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.Perm.subtypePerm_apply_zpow_of_mem | [763, 1] | [775, 23] | apply Finset.coe_mem | 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 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.isInvariant_of_support_le | [779, 1] | [784, 41] | by_cases hx' : x ∈ c.support | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
⊢ x ∈ s ↔ c x ∈ s | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
hx' : x ∈ support c
⊢ x ∈ s ↔ c x ∈ s
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
hx' : x ∉ support c
⊢ x ∈ s ↔ c x ∈ s | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
⊢ x ∈ s ↔ c x ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.isInvariant_of_support_le | [779, 1] | [784, 41] | rw [Equiv.Perm.not_mem_support.mp hx'] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
hx' : x ∉ support c
⊢ x ∈ s ↔ c x ∈ s | 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
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
hx' : x ∉ support c
⊢ x ∈ s ↔ c x ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.isInvariant_of_support_le | [779, 1] | [784, 41] | simp only [hcs hx', true_iff_iff] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
hx' : x ∈ support c
⊢ x ∈ s ↔ c x ∈ s | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
hx' : x ∈ support c
⊢ c x ∈ s | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
hx' : x ∈ support c
⊢ x ∈ s ↔ c x ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.isInvariant_of_support_le | [779, 1] | [784, 41] | exact hcs (Equiv.Perm.apply_mem_support.mpr hx') | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
hx' : x ∈ support c
⊢ c x ∈ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
c : Perm α
s : Finset α
hcs : support c ≤ s
x : α
hx' : x ∈ support c
⊢ c x ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.nonempty_support | [799, 1] | [802, 37] | rw [Finset.nonempty_iff_ne_empty, Ne.def, Equiv.Perm.support_eq_empty_iff] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
hg : IsCycle g
⊢ (support g).Nonempty | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
hg : IsCycle g
⊢ ¬g = 1 | 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
hg : IsCycle g
⊢ (support g).Nonempty
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.nonempty_support | [799, 1] | [802, 37] | exact Equiv.Perm.IsCycle.ne_one hg | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Perm α
hg : IsCycle g
⊢ ¬g = 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 : Perm α
hg : IsCycle g
⊢ ¬g = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | constructor | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
⊢ Commute g c ↔
∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
⊢ Commute g c →
∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
⊢ (∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c),
subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)) →
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 : IsCycle c
⊢ Commute g c ↔
∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | intro hgc | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
⊢ Commute g c →
∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
⊢ ∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | 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 c : Perm α
hc : IsCycle c
⊢ Commute g c →
∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | let hgc' := Equiv.Perm.mem_support_of_commute hgc | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
⊢ ∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
⊢ ∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | 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 c : Perm α
hc : IsCycle c
hgc : Commute g c
⊢ ∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | use hgc' | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
⊢ ∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | 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 c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
⊢ ∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | obtain ⟨a, ha⟩ := Equiv.Perm.IsCycle.nonempty_support hc | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | case h.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | 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 c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | suffices c.SameCycle a (g a) by
simp only [Equiv.Perm.SameCycle] at this
obtain ⟨i, hi⟩ := this; use i
ext ⟨x, hx⟩
simp only [Equiv.Perm.subtypePermOfSupport, Subtype.coe_mk, Equiv.Perm.subtypePerm_apply]
rw [Equiv.Perm.subtypePerm_apply_zpow_of_mem]
suffices c.SameCycle a x by
obtain ⟨j, rfl⟩ := this
simp only [← Equiv.Perm.mul_apply, Commute.eq (Commute.zpow_right hgc j)]
rw [← zpow_add, add_comm i j, zpow_add]
simp only [Equiv.Perm.mul_apply]
simp only [EmbeddingLike.apply_eq_iff_eq]
exact hi
exact hc.sameCycle (mem_support.mp ha) (mem_support.mp hx) | case h.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | case h.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
⊢ SameCycle c a (g a) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | apply hc.sameCycle (mem_support.mp ha) (mem_support.mp ((hgc' a).mp ha)) | case h.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
⊢ SameCycle c a (g a) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
⊢ SameCycle c a (g a)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | simp only [Equiv.Perm.SameCycle] at this | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
this : SameCycle c a (g a)
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
this : ∃ i, (c ^ i) a = g a
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport 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 : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
this : SameCycle c a (g a)
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | obtain ⟨i, hi⟩ := this | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
this : ∃ i, (c ^ i) a = g a
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport 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 : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
this : ∃ i, (c ^ i) a = g a
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | use i | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
⊢ (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hgc' | 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 c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
⊢ subtypePerm g hgc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | ext ⟨x, hx⟩ | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
⊢ (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hgc' | case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ ↑(((fun x => subtypePermOfSupport c ^ x) i) { val := x, property := hx }) =
↑((subtypePerm g hgc') { val := x, property := hx }) | 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 c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
⊢ (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hgc'
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | simp only [Equiv.Perm.subtypePermOfSupport, Subtype.coe_mk, Equiv.Perm.subtypePerm_apply] | case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ ↑(((fun x => subtypePermOfSupport c ^ x) i) { val := x, property := hx }) =
↑((subtypePerm g hgc') { val := x, property := hx }) | case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ ↑((subtypePerm c ⋯ ^ i) { val := x, property := hx }) = g x | Please generate a tactic in lean4 to solve the state.
