints_modEq [DecidableEq α] {f : Function.End α} {p n : ℕ}
+    [hp : Fact p.Prime] (hf : f ^ p ^ n = 1) :
+    Fintype.card α ≡ Fintype.card f.fixedPoints [MOD p] := by
+  let σ : α ≃ α := ⟨f, f ^ (p ^ n - 1),
+    leftInverse_iff_comp.mpr ((pow_sub_mul_pow f (Nat.one_le_pow n p hp.out.pos)).trans hf),
+    leftInverse_iff_comp.mpr ((pow_mul_pow_sub f (Nat.one_le_pow n p hp.out.pos)).trans hf)⟩
+  have hσ : σ ^ p ^ n = 1
+  · rw [FunLike.ext'_iff, coe_pow]
+    exact (hom_coe_pow (fun g : Function.End α ↦ g) rfl (fun g h ↦ rfl) f (p ^ n)).symm.trans hf
+  suffices : Fintype.card f.fixedPoints = (support σ)ᶜ.card
+  · exact this ▸ (card_compl_support_modEq hσ).symm
+  suffices : f.fixedPoints = (support σ)ᶜ
+  · simp only [this]; apply Fintype.card_coe
+  simp [Set.ext_iff, IsFixedPt]
+
 theorem exists_fixed_point_of_prime {p n : ℕ} [hp : Fact p.Prime] (hα : ¬p ∣ Fintype.card α)
     {σ : Perm α} (hσ : σ ^ p ^ n = 1) : ∃ a : α, σ a = a := by
   classical

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

This has nice performance benefits.

@@ -37,7 +37,7 @@ namespace Equiv.Perm
 
 open Equiv List Multiset
 
-variable {α : Type _} [Fintype α]
+variable {α : Type*} [Fintype α]
 
 section CycleType
 
@@ -270,7 +270,7 @@ theorem isConj_iff_cycleType_eq {σ τ : Perm α} : IsConj σ τ ↔ σ.cycleTyp
 #align equiv.perm.is_conj_iff_cycle_type_eq Equiv.Perm.isConj_iff_cycleType_eq
 
 @[simp]
-theorem cycleType_extendDomain {β : Type _} [Fintype β] [DecidableEq β] {p : β → Prop}
+theorem cycleType_extendDomain {β : Type*} [Fintype β] [DecidableEq β] {p : β → Prop}
     [DecidablePred p] (f : α ≃ Subtype p) {g : Perm α} :
     cycleType (g.extendDomain f) = cycleType g := by
   induction g using cycle_induction_on with
@@ -364,7 +364,7 @@ theorem isCycle_of_prime_order'' {σ : Perm α} (h1 : (Fintype.card α).Prime)
 
 section Cauchy
 
-variable (G : Type _) [Group G] (n : ℕ)
+variable (G : Type*) [Group G] (n : ℕ)
 
 /-- The type of vectors with terms from `G`, length `n`, and product equal to `1:G`. -/
 def vectorsProdEqOne : Set (Vector G n) :=
@@ -452,7 +452,7 @@ end VectorsProdEqOne
 
 /-- For every prime `p` dividing the order of a finite group `G` there exists an element of order
 `p` in `G`. This is known as Cauchy's theorem. -/
-theorem _root_.exists_prime_orderOf_dvd_card {G : Type _} [Group G] [Fintype G] (p : ℕ)
+theorem _root_.exists_prime_orderOf_dvd_card {G : Type*} [Group G] [Fintype G] (p : ℕ)
     [hp : Fact p.Prime] (hdvd : p ∣ Fintype.card G) : ∃ x : G, orderOf x = p := by
   have hp' : p - 1 ≠ 0 := mt tsub_eq_zero_iff_le.mp (not_le_of_lt hp.out.one_lt)
   have Scard :=
@@ -485,7 +485,7 @@ theorem _root_.exists_prime_orderOf_dvd_card {G : Type _} [Group G] [Fintype G]
 
 /-- For every prime `p` dividing the order of a finite additive group `G` there exists an element of
 order `p` in `G`. This is the additive version of Cauchy's theorem. -/
-theorem _root_.exists_prime_addOrderOf_dvd_card {G : Type _} [AddGroup G] [Fintype G] (p : ℕ)
+theorem _root_.exists_prime_addOrderOf_dvd_card {G : Type*} [AddGroup G] [Fintype G] (p : ℕ)
     [hp : Fact p.Prime] (hdvd : p ∣ Fintype.card G) : ∃ x : G, addOrderOf x = p :=
   @exists_prime_orderOf_dvd_card (Multiplicative G) _ _ _ _ (by convert hdvd)
 #align exists_prime_add_order_of_dvd_card exists_prime_addOrderOf_dvd_card

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 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.perm.cycle.type
-! leanprover-community/mathlib commit 47adfab39a11a072db552f47594bf8ed2cf8a722
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.GCDMonoid.Multiset
 import Mathlib.Combinatorics.Partition
@@ -15,6 +10,8 @@ import Mathlib.GroupTheory.Perm.Cycle.Basic
 import Mathlib.RingTheory.Int.Basic
 import Mathlib.Tactic.NormNum.GCD
 
+#align_import group_theory.perm.cycle.type from "leanprover-community/mathlib"@"47adfab39a11a072db552f47594bf8ed2cf8a722"
+
 /-!
 # Cycle Types
 

Currently, (for both Set and Finset) insert_subset is an iff lemma stating that insert a s ⊆ t if and only if a ∈ t and s ⊆ t. For both types, this PR renames this lemma to insert_subset_iff, and adds an insert_subset lemma that gives the implication just in the reverse direction : namely theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t .

