url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | rintro ⟨x, hx, rfl⟩ | case h.h1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
g : Perm α
⊢ (∃ a ∈ p, List.formPerm a = g) → Perm.IsCycle g | case h.h1.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
⊢ Perm.IsCycle (List.formPerm x) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
g : Perm α
⊢ (∃ a ∈ p, List.formPerm a = g) → Perm.IsCycle g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | have hx_nodup : x.Nodup := hp_nodup x hx | case h.h1.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
⊢ Perm.IsCycle (List.formPerm x) | case h.h1.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ Perm.IsCycle (List.formPerm x) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h1.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
⊢ Perm.IsCycle (List.formPerm x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | rw [← Cycle.formPerm_coe x hx_nodup] | case h.h1.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ Perm.IsCycle (List.formPerm x) | case h.h1.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ Perm.IsCycle (Cycle.formPerm (↑x) hx_nodup) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h1.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ Perm.IsCycle (List.formPerm x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | apply Cycle.isCycle_formPerm | case h.h1.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ Perm.IsCycle (Cycle.formPerm (↑x) hx_nodup) | case h.h1.intro.intro.hn
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ Cycle.Nontrivial ↑x | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h1.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ Perm.IsCycle (Cycle.formPerm (↑x) hx_nodup)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | rw [Cycle.nontrivial_coe_nodup_iff hx_nodup] | case h.h1.intro.intro.hn
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ Cycle.Nontrivial ↑x | case h.h1.intro.intro.hn
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ 2 ≤ List.length x | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h1.intro.intro.hn
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ Cycle.Nontrivial ↑x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | exact hp2 x hx | case h.h1.intro.intro.hn
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ 2 ≤ List.length x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h1.intro.intro.hn
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
x : List α
hx : x ∈ p
hx_nodup : List.Nodup x
⊢ 2 ≤ List.length x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | rw [List.pairwise_map] | case h.h2
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
⊢ List.Pairwise Perm.Disjoint (List.map (fun l => List.formPerm l) p) | case h.h2
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
⊢ List.Pairwise (fun a b => Perm.Disjoint (List.formPerm a) (List.formPerm b)) p | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
⊢ List.Pairwise Perm.Disjoint (List.map (fun l => List.formPerm l) p)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | apply List.Pairwise.imp_of_mem _ hp_disj | case h.h2
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
⊢ List.Pairwise (fun a b => Perm.Disjoint (List.formPerm a) (List.formPerm b)) p | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
⊢ ∀ {a b : List α}, a ∈ p → b ∈ p → List.Disjoint a b → Perm.Disjoint (List.formPerm a) (List.formPerm b) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
⊢ List.Pairwise (fun a b => Perm.Disjoint (List.formPerm a) (List.formPerm b)) p
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | intro a b ha hb hab | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
⊢ ∀ {a b : List α}, a ∈ p → b ∈ p → List.Disjoint a b → Perm.Disjoint (List.formPerm a) (List.formPerm b) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
a b : List α
ha : a ∈ p
hb : b ∈ p
hab : List.Disjoint a b
⊢ Perm.Disjoint (List.formPerm a) (List.formPerm b) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
⊢ ∀ {a b : List α}, a ∈ p → b ∈ p → List.Disjoint a b → Perm.Disjoint (List.formPerm a) (List.formPerm b)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | rw [List.formPerm_disjoint_iff (hp_nodup a ha) (hp_nodup b hb) (hp2 a ha) (hp2 b hb)] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
a b : List α
ha : a ∈ p
hb : b ∈ p
hab : List.Disjoint a b
⊢ Perm.Disjoint (List.formPerm a) (List.formPerm b) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
a b : List α
ha : a ∈ p
hb : b ∈ p
hab : List.Disjoint a b
⊢ List.Disjoint a b | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
a b : List α
ha : a ∈ p
hb : b ∈ p
hab : List.Disjoint a b
⊢ Perm.Disjoint (List.formPerm a) (List.formPerm b)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.permWithCycleType_nonempty_iff | [495, 1] | [553, 16] | exact hab | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
a b : List α
ha : a ∈ p
hb : b ∈ p
hab : List.Disjoint a b
⊢ List.Disjoint a b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
m : Multiset ℕ
hc : Multiset.sum m ≤ Fintype.card α
h2c : ∀ a ∈ m, 2 ≤ a
hc' : List.sum (Multiset.toList m) ≤ Fintype.card α
p : List (List α)
hp_length : List.map List.length p = Multiset.toList m
hp_nodup : ∀ s ∈ p, List.Nodup s
hp_disj : List.Pairwise List.Disjoint p
hp2 : ∀ x ∈ p, 2 ≤ List.length x
a b : List α
ha : a ∈ p
hb : b ∈ p
hab : List.Disjoint a b
⊢ List.Disjoint a b