STATE:
case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ ↑(((fun x => subtypePermOfSupport c ^ x) i) { val := x, property := hx }) =
↑((subtypePerm g hgc') { val := x, property := hx })
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | rw [Equiv.Perm.subtypePerm_apply_zpow_of_mem] | case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ ↑((subtypePerm c ⋯ ^ i) { val := x, property := hx }) = g x | case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ (c ^ i) x = g x | Please generate a tactic in lean4 to solve the state.
STATE:
case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ ↑((subtypePerm c ⋯ ^ i) { val := x, property := hx }) = g x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | suffices c.SameCycle a x by
obtain ⟨j, rfl⟩ := this
simp only [← Equiv.Perm.mul_apply, Commute.eq (Commute.zpow_right hgc j)]
rw [← zpow_add, add_comm i j, zpow_add]
simp only [Equiv.Perm.mul_apply]
simp only [EmbeddingLike.apply_eq_iff_eq]
exact hi | case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ (c ^ i) x = g x | case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ SameCycle c a x | Please generate a tactic in lean4 to solve the state.
STATE:
case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ (c ^ i) x = g x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | exact hc.sameCycle (mem_support.mp ha) (mem_support.mp hx) | case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ SameCycle c a x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
⊢ SameCycle c a x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | obtain ⟨j, rfl⟩ := this | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
this : SameCycle c a x
⊢ (c ^ i) x = g x | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ i) ((c ^ j) a) = g ((c ^ j) a) | 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 : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
x : α
hx : x ∈ support c
this : SameCycle c a x
⊢ (c ^ i) x = g x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | simp only [← Equiv.Perm.mul_apply, Commute.eq (Commute.zpow_right hgc j)] | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ i) ((c ^ j) a) = g ((c ^ j) a) | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ i * c ^ j) a = (c ^ j * g) 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 c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ i) ((c ^ j) a) = g ((c ^ j) a)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | rw [← zpow_add, add_comm i j, zpow_add] | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ i * c ^ j) a = (c ^ j * g) a | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ j * c ^ i) a = (c ^ j * g) 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 c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ i * c ^ j) a = (c ^ j * g) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | simp only [Equiv.Perm.mul_apply] | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ j * c ^ i) a = (c ^ j * g) a | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ j) ((c ^ i) a) = (c ^ j) (g 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 c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ j * c ^ i) a = (c ^ j * g) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | simp only [EmbeddingLike.apply_eq_iff_eq] | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ j) ((c ^ i) a) = (c ^ j) (g a) | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ i) a = g 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 c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ j) ((c ^ i) a) = (c ^ j) (g a)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | exact hi | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ i) a = g a | no goals | 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 c : Perm α
hc : IsCycle c
hgc : Commute g c
hgc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c := mem_support_of_commute hgc
a : α
ha : a ∈ support c
i : ℤ
hi : (c ^ i) a = g a
j : ℤ
hx : (c ^ j) a ∈ support c
⊢ (c ^ i) a = g a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | rintro ⟨hc', h⟩ | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
⊢ (∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c),
subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)) →
Commute g c | case mpr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
h : subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
⊢ Commute g c | 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 c : Perm α
hc : IsCycle c
⊢ (∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c),
subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)) →
Commute g c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | obtain ⟨i, hi⟩ := h | case mpr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
h : subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
⊢ Commute g c | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
⊢ Commute g c | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
h : subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)
⊢ Commute g c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | intro x hx | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
⊢ ∀ x ∈ support c, g x = (c ^ i) x | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
⊢ g x = (c ^ i) x | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
⊢ ∀ x ∈ support c, g x = (c ^ i) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | let hix := Equiv.Perm.congr_fun hi ⟨x, hx⟩ | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
⊢ g x = (c ^ i) x | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
hix : ((fun x => subtypePermOfSupport c ^ x) i) { val := x, property := hx } =
(subtypePerm g hc') { val := x, property := hx } :=
Perm.congr_fun hi { val := x, property := hx }
