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 | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | apply hc | case neg.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬Equiv.Perm.cycleOf g x = ↑c
hc' : { val := Equiv.Perm.cycleOf g x, property := hx } = c... | case neg.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬Equiv.Perm.cycleOf g x = ↑c
hc' : { val := Equiv.Perm.cycleOf g x, property := hx } = c... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬Equiv.Perm.cycleOf g x = ↑... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | rw [← hc'] | case neg.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬Equiv.Perm.cycleOf g x = ↑c
hc' : { val := Equiv.Perm.cycleOf g x, property := hx } = c... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬Equiv.Perm.cycleOf g x = ↑... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | rw [Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff, Equiv.Perm.not_mem_support] at hx | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : Equiv.Perm.cycleOf g x ∉ Equiv.Perm.cycleFactorsFinset g
⊢ ((θ g) (1, Pi.mulSingle c vc)) x = ↑vc x | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
⊢ ((θ g) (1, Pi.mulSingle c vc)) x = ↑vc 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 : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : Equiv.Perm.cycleOf g x ∉ Equiv.Perm.cycleFactorsFinset g
⊢ ((θ g) (1, Pi.mulSingle c vc)) x... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | rw [hθ_1 _ x hx] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
⊢ ((θ g) (1, Pi.mulSingle c vc)) x = ↑vc x | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
⊢ ↑((1, Pi.mulSingle c vc).1 { val := x, property := hx }) = ↑vc 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 : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
⊢ ((θ g) (1, Pi.mulSingle c vc)) x = ↑vc x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | dsimp only [Equiv.Perm.coe_one, id_eq] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
⊢ ↑((1, Pi.mulSingle c vc).1 { val := x, property := hx }) = ↑vc x | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
⊢ x = ↑vc 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 : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
⊢ ↑((1, Pi.mulSingle c vc).1 { val := x, property := hx }) = ↑vc x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | obtain ⟨m, hm⟩ := vc.prop | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
⊢ x = ↑vc x | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : (fun x => ↑c ^ x) m = ↑vc
⊢ x = ↑vc 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 : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
⊢ x = ↑vc x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | dsimp only at hm | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : (fun x => ↑c ^ x) m = ↑vc
⊢ x = ↑vc x | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ x = ↑vc x | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : (fun x => ↑c ^ x) m = ↑vc
⊢ x = ↑vc x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | rw [← hm] | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ x = ↑vc x | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ x = (↑c ^ m) x | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ x = ↑vc x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | apply symm | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ x = (↑c ^ m) x | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ (↑c ^ m) x = x | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ x = (↑c ^ m) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | rw [← Equiv.Perm.not_mem_support] at hx ⊢ | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ (↑c ^ m) x = x | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ x ∉ Equiv.Perm.support (↑c ^ m) | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : g x = x
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ (↑c ^ m) x = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | intro hx' | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ x ∉ Equiv.Perm.support (↑c ^ m) | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
hx' : x ∈ Equiv.Perm.support (↑c ^ m)
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
⊢ x ∉ Equiv.Perm.support (↑c ^ m)
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | apply hx | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
hx' : x ∈ Equiv.Perm.support (↑c ^ m)
⊢ False | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
hx' : x ∈ Equiv.Perm.support (↑c ^ m)
⊢ x ∈ Equiv.Perm.support g | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
hx' : x ∈ Equiv.Perm.support (↑c ^... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | apply Equiv.Perm.mem_cycleFactorsFinset_support_le c.prop | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