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.conj_support_eq | [558, 1] | [563, 41] | simp only [Equiv.Perm.mem_support, ConjAct.smul_def] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ a ∈ support (k • g) ↔ (ConjAct.ofConjAct k⁻¹) a ∈ support g | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ (ConjAct.ofConjAct k * g * (ConjAct.ofConjAct k)⁻¹) a ≠ a ↔ g ((ConjAct.ofConjAct k⁻¹) a) ≠ (ConjAct.ofConjAct k⁻¹) a | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ a ∈ support (k • g) ↔ (ConjAct.ofConjAct k⁻¹) a ∈ support g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.conj_support_eq | [558, 1] | [563, 41] | rw [not_iff_not] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ (ConjAct.ofConjAct k * g * (ConjAct.ofConjAct k)⁻¹) a ≠ a ↔ g ((ConjAct.ofConjAct k⁻¹) a) ≠ (ConjAct.ofConjAct k⁻¹) a | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ (ConjAct.ofConjAct k * g * (ConjAct.ofConjAct k)⁻¹) a = a ↔ g ((ConjAct.ofConjAct k⁻¹) a) = (ConjAct.ofConjAct k⁻¹) a | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ (ConjAct.ofConjAct k * g * (ConjAct.ofConjAct k)⁻¹) a ≠ a ↔ g ((ConjAct.ofConjAct k⁻¹) a) ≠ (ConjAct.ofConjAct k⁻¹) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.conj_support_eq | [558, 1] | [563, 41] | simp only [Equiv.Perm.coe_mul, Function.comp_apply, ConjAct.ofConjAct_inv] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ (ConjAct.ofConjAct k * g * (ConjAct.ofConjAct k)⁻¹) a = a ↔ g ((ConjAct.ofConjAct k⁻¹) a) = (ConjAct.ofConjAct k⁻¹) a | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ (ConjAct.ofConjAct k) (g ((ConjAct.ofConjAct k)⁻¹ a)) = a ↔ g ((ConjAct.ofConjAct k)⁻¹ a) = (ConjAct.ofConjAct k)⁻¹ a | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ (ConjAct.ofConjAct k * g * (ConjAct.ofConjAct k)⁻¹) a = a ↔ g ((ConjAct.ofConjAct k⁻¹) a) = (ConjAct.ofConjAct k⁻¹) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.conj_support_eq | [558, 1] | [563, 41] | apply Equiv.apply_eq_iff_eq_symm_apply | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ (ConjAct.ofConjAct k) (g ((ConjAct.ofConjAct k)⁻¹ a)) = a ↔ g ((ConjAct.ofConjAct k)⁻¹ a) = (ConjAct.ofConjAct k)⁻¹ a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
a : α
⊢ (ConjAct.ofConjAct k) (g ((ConjAct.ofConjAct k)⁻¹ a)) = a ↔ g ((ConjAct.ofConjAct k)⁻¹ a) = (ConjAct.ofConjAct k)⁻¹ a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | constructor | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) ↔ c ∈ cycleFactorsFinset g | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) → c ∈ cycleFactorsFinset g
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) ↔ c ∈ cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | intro h | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) → c ∈ cycleFactorsFinset g | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ c ∈ cycleFactorsFinset g | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) → c ∈ cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | suffices ∀ h : Equiv.Perm α, h = k⁻¹ * (k * h * k⁻¹) * k by
rw [this g, this c]
apply imp_lemma
exact h | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ c ∈ cycleFactorsFinset g | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ c ∈ cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | intro h | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h✝ : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : Perm α
⊢ h = k⁻¹ * (k * h * k⁻¹) * k | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | group | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h✝ : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : Perm α
⊢ h = k⁻¹ * (k * h * k⁻¹) * k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h✝ : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : Perm α
⊢ h = k⁻¹ * (k * h * k⁻¹) * k
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | rw [this g, this c] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
this : ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k
⊢ c ∈ cycleFactorsFinset g | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
this : ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k
⊢ k⁻¹ * (k * c * k⁻¹) * k ∈ cycleFactorsFinset (k⁻¹ * (k * g * k⁻¹) * k) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
this : ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k
⊢ c ∈ cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | apply imp_lemma | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
this : ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k
⊢ k⁻¹ * (k * c * k⁻¹) * k ∈ cycleFactorsFinset (k⁻¹ * (k * g * k⁻¹) * k) | case x
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
this : ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k
⊢ k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
this : ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k
⊢ k⁻¹ * (k * c * k⁻¹) * k ∈ cycleFactorsFinset (k⁻¹ * (k * g * k⁻¹) * k)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | exact h | case x
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
this : ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k
⊢ k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case x
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
h : k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
this : ∀ (h : Perm α), h = k⁻¹ * (k * h * k⁻¹) * k
⊢ k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | apply imp_lemma g k c | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
imp_lemma : ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
⊢ c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | intro g k c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
⊢ c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ ∀ (g k c : Perm α), c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | simp only [Equiv.Perm.mem_cycleFactorsFinset_iff] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
⊢ c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
⊢ (IsCycle c ∧ ∀ a ∈ support c, c a = g a) →
IsCycle (k * c * k⁻¹) ∧ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
⊢ c ∈ cycleFactorsFinset g → k * c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | rintro ⟨hc, hc'⟩ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
⊢ (IsCycle c ∧ ∀ a ∈ support c, c a = g a) →
IsCycle (k * c * k⁻¹) ∧ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ IsCycle (k * c * k⁻¹) ∧ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