This both aligns the naming with union_subset and union_subset_iff, and removes the need for the awkward insert_subset.mpr ⟨_,_⟩ idiom. It touches a lot of files (too many to list), but in a trivial way.

@@ -507,7 +507,7 @@ theorem subgroup_eq_top_of_swap_mem [DecidableEq α] {H : Subgroup (Perm α)}
   have hσ3 : (σ : Perm α).support = ⊤ :=
     Finset.eq_univ_of_card (σ : Perm α).support (hσ2.orderOf.symm.trans hσ1)
   have hσ4 : Subgroup.closure {↑σ, τ} = ⊤ := closure_prime_cycle_swap h0 hσ2 hσ3 h3
-  rw [eq_top_iff, ← hσ4, Subgroup.closure_le, Set.insert_subset, Set.singleton_subset_iff]
+  rw [eq_top_iff, ← hσ4, Subgroup.closure_le, Set.insert_subset_iff, Set.singleton_subset_iff]
   exact ⟨Subtype.mem σ, h2⟩
 #align equiv.perm.subgroup_eq_top_of_swap_mem Equiv.Perm.subgroup_eq_top_of_swap_mem
 

This completes the porting of these norm_num extensions while adding a new extension for IsCoprime over Int. It also adds the norm_num extension testing file from mathlib3. Closes #3246.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -13,6 +13,7 @@ import Mathlib.Combinatorics.Partition
 import Mathlib.Data.List.Rotate
 import Mathlib.GroupTheory.Perm.Cycle.Basic
 import Mathlib.RingTheory.Int.Basic
+import Mathlib.Tactic.NormNum.GCD
 
 /-!
 # Cycle Types
@@ -613,31 +614,9 @@ theorem orderOf {g : Perm α} (ht : IsThreeCycle g) : orderOf g = 3 := by
   rw [← lcm_cycleType, ht.cycleType, Multiset.lcm_singleton, normalize_eq]
 #align equiv.perm.is_three_cycle.order_of Equiv.Perm.IsThreeCycle.orderOf
 
--- Copied the following lemmas from Data/Int/GCD.lean; see #3246
-private theorem int_gcd_helper' {d : ℕ} {x y a b : ℤ} (h₁ : (d : ℤ) ∣ x) (h₂ : (d : ℤ) ∣ y)
-    (h₃ : x * a + y * b = d) : Int.gcd x y = d := by
-  refine' Nat.dvd_antisymm _ (Int.coe_nat_dvd.1 (Int.dvd_gcd h₁ h₂))
-  rw [← Int.coe_nat_dvd, ← h₃]
-  apply dvd_add
-  · exact (Int.gcd_dvd_left _ _).mul_right _
-  · exact (Int.gcd_dvd_right _ _).mul_right _
-private theorem nat_gcd_helper_2 (d x y a b u v tx ty : ℕ) (hu : d * u = x) (hv : d * v = y)
-    (hx : x * a = tx) (hy : y * b = ty) (h : ty + d = tx) : Nat.gcd x y = d := by
-  rw [← Int.coe_nat_gcd];
-  apply
-    @int_gcd_helper' _ _ _ a (-b) (Int.coe_nat_dvd.2 ⟨_, hu.symm⟩) (Int.coe_nat_dvd.2
-     ⟨_, hv.symm⟩)
-  rw [mul_neg, ← sub_eq_add_neg, sub_eq_iff_eq_add']
-  norm_cast; rw [hx, hy, h]
-private theorem nat_gcd_helper_1 (d x y a b u v tx ty : ℕ) (hu : d * u = x) (hv : d * v = y)
-    (hx : x * a = tx) (hy : y * b = ty) (h : tx + d = ty) : Nat.gcd x y = d :=
-  (Nat.gcd_comm _ _).trans <| nat_gcd_helper_2 _ _ _ _ _ _ _ _ _ hv hu hy hx h
-
 theorem isThreeCycle_sq {g : Perm α} (ht : IsThreeCycle g) : IsThreeCycle (g * g) := by
   rw [← pow_two, ← card_support_eq_three_iff, support_pow_coprime, ht.card_support]
-  rw [ht.orderOf, Nat.coprime_iff_gcd_eq_one]
-  -- Porting note: was `norm_num`
-  apply nat_gcd_helper_1 _ _ _ _ _ _ _ _ _ (one_mul _) (one_mul _) (mul_one _) (mul_one _)
+  rw [ht.orderOf]
   norm_num
 #align equiv.perm.is_three_cycle.is_three_cycle_sq Equiv.Perm.IsThreeCycle.isThreeCycle_sq
 

Enable the cancelDenoms preprocessor in linarith. Closes #2714.

• depends on: #3797

Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -583,8 +583,7 @@ theorem _root_.card_support_eq_three_iff : σ.support.card = 3 ↔ σ.IsThreeCyc
   obtain ⟨m, hm⟩ := exists_mem_of_ne_zero h1
   rw [← sum_cycleType, ← cons_erase hn, ← cons_erase hm, Multiset.sum_cons, Multiset.sum_cons] at h
   -- TODO: linarith [...] should solve this directly
-  have : ∀ {k}, 2 ≤ m → 2 ≤ n → n + (m + k) = 3 → False :=
-    by
+  have : ∀ {k}, 2 ≤ m → 2 ≤ n → n + (m + k) = 3 → False := by
     intros
     linarith
   cases this (two_le_of_mem_cycleType (mem_of_mem_erase hm)) (two_le_of_mem_cycleType hn) h

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>