hx' : x ∈ Equiv.Perm.support (↑c ^ m)
⊢ x ∈ Equiv.Perm.support g | case neg.intro.a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
hx' : x ∈ Equiv.Perm.support (↑c ^ m)
⊢ x ∈ Equiv.Perm.support ↑c | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
hx' : x ∈ Equiv.Perm.support (↑c ^... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θ_apply_single | [3240, 1] | [3279, 45] | apply Equiv.Perm.support_zpow_le _ _ hx' | case neg.intro.a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
hx' : x ∈ Equiv.Perm.support (↑c ^ m)
⊢ x ∈ Equiv.Perm.support ↑c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
vc : ↥(Subgroup.zpowers ↑c)
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ
hm : ↑c ^ m = ↑vc
hx' : x ∈ Equiv.Perm.support (↑c... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | rw [← Prod.fst_mul_snd ⟨k, v⟩] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (k, v)) = Equiv.Perm.sign k * Finset.prod Finset.univ fun c => Equiv.Perm.sign ↑(v c) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (((k, v).1, 1) * (1, (k, v).2))) =
Equiv.Perm.sign k * Finset.prod Finset.univ fun c => Equiv.Perm.s... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (k, v)) = Equiv.Perm.sign k * Finset.prod F... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | simp only [map_mul] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (((k, v).1, 1) * (1, (k, v).2))) =
Equiv.Perm.sign k * Finset.prod Finset.univ fun c => Equiv.Perm.s... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (k, 1)) * Equiv.Perm.sign ((θ g) (1, v)) =
Equiv.Perm.sign k * Finset.prod Finset.univ fun c => Equi... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (((k, v).1, 1) * (1, (k, v).2))) =
Equi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | apply congr_arg₂ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (k, 1)) * Equiv.Perm.sign ((θ g) (1, v)) =
Equiv.Perm.sign k * Finset.prod Finset.univ fun c => Equi... | case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (k, 1)) = Equiv.Perm.sign k
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : E... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (k, 1)) * Equiv.Perm.sign ((θ g) (1, v)) =
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | rw [θ_apply_fst, Equiv.Perm.sign_ofSubtype] | case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (k, 1)) = Equiv.Perm.sign k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (k, 1)) = Equiv.Perm.sign k
TACTIC:... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | rw [← MonoidHom.inr_apply, ← MonoidHom.comp_apply] | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (1, v)) = Finset.prod Finset.univ fun c => Equiv.Perm.sign ↑(v c) | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.inr (Equiv.Perm ↑(MulAction.fixedBy α g))
((c : { x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Equiv.Perm.sign ((θ g) (1, v)) = Finset.prod Finset.univ f... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | conv_lhs => rw [← Finset.noncommProd_mul_single v] | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.inr (Equiv.Perm ↑(MulAction.fixedBy α g))
((c : { x ... | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.inr (Equiv.Perm ↑(MulAction.fixedBy α g))
((c : { x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.i... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | simp only [Finset.noncommProd_map] | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.inr (Equiv.Perm ↑(MulAction.fixedBy α g))
((c : { x ... | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Finset.noncommProd Finset.univ
(fun i =>
(MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.inr... | Please generate a tactic in lean4 to solve the state.
STATE:
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.i... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | rw [Finset.noncommProd_eq_prod] | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Finset.noncommProd Finset.univ
(fun i =>
(MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.inr... | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (Finset.prod Finset.univ fun i =>
(MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.inr (Equiv.Perm ↑(Mu... | Please generate a tactic in lean4 to solve the state.
STATE:
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Finset.noncommProd Finset.univ
(fun i =>
(Mo... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | apply Finset.prod_congr rfl | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (Finset.prod Finset.univ fun i =>
(MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.inr (Equiv.Perm ↑(Mu... | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ ∀ x ∈ Finset.univ,
(MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.inr (Equiv.Perm ↑(MulAction.fixedBy α... | Please generate a tactic in lean4 to solve the state.