⊢ (IsCycle c ∧ ∀ a ∈ support c, c a = g a) →
IsCycle (k * c * k⁻¹) ∧ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | constructor | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ IsCycle (k * c * k⁻¹) ∧ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a | case intro.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ IsCycle (k * c * k⁻¹)
case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ IsCycle (k * c * k⁻¹) ∧ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | exact Equiv.Perm.IsCycle.conj hc | case intro.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ IsCycle (k * c * k⁻¹)
case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a | case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ IsCycle (k * c * k⁻¹)
case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | intro a ha | case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a | case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : a ∈ support (k * c * k⁻¹)
⊢ (k * c * k⁻¹) a = (k * g * k⁻¹) a | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
⊢ ∀ a ∈ support (k * c * k⁻¹), (k * c * k⁻¹) a = (k * g * k⁻¹) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | simp only [coe_mul, Function.comp_apply, EmbeddingLike.apply_eq_iff_eq] | case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : a ∈ support (k * c * k⁻¹)
⊢ (k * c * k⁻¹) a = (k * g * k⁻¹) a | case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : a ∈ support (k * c * k⁻¹)
⊢ c (k⁻¹ a) = g (k⁻¹ a) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : a ∈ support (k * c * k⁻¹)
⊢ (k * c * k⁻¹) a = (k * g * k⁻¹) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | apply hc' | case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : a ∈ support (k * c * k⁻¹)
⊢ c (k⁻¹ a) = g (k⁻¹ a) | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : a ∈ support (k * c * k⁻¹)
⊢ k⁻¹ a ∈ support c | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : a ∈ support (k * c * k⁻¹)
⊢ c (k⁻¹ a) = g (k⁻¹ a)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | rw [Equiv.Perm.mem_support] at ha ⊢ | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : a ∈ support (k * c * k⁻¹)
⊢ k⁻¹ a ∈ support c | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
⊢ c (k⁻¹ a) ≠ k⁻¹ a | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : a ∈ support (k * c * k⁻¹)
⊢ k⁻¹ a ∈ support c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | intro ha' | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
⊢ c (k⁻¹ a) ≠ k⁻¹ a | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c (k⁻¹ a) = k⁻¹ a
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
⊢ c (k⁻¹ a) ≠ k⁻¹ a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | apply ha | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c (k⁻¹ a) = k⁻¹ a
⊢ False | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c (k⁻¹ a) = k⁻¹ a
⊢ (k * c * k⁻¹) a = a | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c (k⁻¹ a) = k⁻¹ a
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | simp only [mul_smul, ← Equiv.Perm.smul_def] at ha' ⊢ | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c (k⁻¹ a) = k⁻¹ a
⊢ (k * c * k⁻¹) a = a | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c • k⁻¹ • a = k⁻¹ • a
⊢ k • c • k⁻¹ • a = a | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c (k⁻¹ a) = k⁻¹ a
⊢ (k * c * k⁻¹) a = a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | rw [ha'] | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c • k⁻¹ • a = k⁻¹ • a
⊢ k • c • k⁻¹ • a = a | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c • k⁻¹ • a = k⁻¹ • a
⊢ k • k⁻¹ • a = a | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c • k⁻¹ • a = k⁻¹ • a
⊢ k • c • k⁻¹ • a = a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj | [567, 1] | [593, 63] | simp only [Equiv.Perm.smul_def, Equiv.Perm.apply_inv_self] | case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c • k⁻¹ • a = k⁻¹ • a
⊢ k • k⁻¹ • a = a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.right.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ k✝ c✝ g k c : Perm α
hc : IsCycle c
hc' : ∀ a ∈ support c, c a = g a
a : α
ha : (k * c * k⁻¹) a ≠ a
ha' : c • k⁻¹ • a = k⁻¹ • a
⊢ k • k⁻¹ • a = a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj | [596, 1] | [606, 8] | ext c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k : Perm α
⊢ cycleFactorsFinset (k * g * k⁻¹) = Finset.map (Equiv.toEmbedding (MulAut.conj k).toEquiv) (cycleFactorsFinset g) | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c ∈ cycleFactorsFinset (k * g * k⁻¹) ↔
c ∈ Finset.map (Equiv.toEmbedding (MulAut.conj k).toEquiv) (cycleFactorsFinset g) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k : Perm α
⊢ cycleFactorsFinset (k * g * k⁻¹) = Finset.map (Equiv.toEmbedding (MulAut.conj k).toEquiv) (cycleFactorsFinset g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj | [596, 1] | [606, 8] | rw [Finset.mem_map_equiv] | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c ∈ cycleFactorsFinset (k * g * k⁻¹) ↔
c ∈ Finset.map (Equiv.toEmbedding (MulAut.conj k).toEquiv) (cycleFactorsFinset g) | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c ∈ cycleFactorsFinset (k * g * k⁻¹) ↔ (MulAut.conj k).symm c ∈ cycleFactorsFinset g | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c ∈ cycleFactorsFinset (k * g * k⁻¹) ↔