⊢ g x = (c ^ i) x | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
⊢ g x = (c ^ i) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | simp only [← Subtype.coe_inj, Equiv.Perm.subtypePermOfSupport] at hix | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
hix : ((fun x => subtypePermOfSupport c ^ x) i) { val := x, property := hx } =
(subtypePerm g hc') { val := x, property := hx } :=
Perm.congr_fun hi { val := x, property := hx }
⊢ g x = (c ^ i) x | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
hix : ↑((subtypePerm c ⋯ ^ i) { val := x, property := hx }) = ↑((subtypePerm g hc') { val := x, property := hx })
⊢ g x = (c ^ i) x | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
hix : ((fun x => subtypePermOfSupport c ^ x) i) { val := x, property := hx } =
(subtypePerm g hc') { val := x, property := hx } :=
Perm.congr_fun hi { val := x, property := hx }
⊢ g x = (c ^ i) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | simp only [Subtype.coe_mk, Equiv.Perm.subtypePerm_apply,
Equiv.Perm.subtypePerm_apply_zpow_of_mem] at hix | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
hix : ↑((subtypePerm c ⋯ ^ i) { val := x, property := hx }) = ↑((subtypePerm g hc') { val := x, property := hx })
⊢ g x = (c ^ i) x | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
hix : (c ^ i) x = g x
⊢ g x = (c ^ i) x | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
hix : ↑((subtypePerm c ⋯ ^ i) { val := x, property := hx }) = ↑((subtypePerm g hc') { val := x, property := hx })
⊢ g x = (c ^ i) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | exact hix.symm | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
hix : (c ^ i) x = g x
⊢ g x = (c ^ i) x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
x : α
hx : x ∈ support c
hix : (c ^ i) x = g x
⊢ g x = (c ^ i) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | ext x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
⊢ Commute g c | case H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
⊢ (g * c) x = (c * 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
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
⊢ Commute g c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | simp only [Equiv.Perm.coe_mul, Function.comp_apply] | case H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
⊢ (g * c) x = (c * g) x | case H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
⊢ g (c x) = c (g 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 c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
⊢ (g * c) x = (c * g) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | by_cases hx : x ∈ c.support | case H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
⊢ g (c x) = c (g x) | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ g (c x) = c (g x)
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ g (c x) = c (g 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 c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
⊢ g (c x) = c (g x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | rw [hi' x hx] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ g (c x) = c (g x) | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ g (c x) = c ((c ^ i) 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 c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ g (c x) = c (g x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | rw [hi' (c x) (apply_mem_support.mpr hx)] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ g (c x) = c ((c ^ i) x) | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ (c ^ i) (c x) = c ((c ^ i) 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 c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ g (c x) = c ((c ^ i) x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | simp only [← Equiv.Perm.mul_apply, ← zpow_add_one, ← zpow_one_add] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ (c ^ i) (c x) = c ((c ^ i) x) | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ (c ^ (i + 1)) x = (c ^ (1 + i)) 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 c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ (c ^ i) (c x) = c ((c ^ i) x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | rw [Int.add_comm 1 i] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ (c ^ (i + 1)) x = (c ^ (1 + i)) x | no goals | 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 : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∈ support c
⊢ (c ^ (i + 1)) x = (c ^ (1 + i)) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | rw [not_mem_support.mp hx] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ g (c x) = c (g x) | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ g x = c (g x) | 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 : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ g (c x) = c (g x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | apply symm | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ g x = c (g x) | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ c (g x) = g x | 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 : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ g x = c (g x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | rw [← Equiv.Perm.not_mem_support] | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ c (g x) = g x | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ g x ∉ support c | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ c (g x) = g x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | intro hx' | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ g x ∉ support c | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
hx' : g x ∈ support c
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
⊢ g x ∉ support c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | apply hx | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