STATE:
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (Finset.prod Finset.univ fun i =>
(MonoidHom.comp Eq... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | intro c _ | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ ∀ x ∈ Finset.univ,
(MonoidHom.comp Equiv.Perm.sign (θ g))
((MonoidHom.inr (Equiv.Perm ↑(MulAction.fixedBy α... | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
a✝ : c ∈ Finset.univ
⊢ (MonoidHom.comp Equiv.Perm.sign (θ g))
((Mo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ ∀ x ∈ Finset.univ,
(MonoidHom.comp Equiv.Perm.sign (θ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.sign_ψ | [3285, 1] | [3302, 93] | simp only [MonoidHom.inr_apply, MonoidHom.coe_comp, Function.comp_apply, θ_apply_single] | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
a✝ : c ∈ Finset.univ
⊢ (MonoidHom.comp Equiv.Perm.sign (θ g))
((Mo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(MulAction.fixedBy α g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
a✝ : c ∈ Fi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | intro i hi | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ∀ i ∈ Equiv.Perm.cycleType g, Odd i | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
i : ℕ
hi : i ∈ Equiv.Perm.cycleType g
⊢ Odd i | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ∀ i ∈ Equiv.Perm.cycleType g, Odd i
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | rw [Equiv.Perm.cycleType_def g, Multiset.mem_map] at hi | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
i : ℕ
hi : i ∈ Equiv.Perm.cycleType g
⊢ Odd i | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
i : ℕ
hi : ∃ a ∈ (Equiv.Perm.cycleFactorsFinset g).val, (Finset.card ∘ Equiv.Perm.support) a = i
⊢ Odd i | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
i : ℕ
hi : i ∈ Equiv.Perm.cycleType g
⊢ Odd i
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | obtain ⟨c, hc, rfl⟩ := hi | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
i : ℕ
hi : ∃ a ∈ (Equiv.Perm.cycleFactorsFinset g).val, (Finset.card ∘ Equiv.Perm.support) a = i
⊢ Odd i | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ (Equiv.Perm.cycleFactorsFinset g).val
⊢ Odd ((Finset.card ∘ Equiv.Perm.support) c) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
i : ℕ
hi : ∃ a ∈ (Equiv.Perm.cycleFactorsFinset g).val, (Finset.card ∘ Equiv.Perm.support) a = i
⊢ Odd i
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | rw [← Finset.mem_def] at hc | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ (Equiv.Perm.cycleFactorsFinset g).val
⊢ Odd ((Finset.card ∘ Equiv.Perm.support) c) | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
⊢ Odd ((Finset.card ∘ Equiv.Perm.support) c) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ (Equiv.Perm.cycleFactorsFinset g).val
⊢ Odd ((Finset.card ∘ Equiv.Perm.s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | suffices c = θ g ⟨1, Pi.mulSingle ⟨c, hc⟩ ⟨c, Subgroup.mem_zpowers c⟩⟩ by
rw [this]
apply h
change ConjAct.toConjAct _ ∈ _
apply Subgroup.map_subtype_le
rw [OnCycleFactors.hφ_ker_eq_θ_range]
exact Set.mem_range_self _ | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
⊢ Equiv.Perm.sign c = 1 | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
⊢ c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ }) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
⊢ Equiv.Perm.sign c = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | rw [θ_apply_single] | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
⊢ c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ }) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
⊢ c = (θ g) (1, Pi.mulSingle { val := c,... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | rw [Equiv.Perm.IsCycle.sign _, neg_eq_iff_eq_neg] at this | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : Equiv.Perm.sign c = 1
⊢ Odd ((Finset.card ∘ Equiv.Perm.support) c) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ Odd ((Finset.card ∘ Equiv.Perm.support) c)
α : Type u_1
inst✝¹ : Dec... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : Equiv.Perm.sign c = 1
⊢ Odd ((Finset.card ∘ Equiv.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | rw [Nat.odd_iff_not_even, Function.comp_apply] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ Odd ((Finset.card ∘ Equiv.Perm.support) c) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ ¬Even (Equiv.Perm.support c).card | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ Odd ((Fi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | rw [← neg_one_pow_eq_one_iff_even (R := ℤˣ) (by norm_num), this, ← Units.eq_iff] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ ¬Even (Equiv.Perm.support c).card | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ ¬↑(-1) = ↑1 | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ ¬Even (E... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | norm_num | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ ¬↑(-1) = ↑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 : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ ¬↑(-1) =... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | norm_num | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ -1 ≠ 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 : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : (-1) ^ (Equiv.Perm.support c).card = -1
⊢ -1 ≠ 1
T... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | rw [Equiv.Perm.mem_cycleFactorsFinset_iff] at hc | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : Equiv.Perm.sign c = 1
⊢ Equiv.Perm.IsCycle c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : Equiv.Perm.IsCycle c ∧ ∀ a ∈ Equiv.Perm.support c, c a = g a
this : Equiv.Perm.sign c = 1