c ∈ Finset.map (Equiv.toEmbedding (MulAut.conj k).toEquiv) (cycleFactorsFinset g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj | [596, 1] | [606, 8] | rw [← Equiv.Perm.mem_cycleFactorsFinset_conj g k] | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c ∈ cycleFactorsFinset (k * g * k⁻¹) ↔ (MulAut.conj k).symm c ∈ cycleFactorsFinset g | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c ∈ cycleFactorsFinset (k * g * k⁻¹) ↔ k * (MulAut.conj k).symm c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c ∈ cycleFactorsFinset (k * g * k⁻¹) ↔ (MulAut.conj k).symm c ∈ cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj | [596, 1] | [606, 8] | apply iff_of_eq | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c ∈ cycleFactorsFinset (k * g * k⁻¹) ↔ k * (MulAut.conj k).symm c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹) | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ (c ∈ cycleFactorsFinset (k * g * k⁻¹)) = (k * (MulAut.conj k).symm c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c ∈ cycleFactorsFinset (k * g * k⁻¹) ↔ k * (MulAut.conj k).symm c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj | [596, 1] | [606, 8] | apply congr_arg₂ _ _ | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ (c ∈ cycleFactorsFinset (k * g * k⁻¹)) = (k * (MulAut.conj k).symm c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹)) | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ cycleFactorsFinset (k * g * k⁻¹) = cycleFactorsFinset (k * g * k⁻¹)
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c = k * (MulAut.conj k).symm c * k⁻¹ | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ (c ∈ cycleFactorsFinset (k * g * k⁻¹)) = (k * (MulAut.conj k).symm c * k⁻¹ ∈ cycleFactorsFinset (k * g * k⁻¹))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj | [596, 1] | [606, 8] | rfl | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ cycleFactorsFinset (k * g * k⁻¹) = cycleFactorsFinset (k * g * k⁻¹)
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c = k * (MulAut.conj k).symm c * k⁻¹ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c = k * (MulAut.conj k).symm c * k⁻¹ | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ cycleFactorsFinset (k * g * k⁻¹) = cycleFactorsFinset (k * g * k⁻¹)
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c = k * (MulAut.conj k).symm c * k⁻¹
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj | [596, 1] | [606, 8] | simp only [MulEquiv.toEquiv_eq_coe, MulEquiv.coe_toEquiv_symm, MulAut.conj_symm_apply] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c = k * (MulAut.conj k).symm c * k⁻¹ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c = k * (k⁻¹ * c * k) * k⁻¹ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c = k * (MulAut.conj k).symm c * k⁻¹
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj | [596, 1] | [606, 8] | group | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c = k * (k⁻¹ * c * k) * k⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g k c : Perm α
⊢ c = k * (k⁻¹ * c * k) * k⁻¹
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj' | [610, 1] | [614, 47] | simp only [ConjAct.smul_def] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ k • c ∈ cycleFactorsFinset (k • g) ↔ c ∈ cycleFactorsFinset g | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ ConjAct.ofConjAct k * c * (ConjAct.ofConjAct k)⁻¹ ∈
cycleFactorsFinset (ConjAct.ofConjAct k * g * (ConjAct.ofConjAct k)⁻¹) ↔
c ∈ cycleFactorsFinset g | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ k • c ∈ cycleFactorsFinset (k • g) ↔ c ∈ cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_conj' | [610, 1] | [614, 47] | apply Equiv.Perm.mem_cycleFactorsFinset_conj | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ ConjAct.ofConjAct k * c * (ConjAct.ofConjAct k)⁻¹ ∈
cycleFactorsFinset (ConjAct.ofConjAct k * g * (ConjAct.ofConjAct k)⁻¹) ↔
c ∈ cycleFactorsFinset g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ ConjAct.ofConjAct k * c * (ConjAct.ofConjAct k)⁻¹ ∈
cycleFactorsFinset (ConjAct.ofConjAct k * g * (ConjAct.ofConjAct k)⁻¹) ↔
c ∈ cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj_eq | [617, 1] | [623, 32] | ext c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
⊢ cycleFactorsFinset (k • g) = k • cycleFactorsFinset g | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ c ∈ cycleFactorsFinset (k • g) ↔ c ∈ k • cycleFactorsFinset g | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g : Perm α
⊢ cycleFactorsFinset (k • g) = k • cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj_eq | [617, 1] | [623, 32] | rw [← Equiv.Perm.mem_cycleFactorsFinset_conj' k⁻¹ (k • g) c] | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ c ∈ cycleFactorsFinset (k • g) ↔ c ∈ k • cycleFactorsFinset g | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ k⁻¹ • c ∈ cycleFactorsFinset (k⁻¹ • k • g) ↔ c ∈ k • cycleFactorsFinset g | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ c ∈ cycleFactorsFinset (k • g) ↔ c ∈ k • cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj_eq | [617, 1] | [623, 32] | simp only [inv_smul_smul] | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ k⁻¹ • c ∈ cycleFactorsFinset (k⁻¹ • k • g) ↔ c ∈ k • cycleFactorsFinset g | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ k⁻¹ • c ∈ cycleFactorsFinset g ↔ c ∈ k • cycleFactorsFinset g | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ k⁻¹ • c ∈ cycleFactorsFinset (k⁻¹ • k • g) ↔ c ∈ k • cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.cycleFactorsFinset_conj_eq | [617, 1] | [623, 32] | exact Finset.inv_smul_mem_iff | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ k⁻¹ • c ∈ cycleFactorsFinset g ↔ c ∈ k • cycleFactorsFinset g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k : ConjAct (Perm α)
g c : Perm α