hx' : g x ∈ support c
⊢ False | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
hx' : g x ∈ support c
⊢ x ∈ support c | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
hx' : g x ∈ support c
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff' | [806, 1] | [854, 19] | exact (hc' x).mpr hx' | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
hx' : g x ∈ support c
⊢ x ∈ support c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
i : ℤ
hi : (fun x => subtypePermOfSupport c ^ x) i = subtypePerm g hc'
hi' : ∀ x ∈ support c, g x = (c ^ i) x
x : α
hx : x ∉ support c
hx' : g x ∈ support c
⊢ x ∈ support c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | simp only [Equiv.ext_iff, subtypePerm_apply, Subtype.mk.injEq, Subtype.forall] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ ofSubtype (subtypePerm g hg) = c ↔
support c ≤ s ∧ ∀ (hc' : ∀ (x : α), x ∈ s ↔ c x ∈ s), subtypePerm c hc' = subtypePerm g hg | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ (∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x) ↔
support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a) | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ ofSubtype (subtypePerm g hg) = c ↔
support c ≤ s ∧ ∀ (hc' : ∀ (x : α), x ∈ s ↔ c x ∈ s), subtypePerm c hc' = subtypePerm g hg
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | constructor | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ (∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x) ↔
support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ (∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x) →
support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a)
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a) →
∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ (∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x) ↔
support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | intro h | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ (∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x) →
support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
⊢ support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a) | 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ (∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x) →
support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | suffices hc : support c ≤ s by
use hc
intro _ a ha
rw [← h a, ofSubtype_apply_of_mem]
rfl
exact ha | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
⊢ support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
⊢ support c ≤ s | 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
⊢ support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | intro a ha | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
⊢ support c ≤ s | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : a ∈ support c
⊢ a ∈ s | 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
⊢ support c ≤ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | by_contra ha' | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : a ∈ support c
⊢ a ∈ s | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : a ∈ support c
ha' : a ∉ s
⊢ False | 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : a ∈ support c
⊢ a ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | rw [Equiv.Perm.mem_support, ← h a, ofSubtype_apply_of_not_mem] at ha | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : a ∈ support c
ha' : a ∉ s
⊢ False | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : a ≠ a
ha' : a ∉ s
⊢ False
case mp.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : (ofSubtype (subtypePerm g hg)) a ≠ a
ha' : a ∉ s
⊢ a ∉ s | 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : a ∈ support c
ha' : a ∉ s
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | exact ha rfl | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : a ≠ a
ha' : a ∉ s
⊢ False
case mp.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : (ofSubtype (subtypePerm g hg)) a ≠ a
ha' : a ∉ s
⊢ a ∉ s | case mp.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : (ofSubtype (subtypePerm g hg)) a ≠ a
ha' : a ∉ s
⊢ a ∉ s | 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : a ≠ a
ha' : a ∉ s
⊢ False
case mp.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : (ofSubtype (subtypePerm g hg)) a ≠ a
ha' : a ∉ s
⊢ a ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | exact ha' | case mp.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : (ofSubtype (subtypePerm g hg)) a ≠ a
ha' : a ∉ s
⊢ a ∉ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
a : α
ha : (ofSubtype (subtypePerm g hg)) a ≠ a
ha' : a ∉ s
⊢ a ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | use hc | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
⊢ support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a) | case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
⊢ (∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
⊢ support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | intro _ a ha | case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
⊢ (∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a | case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ c a = g a | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
⊢ (∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | rw [← h a, ofSubtype_apply_of_mem] | case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ c a = g a | case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ ↑((subtypePerm g hg) { val := a, property := ?right.ha }) = g a
case right.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ a ∈ s | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ c a = g a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | rfl | case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ ↑((subtypePerm g hg) { val := a, property := ?right.ha }) = g a