⊢ Equiv.Perm.IsCycle c | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : Equiv.Perm.sign c = 1
⊢ Equiv.Perm.IsCycle c
TACTI... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | exact hc.left | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : Equiv.Perm.IsCycle c ∧ ∀ a ∈ Equiv.Perm.support c, c a = g a
this : Equiv.Perm.sign c = 1
⊢ Equiv.Perm.IsCycle c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : Equiv.Perm.IsCycle c ∧ ∀ a ∈ Equiv.Perm.support c, c a = g a
this : Equiv.Perm.sign c = 1
⊢ E... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | rw [this] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ Equiv.Perm.sign c = 1 | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ Equiv.Perm.sign ((θ g) (... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property :=... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | apply h | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ Equiv.Perm.sign ((θ g) (... | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ (θ g) (1, Pi.mulS... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property :=... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | change ConjAct.toConjAct _ ∈ _ | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ (θ g) (1, Pi.mulS... | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ ConjAct.toConjAct... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, prop... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | apply Subgroup.map_subtype_le | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ ConjAct.toConjAct... | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ ConjAct.toConjA... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, prop... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | rw [OnCycleFactors.hφ_ker_eq_θ_range] | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ ConjAct.toConjA... | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ {
toFun :... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, pr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.odd_of_mem_kerφ | [3305, 1] | [3326, 22] | exact Set.mem_range_self _ | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, property := hc } { val := c, property := ⋯ })
⊢ {
toFun :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
this : c = (θ g) (1, Pi.mulSingle { val := c, pr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | rw [← not_lt] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ¬Multiset.sum (Equiv.Perm.cycleType g) + 1 < Fintype.card α | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | intro hm | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ¬Multiset.sum (Equiv.Perm.cycleType g) + 1 < Fintype.card α | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 1 < Fintype.card α
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ¬Multiset.sum (Equiv.Perm.cycleType g) + 1 < Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | rw [Nat.lt_iff_add_one_le, add_assoc] at hm | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 1 < Fintype.card α
⊢ False | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + (1 + 1) ≤ Fintype.card α
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 1 < Fintype.card α
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | change g.cycleType.sum + 2 ≤ _ at hm | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + (1 + 1) ≤ Fintype.card α
⊢ False | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + (1 + 1) ≤ Fintype.card α
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | suffices 1 < Fintype.card (MulAction.fixedBy α g) by
obtain ⟨a, b, hab⟩ := Fintype.exists_pair_of_one_lt_card this
suffices Equiv.Perm.sign (θ g ⟨Equiv.swap a b, 1⟩) ≠ 1 by
apply this
apply h
change ConjAct.toConjAct _ ∈ _
apply Subgroup.map_subtype_le
rw [OnCycleFactors.hφ_ker_eq_θ_range]
e... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
⊢ False | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
⊢ 1 < Fintype.card ↑(MulAction.fixedBy α g) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | obtain ⟨a, b, hab⟩ := Fintype.exists_pair_of_one_lt_card this | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
⊢ False | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
⊢ F... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
⊢ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | suffices Equiv.Perm.sign (θ g ⟨Equiv.swap a b, 1⟩) ≠ 1 by
apply this
apply h
change ConjAct.toConjAct _ ∈ _
apply Subgroup.map_subtype_le
rw [OnCycleFactors.hφ_ker_eq_θ_range]
exact Set.mem_range_self _ | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
⊢ F... | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
⊢ E... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulActio... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | rw [θ_apply_fst] | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
⊢ E... | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
⊢ E... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulActio... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | simp only [Equiv.Perm.ofSubtype_swap_eq, Equiv.Perm.sign_swap', ne_eq, ite_eq_left_iff,
neg_units_ne_self, imp_false, not_not] | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
⊢ E... | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
⊢ ¬... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulActio... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | rw [Subtype.coe_inj] | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
⊢ ¬... | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
⊢ ¬... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulActio... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | exact hab | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