⊢ k⁻¹ • c ∈ cycleFactorsFinset g ↔ c ∈ k • cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.commute_of_mem_cycleFactorsFinset_commute | [644, 1] | [650, 11] | rw [← Equiv.Perm.cycleFactorsFinset_noncommProd g (Equiv.Perm.cycleFactorsFinset_mem_commute g)] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ Commute k g | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ Commute k (Finset.noncommProd (cycleFactorsFinset g) id ⋯) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ Commute k g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.commute_of_mem_cycleFactorsFinset_commute | [644, 1] | [650, 11] | apply Finset.noncommProd_commute | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ Commute k (Finset.noncommProd (cycleFactorsFinset g) id ⋯) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ ∀ x ∈ cycleFactorsFinset g, Commute k (id x) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ Commute k (Finset.noncommProd (cycleFactorsFinset g) id ⋯)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.commute_of_mem_cycleFactorsFinset_commute | [644, 1] | [650, 11] | simp only [id.def] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ ∀ x ∈ cycleFactorsFinset g, Commute k (id x) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ ∀ x ∈ cycleFactorsFinset g, Commute k x | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ ∀ x ∈ cycleFactorsFinset g, Commute k (id x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.commute_of_mem_cycleFactorsFinset_commute | [644, 1] | [650, 11] | exact hk | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ ∀ x ∈ cycleFactorsFinset g, Commute k x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
k g : Perm α
hk : ∀ c ∈ cycleFactorsFinset g, Commute k c
⊢ ∀ x ∈ cycleFactorsFinset g, Commute k x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.self_mem_cycle_factors_commute | [654, 1] | [660, 60] | apply Equiv.Perm.commute_of_mem_cycleFactorsFinset_commute | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
⊢ Commute c g | case hk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
⊢ ∀ c_1 ∈ cycleFactorsFinset g, Commute c c_1 | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
⊢ Commute c g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.self_mem_cycle_factors_commute | [654, 1] | [660, 60] | intro c' hc' | case hk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
⊢ ∀ c_1 ∈ cycleFactorsFinset g, Commute c c_1 | case hk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
⊢ Commute c c' | Please generate a tactic in lean4 to solve the state.
STATE:
case hk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
⊢ ∀ c_1 ∈ cycleFactorsFinset g, Commute c c_1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.self_mem_cycle_factors_commute | [654, 1] | [660, 60] | by_cases hcc' : c = c' | case hk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
⊢ Commute c c' | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : c = c'
⊢ Commute c c'
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : ¬c = c'
⊢ Commute c c' | Please generate a tactic in lean4 to solve the state.
STATE:
case hk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
⊢ Commute c c'
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.self_mem_cycle_factors_commute | [654, 1] | [660, 60] | rw [hcc'] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : c = c'
⊢ Commute c c'
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : ¬c = c'
⊢ Commute c c' | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : ¬c = c'
⊢ Commute c c' | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : c = c'
⊢ Commute c c'
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : ¬c = c'
⊢ Commute c c'
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.self_mem_cycle_factors_commute | [654, 1] | [660, 60] | apply g.cycleFactorsFinset_mem_commute hc hc' | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : ¬c = c'
⊢ Commute c c' | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : ¬c = c'
⊢ c ≠ c' | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : ¬c = c'
⊢ Commute c c'
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.self_mem_cycle_factors_commute | [654, 1] | [660, 60] | exact hcc' | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : ¬c = c'
⊢ c ≠ c' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
c' : Perm α
hc' : c' ∈ cycleFactorsFinset g
hcc' : ¬c = c'
⊢ c ≠ c'
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_support_of_commute | [683, 1] | [688, 39] | intro x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
⊢ ∀ (x : α), x ∈ support c ↔ g x ∈ support c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
x : α
⊢ x ∈ support c ↔ g x ∈ support c | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
⊢ ∀ (x : α), x ∈ support c ↔ g x ∈ support c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_support_of_commute | [683, 1] | [688, 39] | simp only [Equiv.Perm.mem_support, not_iff_not, ← Equiv.Perm.mul_apply] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
x : α
⊢ x ∈ support c ↔ g x ∈ support c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
x : α
⊢ c x = x ↔ (c * g) x = g x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
x : α
⊢ x ∈ support c ↔ g x ∈ support c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_support_of_commute | [683, 1] | [688, 39] | rw [← hgc, Equiv.Perm.mul_apply] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
x : α
⊢ c x = x ↔ (c * g) x = g x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
x : α
⊢ c x = x ↔ g (c x) = g x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
x : α
⊢ c x = x ↔ (c * g) x = g x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_support_of_commute | [683, 1] | [688, 39] | exact (Equiv.apply_eq_iff_eq g).symm | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
x : α
⊢ c x = x ↔ g (c x) = g x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hgc : Commute g c
x : α
⊢ c x = x ↔ g (c x) = g x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_support_cycle_of_cycle | [694, 1] | [703, 59] | intro x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
⊢ ∀ (x : α), x ∈ support c ↔ d x ∈ support c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
⊢ x ∈ support c ↔ d x ∈ support c | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
⊢ ∀ (x : α), x ∈ support c ↔ d x ∈ support c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_support_cycle_of_cycle | [694, 1] | [703, 59] | simp only [Equiv.Perm.mem_support, not_iff_not] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
⊢ x ∈ support c ↔ d x ∈ support c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