case right.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ a ∈ s | case right.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ a ∈ s | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ ↑((subtypePerm g hg) { val := a, property := ?right.ha }) = g a
case right.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ a ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | exact ha | case right.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ a ∈ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
h : ∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
hc : support c ≤ s
hc'✝ : ∀ (x : α), x ∈ s ↔ c x ∈ s
a : α
ha : a ∈ s
⊢ a ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | rintro ⟨hc, h⟩ a | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a) →
∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x | case mpr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
h : (∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a
a : α
⊢ (ofSubtype (subtypePerm g hg)) a = c a | 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
⊢ support c ≤ s ∧ ((∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a) →
∀ (x : α), (ofSubtype (subtypePerm g hg)) x = c x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | specialize h (isInvariant_of_support_le hc) | case mpr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
h : (∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a
a : α
⊢ (ofSubtype (subtypePerm g hg)) a = c a | case mpr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
⊢ (ofSubtype (subtypePerm g hg)) a = c a | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
h : (∀ (x : α), x ∈ s ↔ c x ∈ s) → ∀ a ∈ s, c a = g a
a : α
⊢ (ofSubtype (subtypePerm g hg)) a = c a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | by_cases ha : a ∈ s | case mpr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
⊢ (ofSubtype (subtypePerm g hg)) a = c a | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ (ofSubtype (subtypePerm g hg)) a = c a
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ (ofSubtype (subtypePerm g hg)) a = c a | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
⊢ (ofSubtype (subtypePerm g hg)) a = c a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | rw [h a ha, ofSubtype_apply_of_mem] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ (ofSubtype (subtypePerm g hg)) a = c a | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ ↑((subtypePerm g hg) { val := a, property := ?pos.ha✝ }) = g a
case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ a ∈ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ (ofSubtype (subtypePerm g hg)) a = c a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | rfl | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ ↑((subtypePerm g hg) { val := a, property := ?pos.ha✝ }) = g a
case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ a ∈ s | case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ a ∈ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ ↑((subtypePerm g hg) { val := a, property := ?pos.ha✝ }) = g a
case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ a ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | exact ha | case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ a ∈ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∈ s
⊢ a ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | rw [ofSubtype_apply_of_not_mem] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ (ofSubtype (subtypePerm g hg)) a = c a | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a = c a
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ (ofSubtype (subtypePerm g hg)) a = c a
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | apply symm | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a = c a
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ c a = a
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a = c a
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | rw [← Equiv.Perm.not_mem_support] | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ c a = a
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ support c
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ c a = a
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | intro ha' | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ support c
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
ha' : a ∈ support c
⊢ False
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ support c
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | exact ha (hc ha') | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
ha' : a ∈ support c
⊢ False
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
ha' : a ∈ support c
⊢ False
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.ofSubtype_eq_iff | [857, 1] | [887, 15] | exact ha | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ≤ s
a : α
h : ∀ a ∈ s, c a = g a
ha : a ∉ s
⊢ a ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | constructor | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
⊢ c ^ n = ofSubtype (subtypePerm g hg) ↔ subtypePerm c ⋯ ^ n = subtypePerm g hg | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
⊢ c ^ n = ofSubtype (subtypePerm g hg) → subtypePerm c ⋯ ^ n = subtypePerm g hg
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
⊢ subtypePerm c ⋯ ^ n = subtypePerm g hg → c ^ n = ofSubtype (subtypePerm g hg) | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
⊢ c ^ n = ofSubtype (subtypePerm g hg) ↔ subtypePerm c ⋯ ^ n = subtypePerm g hg
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | intro h | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