⊢ ¬... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this : 1 < Fintype.card ↑(MulActio... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | apply this | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equiv.Perm.s... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equiv.Perm.s... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | apply h | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equiv.Perm.s... | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equiv... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | change ConjAct.toConjAct _ ∈ _ | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equiv... | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equiv... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | apply Subgroup.map_subtype_le | case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equiv... | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | rw [OnCycleFactors.hφ_ker_eq_θ_range] | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equ... | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixed... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | exact Set.mem_range_self _ | case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixedBy α g)
a b : ↑(MulAction.fixedBy α g)
hab : a ≠ b
this : Equ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
this✝ : 1 < Fintype.card ↑(MulAction.fixed... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | rw [OnCycleFactors.Equiv.Perm.card_fixedBy g] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
⊢ 1 < Fintype.card ↑(MulAction.fixedBy α g) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
⊢ 1 < Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
⊢ 1 < Fintype.card ↑(MulAction.fixedBy α g)
TACTIC:... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | rw [add_comm] at hm | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
⊢ 1 < Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ 1 < Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : Multiset.sum (Equiv.Perm.cycleType g) + 2 ≤ Fintype.card α
⊢ 1 < Fintype.card α - Multiset.sum (Equiv.Perm.cyc... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | rw [Nat.lt_iff_add_one_le, Nat.le_sub_iff_add_le] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ 1 < Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ 1 + 1 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fi... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ 1 < Fintype.card α - Multiset.sum (Equiv.Perm.cyc... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | exact hm | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ 1 + 1 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fi... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ 1 + 1 + Multiset.sum (Equiv.Perm.cycleType g) ≤ F... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | rw [Equiv.Perm.sum_cycleType] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ (Equiv.Perm.support g).card ≤ Fintype.card α | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.c... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.card_le_of_mem_kerφ | [3328, 1] | [3354, 32] | exact Finset.card_le_univ _ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ (Equiv.Perm.support g).card ≤ Fintype.card α | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm : 2 + Multiset.sum (Equiv.Perm.cycleType g) ≤ Fintype.card α
⊢ (Equiv.Perm.support g).card ≤ Fintype.card α
TACT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [← Multiset.nodup_iff_count_le_one, Equiv.Perm.cycleType_def] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1 | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ Multiset.Nodup (Multiset.map (Finset.card ∘ Equiv.Perm.support) (Equiv.Perm.cycleFactorsFinset g).val) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [Multiset.nodup_map_iff_inj_on g.cycleFactorsFinset.nodup] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ Multiset.Nodup (Multiset.map (Finset.card ∘ Equiv.Perm.support) (Equiv.Perm.cycleFactorsFinset g).val) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ∀ x ∈ (Equiv.Perm.cycleFactorsFinset g).val,
∀ y ∈ (Equiv.Perm.cycleFactorsFinset g).val,
(Finset.card ∘ Equiv.Perm.support) x = (Finset.card ∘ Equiv.Perm.support) ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ Multiset.Nodup (Multiset.map (Finset.card ∘ Equiv.Perm.support) (Equiv.Perm.cycleFactorsFinset g).val)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | simp only [Function.comp_apply, ← Finset.mem_def] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ∀ x ∈ (Equiv.Perm.cycleFactorsFinset g).val,
∀ y ∈ (Equiv.Perm.cycleFactorsFinset g).val,
(Finset.card ∘ Equiv.Perm.support) x = (Finset.card ∘ Equiv.Perm.support) ... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ∀ x ∈ Equiv.Perm.cycleFactorsFinset g,
∀ y ∈ Equiv.Perm.cycleFactorsFinset g, (Equiv.Perm.support x).card = (Equiv.Perm.support y).card → x = y | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ∀ x ∈ (Equiv.Perm.cycleFactorsFinset g).val,
∀ y ∈ (Equiv.Perm.cycleFactorsFinset g).val,
(Finset.card ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | by_contra hm | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ∀ x ∈ Equiv.Perm.cycleFactorsFinset g,
∀ y ∈ Equiv.Perm.cycleFactorsFinset g, (Equiv.Perm.support x).card = (Equiv.Perm.support y).card → x = y | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm :
¬∀ x ∈ Equiv.Perm.cycleFactorsFinset g,
∀ y ∈ Equiv.Perm.cycleFactorsFinset g, (Equiv.Perm.support x).card = (Equiv.Perm.support y).card → x = y
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
⊢ ∀ x ∈ Equiv.Perm.cycleFactorsFinset g,
∀ y ∈ Equiv.Perm.cycleFactorsFinset g, (Equiv.Perm.support x).card = (... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | push_neg at hm | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm :
¬∀ x ∈ Equiv.Perm.cycleFactorsFinset g,
∀ y ∈ Equiv.Perm.cycleFactorsFinset g, (Equiv.Perm.support x).card = (Equiv.Perm.support y).card → x = y
⊢ False | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm :
∃ x ∈ Equiv.Perm.cycleFactorsFinset g,
∃ y ∈ Equiv.Perm.cycleFactorsFinset g, (Equiv.Perm.support x).card = (Equiv.Perm.support y).card ∧ x ≠ y
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm :
¬∀ x ∈ Equiv.Perm.cycleFactorsFinset g,
∀ y ∈ Equiv.Perm.cycleFactorsFinset g, (Equiv.Perm.support x).... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | obtain ⟨c, hc, d, hd, hm, hm'⟩ := hm | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm :
∃ x ∈ Equiv.Perm.cycleFactorsFinset g,
∃ y ∈ Equiv.Perm.cycleFactorsFinset g, (Equiv.Perm.support x).card = (Equiv.Perm.support y).card ∧ x ≠ y
⊢ False | case intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
hm :
∃ x ∈ Equiv.Perm.cycleFactorsFinset g,
∃ y ∈ Equiv.Perm.cycleFactorsFinset g, (Equiv.Perm.support x).car... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | let τ : Equiv.Perm g.cycleFactorsFinset := Equiv.swap ⟨c, hc⟩ ⟨d, hd⟩ | case intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support ... | case intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | obtain ⟨a⟩ := g.existsBasis | case intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support ... | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.su... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | let k : Equiv.Perm α := ConjAct.ofConjAct (φ' a ⟨τ, hτ⟩ : ConjAct (Equiv.Perm α)) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | have hk2 : ∀ c : g.cycleFactorsFinset, ConjAct.toConjAct k • (c : Equiv.Perm α) = τ c := by
intro c
rw [ConjAct.smul_def]
simp only [ConjAct.ofConjAct_toConjAct]
rw [mul_inv_eq_iff_eq_mul]
ext x
exact OnCycleFactors.k_cycle_apply hτ c x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | have hksup : k.support ≤ g.support := by
intro x
simp only [Equiv.Perm.mem_support]
intro hx' hx; apply hx'
rw [← Equiv.Perm.not_mem_support] at hx
exact OnCycleFactors.k_apply_of_not_mem_support x hx | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | suffices hsign_k : Equiv.Perm.sign k = -1 by
rw [h _, ← Units.eq_iff] at hsign_k
exact Int.noConfusion hsign_k
exact (φ' a ⟨τ, hτ⟩).prop | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | suffices k.cycleType = Multiset.replicate c.support.card 2 by
rw [Equiv.Perm.sign_of_cycleType]; rw [this]
simp only [Multiset.sum_replicate, Algebra.id.smul_eq_mul, Multiset.card_replicate]
rw [Odd.neg_one_pow]
rw [Nat.odd_add']
simp only [odd_of_mem_kerφ h c.support.card
(by rw [Equiv.Perm.cycleType_def... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | suffices hk2 : orderOf k = 2 by
have hk2' : Nat.Prime (orderOf k) := by
rw [hk2]
exact Nat.prime_two
obtain ⟨n, hn⟩ := Equiv.Perm.cycleType_prime_order hk2'
intro i hi
rw [hn, hk2, Multiset.mem_replicate] at hi
exact hi.right | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | apply orderOf_eq_prime | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | case hg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.suppo... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | intro hk | case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | apply hm' | case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | specialize hk2 ⟨c, hc⟩ | case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | simpa only [hk, map_one, one_smul, Equiv.swap_apply_left, τ] using hk2 | case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hg1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | intro c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c✝).card = (Equiv.Perm.support d)... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [ConjAct.smul_def] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c✝).card = (Equiv.Perm.support d)... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c✝).card = (Equiv.Perm.support d)... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | simp only [ConjAct.ofConjAct_toConjAct] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c✝).card = (Equiv.Perm.support d)... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c✝).card = (Equiv.Perm.support d)... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [mul_inv_eq_iff_eq_mul] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c✝).card = (Equiv.Perm.support d)... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c✝).card = (Equiv.Perm.support d)... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | ext x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c✝).card = (Equiv.Perm.support d)... | case H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c✝).card = (Equiv.Perm.sup... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact OnCycleFactors.k_cycle_apply hτ c x | case H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c✝).card = (Equiv.Perm.sup... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c✝ : Equiv.Perm α
hc : c✝ ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | intro x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | simp only [Equiv.Perm.mem_support] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | intro hx' hx | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | apply hx' | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [← Equiv.Perm.not_mem_support] at hx | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact OnCycleFactors.k_apply_of_not_mem_support x hx | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [h _, ← Units.eq_iff] at hsign_k | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact Int.noConfusion hsign_k | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.