⊢ c x = x ↔ c (d x) = d x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
⊢ x ∈ support c ↔ d x ∈ support c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_support_cycle_of_cycle | [694, 1] | [703, 59] | by_cases h : c = d | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
⊢ c x = x ↔ c (d x) = d x | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
h : c = d
⊢ c x = x ↔ c (d x) = d x
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
h : ¬c = d
⊢ c x = x ↔ c (d x) = d x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
⊢ c x = x ↔ c (d x) = d x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_support_cycle_of_cycle | [694, 1] | [703, 59] | rw [← h, EmbeddingLike.apply_eq_iff_eq] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
h : c = d
⊢ c x = x ↔ c (d x) = d x
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
h : ¬c = d
⊢ c x = x ↔ c (d x) = d x | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
h : ¬c = d
⊢ c x = x ↔ c (d x) = d x | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
h : c = d
⊢ c x = x ↔ c (d x) = d x
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
h : ¬c = d
⊢ c x = x ↔ c (d x) = d x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_support_cycle_of_cycle | [694, 1] | [703, 59] | rw [← Equiv.Perm.mul_apply,
Commute.eq (Equiv.Perm.cycleFactorsFinset_mem_commute g hc hd h),
Equiv.Perm.mul_apply, EmbeddingLike.apply_eq_iff_eq] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
h : ¬c = d
⊢ c x = x ↔ c (d x) = d x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g d c : Perm α
hc : c ∈ cycleFactorsFinset g
hd : d ∈ cycleFactorsFinset g
x : α
h : ¬c = d
⊢ c x = x ↔ c (d x) = d x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_support | [706, 1] | [709, 60] | apply Equiv.Perm.mem_support_of_commute | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
a : α
⊢ a ∈ support c ↔ g a ∈ support c | case hgc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
a : α
⊢ Commute g c | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
a : α
⊢ a ∈ support c ↔ g a ∈ support c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.mem_cycleFactorsFinset_support | [706, 1] | [709, 60] | exact (Equiv.Perm.self_mem_cycle_factors_commute hc).symm | case hgc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
a : α
⊢ Commute g c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hgc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : c ∈ cycleFactorsFinset g
a : α
⊢ Commute g c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.eq_cycleOf_iff_sameCycle | [716, 1] | [728, 45] | rw [Equiv.Perm.cycle_is_cycleOf hy c.prop] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ ↑c = Equiv.Perm.cycleOf g x ↔ Equiv.Perm.SameCycle g y x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x ↔ Equiv.Perm.SameCycle g y x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ ↑c = Equiv.Perm.cycleOf g x ↔ Equiv.Perm.SameCycle g y x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.eq_cycleOf_iff_sameCycle | [716, 1] | [728, 45] | constructor | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x ↔ Equiv.Perm.SameCycle g y x | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x → Equiv.Perm.SameCycle g y x
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ Equiv.Perm.SameCycle g y x → Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x ↔ Equiv.Perm.SameCycle g y x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.eq_cycleOf_iff_sameCycle | [716, 1] | [728, 45] | intro hx' | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x → Equiv.Perm.SameCycle g y x | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ Equiv.Perm.SameCycle g y x | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x → Equiv.Perm.SameCycle g y x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.eq_cycleOf_iff_sameCycle | [716, 1] | [728, 45] | apply And.left | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ Equiv.Perm.SameCycle g y x | case mp.self
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ Equiv.Perm.SameCycle g y x ∧ ?mp.b
case mp.b
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ Prop | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ Equiv.Perm.SameCycle g y x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.eq_cycleOf_iff_sameCycle | [716, 1] | [728, 45] | rw [← Equiv.Perm.mem_support_cycleOf_iff] | case mp.self
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ Equiv.Perm.SameCycle g y x ∧ ?mp.b
case mp.b
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ Prop | case mp.self
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ x ∈ Equiv.Perm.support (Equiv.Perm.cycleOf g y) | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.self
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ Equiv.Perm.SameCycle g y x ∧ ?mp.b
case mp.b
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ Prop
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.eq_cycleOf_iff_sameCycle | [716, 1] | [728, 45] | rw [hx', Equiv.Perm.mem_support, Equiv.Perm.cycleOf_apply_self, ← Equiv.Perm.mem_support] | case mp.self
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ x ∈ Equiv.Perm.support (Equiv.Perm.cycleOf g y) | case mp.self
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ x ∈ Equiv.Perm.support g | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.self
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ x ∈ Equiv.Perm.support (Equiv.Perm.cycleOf g y)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.eq_cycleOf_iff_sameCycle | [716, 1] | [728, 45] | exact hx | case mp.self
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ x ∈ Equiv.Perm.support g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.self
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hx' : Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