⊢ c ^ n = ofSubtype (subtypePerm g hg) → subtypePerm c ⋯ ^ n = subtypePerm g hg | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
⊢ subtypePerm c ⋯ ^ n = subtypePerm g hg | 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
⊢ c ^ n = ofSubtype (subtypePerm g hg) → subtypePerm c ⋯ ^ n = subtypePerm g hg
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | ext ⟨x, hx⟩ | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
⊢ subtypePerm c ⋯ ^ n = subtypePerm g hg | case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
⊢ ↑((subtypePerm c ⋯ ^ n) { val := x, property := hx }) = ↑((subtypePerm g hg) { val := x, property := hx }) | 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
⊢ subtypePerm c ⋯ ^ n = subtypePerm g hg
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | let h' := Equiv.Perm.congr_fun h x | case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
⊢ ↑((subtypePerm c ⋯ ^ n) { val := x, property := hx }) = ↑((subtypePerm g hg) { val := x, property := hx }) | case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ ↑((subtypePerm c ⋯ ^ n) { val := x, property := hx }) = ↑((subtypePerm g hg) { val := x, property := hx }) | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
⊢ ↑((subtypePerm c ⋯ ^ n) { val := x, property := hx }) = ↑((subtypePerm g hg) { val := x, property := hx })
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | simp only [h', Equiv.Perm.subtypePerm_apply_zpow_of_mem, Subtype.coe_mk,
Equiv.Perm.subtypePerm_apply] | case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ ↑((subtypePerm c ⋯ ^ n) { val := x, property := hx }) = ↑((subtypePerm g hg) { val := x, property := hx }) | case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ (ofSubtype (subtypePerm g hg)) x = g x | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ ↑((subtypePerm c ⋯ ^ n) { val := x, property := hx }) = ↑((subtypePerm g hg) { val := x, property := hx })
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | rw [Equiv.Perm.ofSubtype_apply_of_mem] | case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ (ofSubtype (subtypePerm g hg)) x = g x | case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ ↑((subtypePerm g hg) { val := x, property := ?mp.H.mk.a.ha }) = g x
case mp.H.mk.a.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ x ∈ s | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ (ofSubtype (subtypePerm g hg)) x = g x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | simp only [Subtype.coe_mk, Equiv.Perm.subtypePerm_apply] | case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ ↑((subtypePerm g hg) { val := x, property := ?mp.H.mk.a.ha }) = g x
case mp.H.mk.a.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ x ∈ s | case mp.H.mk.a.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ x ∈ s | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ ↑((subtypePerm g hg) { val := x, property := ?mp.H.mk.a.ha }) = g x
case mp.H.mk.a.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ x ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | exact hx | case mp.H.mk.a.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ x ∈ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.H.mk.a.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : c ^ n = ofSubtype (subtypePerm g hg)
x : α
hx : x ∈ s
h' : (c ^ n) x = (ofSubtype (subtypePerm g hg)) x := Perm.congr_fun h x
⊢ x ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | intro h | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
⊢ subtypePerm c ⋯ ^ n = subtypePerm g hg → c ^ n = ofSubtype (subtypePerm g hg) | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
⊢ c ^ n = ofSubtype (subtypePerm g hg) | 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
⊢ subtypePerm c ⋯ ^ n = subtypePerm g hg → c ^ n = ofSubtype (subtypePerm g hg)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | ext x | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
⊢ c ^ n = ofSubtype (subtypePerm g hg) | case mpr.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
⊢ (c ^ n) x = (ofSubtype (subtypePerm g hg)) 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 c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
⊢ c ^ n = ofSubtype (subtypePerm g hg)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | rw [← h] | case mpr.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
⊢ (c ^ n) x = (ofSubtype (subtypePerm g hg)) x | case mpr.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
⊢ (c ^ n) x = (ofSubtype (subtypePerm c ⋯ ^ n)) x | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
⊢ (c ^ n) x = (ofSubtype (subtypePerm g hg)) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | by_cases hx : x ∈ s | case mpr.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
⊢ (c ^ n) x = (ofSubtype (subtypePerm c ⋯ ^ n)) x | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ (c ^ n) x = (ofSubtype (subtypePerm c ⋯ ^ n)) x
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ (c ^ n) x = (ofSubtype (subtypePerm c ⋯ ^ n)) x | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
⊢ (c ^ n) x = (ofSubtype (subtypePerm c ⋯ ^ n)) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | rw [Equiv.Perm.ofSubtype_apply_of_mem] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ (c ^ n) x = (ofSubtype (subtypePerm c ⋯ ^ n)) x | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ (c ^ n) x = ↑((subtypePerm c ⋯ ^ n) { val := x, property := ?pos.ha✝ })
case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ x ∈ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ (c ^ n) x = (ofSubtype (subtypePerm c ⋯ ^ n)) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | simp only [subtypePerm_zpow, subtypePerm_apply] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ (c ^ n) x = ↑((subtypePerm c ⋯ ^ n) { val := x, property := ?pos.ha✝ })
case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ x ∈ s | case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ x ∈ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ (c ^ n) x = ↑((subtypePerm c ⋯ ^ n) { val := x, property := ?pos.ha✝ })
case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ x ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | exact hx | case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ x ∈ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∈ s
⊢ x ∈ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | rw [Equiv.Perm.ofSubtype_apply_of_not_mem] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ (c ^ n) x = (ofSubtype (subtypePerm c ⋯ ^ n)) x | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ (c ^ n) x = x
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ (c ^ n) x = (ofSubtype (subtypePerm c ⋯ ^ n)) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | rw [← Equiv.Perm.not_mem_support] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ (c ^ n) x = x
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ support (c ^ n)
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ (c ^ n) x = x
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | intro hx' | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ support (c ^ n)
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ False
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ support (c ^ n)
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | apply hx | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ False
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ x ∈ s
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ False
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | apply hc | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ x ∈ s
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ x ∈ support c
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | 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
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ x ∈ s
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | apply Equiv.Perm.support_zpow_le | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ x ∈ support c
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | case neg.a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ x ∈ support (c ^ ?neg.a.n✝)
case neg.a.n
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ ℤ
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ x ∈ support c
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | exact hx' | case neg.a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ x ∈ support (c ^ ?neg.a.n✝)
case neg.a.n
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ ℤ
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ x ∈ support (c ^ ?neg.a.n✝)
case neg.a.n
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
hx' : x ∈ support (c ^ n)
⊢ ℤ
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.zpow_eq_ofSubtype_subtypePerm_iff | [913, 1] | [936, 15] | exact hx | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
s : Finset α
hg : ∀ (x : α), x ∈ s ↔ g x ∈ s
hc : support c ⊆ s
n : ℤ
h : subtypePerm c ⋯ ^ n = subtypePerm g hg
x : α
hx : x ∉ s
⊢ x ∉ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff | [941, 1] | [969, 37] | rw [Equiv.Perm.IsCycle.commute_iff' hc] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
⊢ Commute g c ↔ ∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), ofSubtype (subtypePerm g hc') ∈ Subgroup.zpowers c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
⊢ (∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c),
subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)) ↔
∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), ofSubtype (subtypePerm g hc') ∈ Subgroup.zpowers 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 : IsCycle c
⊢ Commute g c ↔ ∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), ofSubtype (subtypePerm g hc') ∈ Subgroup.zpowers c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff | [941, 1] | [969, 37] | apply exists_congr | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
⊢ (∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c),
subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)) ↔
∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), ofSubtype (subtypePerm g hc') ∈ Subgroup.zpowers c | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
⊢ ∀ (a : ∀ (x : α), x ∈ support c ↔ g x ∈ support c),
subtypePerm g a ∈ Subgroup.zpowers (subtypePermOfSupport c) ↔ ofSubtype (subtypePerm g a) ∈ Subgroup.zpowers 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 : IsCycle c
⊢ (∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c),
subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c)) ↔
∃ (hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c), ofSubtype (subtypePerm g hc') ∈ Subgroup.zpowers c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.IsCycle.commute_iff | [941, 1] | [969, 37] | intro hc' | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
⊢ ∀ (a : ∀ (x : α), x ∈ support c ↔ g x ∈ support c),
subtypePerm g a ∈ Subgroup.zpowers (subtypePermOfSupport c) ↔ ofSubtype (subtypePerm g a) ∈ Subgroup.zpowers c | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g c : Perm α
hc : IsCycle c
hc' : ∀ (x : α), x ∈ support c ↔ g x ∈ support c
⊢ subtypePerm g hc' ∈ Subgroup.zpowers (subtypePermOfSupport c) ↔ ofSubtype (subtypePerm g hc') ∈ Subgroup.zpowers c | 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 c : Perm α
hc : IsCycle c
⊢ ∀ (a : ∀ (x : α), x ∈ support c ↔ g x ∈ support c),
subtypePerm g a ∈ Subgroup.zpowers (subtypePermOfSupport c) ↔ ofSubtype (subtypePerm g a) ∈ Subgroup.zpowers c
TACTIC:
|
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