⊢ x ∈ Equiv.Perm.support g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.eq_cycleOf_iff_sameCycle | [716, 1] | [728, 45] | intro hxy | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ Equiv.Perm.SameCycle g y x → Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hxy : Equiv.Perm.SameCycle g y x
⊢ Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
⊢ Equiv.Perm.SameCycle g y x → Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.eq_cycleOf_iff_sameCycle | [716, 1] | [728, 45] | rw [Equiv.Perm.SameCycle.cycleOf_eq hxy] | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hxy : Equiv.Perm.SameCycle g y x
⊢ Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : x ∈ Equiv.Perm.support g
hy : y ∈ Equiv.Perm.support ↑c
hxy : Equiv.Perm.SameCycle g y x
⊢ Equiv.Perm.cycleOf g y = Equiv.Perm.cycleOf g x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.SameCycle.eq_cycleOf | [734, 1] | [738, 81] | rw [Equiv.Perm.cycle_is_cycleOf hy c.prop, Equiv.Perm.SameCycle.cycleOf_eq hx] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : Equiv.Perm.SameCycle g y x
hy : y ∈ Equiv.Perm.support ↑c
⊢ ↑c = Equiv.Perm.cycleOf g x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x y : α
hx : Equiv.Perm.SameCycle g y x
hy : y ∈ Equiv.Perm.support ↑c
⊢ ↑c = Equiv.Perm.cycleOf g x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.sameCycle_of_mem_support | [741, 1] | [746, 51] | use ⟨g.cycleOf x, Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff.mpr hx⟩ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
x : α
hx : x ∈ Equiv.Perm.support g
⊢ ∃ c, ∀ y ∈ Equiv.Perm.support ↑c, Equiv.Perm.SameCycle g y x | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
x : α
hx : x ∈ Equiv.Perm.support g
⊢ ∀ y ∈ Equiv.Perm.support ↑{ val := Equiv.Perm.cycleOf g x, property := ⋯ }, Equiv.Perm.SameCycle g y x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
x : α
hx : x ∈ Equiv.Perm.support g
⊢ ∃ c, ∀ y ∈ Equiv.Perm.support ↑c, Equiv.Perm.SameCycle g y x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.sameCycle_of_mem_support | [741, 1] | [746, 51] | intro y hy | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
x : α
hx : x ∈ Equiv.Perm.support g
⊢ ∀ y ∈ Equiv.Perm.support ↑{ val := Equiv.Perm.cycleOf g x, property := ⋯ }, Equiv.Perm.SameCycle g y x | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
x : α
hx : x ∈ Equiv.Perm.support g
y : α
hy : y ∈ Equiv.Perm.support ↑{ val := Equiv.Perm.cycleOf g x, property := ⋯ }
⊢ Equiv.Perm.SameCycle g y x | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
x : α
hx : x ∈ Equiv.Perm.support g
⊢ ∀ y ∈ Equiv.Perm.support ↑{ val := Equiv.Perm.cycleOf g x, property := ⋯ }, Equiv.Perm.SameCycle g y x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.sameCycle_of_mem_support | [741, 1] | [746, 51] | rw [← Equiv.Perm.eq_cycleOf_iff_sameCycle hx hy] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
x : α
hx : x ∈ Equiv.Perm.support g
y : α
hy : y ∈ Equiv.Perm.support ↑{ val := Equiv.Perm.cycleOf g x, property := ⋯ }
⊢ Equiv.Perm.SameCycle g y x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
x : α
hx : x ∈ Equiv.Perm.support g
y : α
hy : y ∈ Equiv.Perm.support ↑{ val := Equiv.Perm.cycleOf g x, property := ⋯ }
⊢ Equiv.Perm.SameCycle g y x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_pow_of_mem | [749, 1] | [760, 15] | revert x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
⊢ ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_pow_of_mem | [749, 1] | [760, 15] | induction' n with n hrec | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
⊢ ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x | case zero
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ Nat.zero) { val := x, property := hx }) = (g ^ Nat.zero) x
case succ
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
hrec : ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
⊢ ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ Nat.succ n) { val := x, property := hx }) = (g ^ Nat.succ n) x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
⊢ ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_pow_of_mem | [749, 1] | [760, 15] | intro x hx | case zero
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ Nat.zero) { val := x, property := hx }) = (g ^ Nat.zero) x | case zero
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ Nat.zero) { val := x, property := hx }) = (g ^ Nat.zero) x | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ Nat.zero) { val := x, property := hx }) = (g ^ Nat.zero) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_pow_of_mem | [749, 1] | [760, 15] | simp only [pow_zero, Equiv.Perm.coe_one, id.def, Subtype.coe_mk] | case zero
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ Nat.zero) { val := x, property := hx }) = (g ^ Nat.zero) x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ Nat.zero) { val := x, property := hx }) = (g ^ Nat.zero) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_pow_of_mem | [749, 1] | [760, 15] | intro x hx | case succ
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
hrec : ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
⊢ ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ Nat.succ n) { val := x, property := hx }) = (g ^ Nat.succ n) x | case succ
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
hrec : ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ Nat.succ n) { val := x, property := hx }) = (g ^ Nat.succ n) x | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
hrec : ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
⊢ ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ Nat.succ n) { val := x, property := hx }) = (g ^ Nat.succ n) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_pow_of_mem | [749, 1] | [760, 15] | simp only [pow_succ, Equiv.Perm.coe_mul, Function.comp_apply] | case succ
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
hrec : ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ Nat.succ n) { val := x, property := hx }) = (g ^ Nat.succ n) x | case succ
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
hrec : ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ n) ((subtypePerm g hs) { val := x, property := hx })) = (g ^ n) (g x) | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
hrec : ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ Nat.succ n) { val := x, property := hx }) = (g ^ Nat.succ n) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_pow_of_mem | [749, 1] | [760, 15] | apply hrec | case succ
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
hrec : ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ n) ((subtypePerm g hs) { val := x, property := hx })) = (g ^ n) (g x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
n : ℕ
hrec : ∀ (x : α) (hx : x ∈ s), ↑((subtypePerm g hs ^ n) { val := x, property := hx }) = (g ^ n) x
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ n) ((subtypePerm g hs) { val := x, property := hx })) = (g ^ n) (g x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_zpow_of_mem | [763, 1] | [775, 23] | induction' i with i i | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
i : ℤ
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ i) { val := x, property := hx }) = (g ^ i) x | case ofNat
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ Int.ofNat i) { val := x, property := hx }) = (g ^ Int.ofNat i) x
case negSucc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ Int.negSucc i) { val := x, property := hx }) = (g ^ Int.negSucc i) x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
i : ℤ
x : α
hx : x ∈ s
⊢ ↑((subtypePerm g hs ^ i) { val := x, property := hx }) = (g ^ i) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_zpow_of_mem | [763, 1] | [775, 23] | apply Equiv.Perm.subtypePerm_apply_pow_of_mem | case ofNat
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ Int.ofNat i) { val := x, property := hx }) = (g ^ Int.ofNat i) x
case negSucc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ Int.negSucc i) { val := x, property := hx }) = (g ^ Int.negSucc i) x | case negSucc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ Int.negSucc i) { val := x, property := hx }) = (g ^ Int.negSucc i) x | Please generate a tactic in lean4 to solve the state.
STATE:
case ofNat
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ Int.ofNat i) { val := x, property := hx }) = (g ^ Int.ofNat i) x
case negSucc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ Int.negSucc i) { val := x, property := hx }) = (g ^ Int.negSucc i) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_zpow_of_mem | [763, 1] | [775, 23] | simp only [zpow_negSucc] | case negSucc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ Int.negSucc i) { val := x, property := hx }) = (g ^ Int.negSucc i) x | case negSucc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) = (g ^ (i + 1))⁻¹ x | Please generate a tactic in lean4 to solve the state.
STATE:
case negSucc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ Int.negSucc i) { val := x, property := hx }) = (g ^ Int.negSucc i) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_zpow_of_mem | [763, 1] | [775, 23] | apply Equiv.injective (g ^ (i + 1)) | case negSucc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) = (g ^ (i + 1))⁻¹ x | case negSucc.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ (g ^ (i + 1)) ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) = (g ^ (i + 1)) ((g ^ (i + 1))⁻¹ x) | Please generate a tactic in lean4 to solve the state.
STATE:
case negSucc
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) = (g ^ (i + 1))⁻¹ x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_zpow_of_mem | [763, 1] | [775, 23] | simp only [Equiv.Perm.apply_inv_self] | case negSucc.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ (g ^ (i + 1)) ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) = (g ^ (i + 1)) ((g ^ (i + 1))⁻¹ x) | case negSucc.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ (g ^ (i + 1)) ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) = x | Please generate a tactic in lean4 to solve the state.
STATE:
case negSucc.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ (g ^ (i + 1)) ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) = (g ^ (i + 1)) ((g ^ (i + 1))⁻¹ x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_zpow_of_mem | [763, 1] | [775, 23] | rw [← Equiv.Perm.subtypePerm_apply_pow_of_mem g s hs] | case negSucc.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ (g ^ (i + 1)) ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) = x | case negSucc.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ (i + 1))
{ val := ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }), property := ?negSucc.a.hx }) =
x
case negSucc.a.hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) ∈ s | Please generate a tactic in lean4 to solve the state.
STATE:
case negSucc.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ (g ^ (i + 1)) ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.subtypePerm_apply_zpow_of_mem | [763, 1] | [775, 23] | rw [Finset.mk_coe, Equiv.Perm.apply_inv_self, Subtype.coe_mk] | case negSucc.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ (i + 1))
{ val := ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }), property := ?negSucc.a.hx }) =
x
case negSucc.a.hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) ∈ s | case negSucc.a.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) ∈ ↑s | Please generate a tactic in lean4 to solve the state.
STATE:
case negSucc.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ (i + 1))
{ val := ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }), property := ?negSucc.a.hx }) =
x
case negSucc.a.hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
s : Finset α
hs : ∀ (x : α), x ∈ s ↔ g x ∈ s
x : α
hx : x ∈ s
i : ℕ
⊢ ↑((subtypePerm g hs ^ (i + 1))⁻¹ { val := x, property := hx }) ∈ s
TACTIC:
|
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