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.θAux_mul | [2228, 1] | [2248, 65] | simp only [ne_eq, Pi.mul_apply, Submonoid.coe_mul,
Subgroup.coe_toSubmonoid, Equiv.Perm.coe_mul, Function.comp_apply] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpower... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θAux_mul | [2228, 1] | [2248, 65] | have hx' : g.cycleOf (θAux g k v x) ∉ g.cycleFactorsFinset := by
rw [θAux_cycleOf_apply_eq]
exact hx | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpower... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpower... | 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
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θAux_mul | [2228, 1] | [2248, 65] | nth_rewrite 1 [θAux, dif_neg hx'] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpower... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpower... | 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
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θAux_mul | [2228, 1] | [2248, 65] | simp only [θAux, dif_neg hx] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpower... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpower... | 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
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θAux_mul | [2228, 1] | [2248, 65] | simp only [map_mul, Equiv.Perm.coe_mul, Function.comp_apply] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpower... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θAux_mul | [2228, 1] | [2248, 65] | rw [θAux_cycleOf_apply_eq] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x :... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Eq... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θAux_mul | [2228, 1] | [2248, 65] | exact hx | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k' : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v' : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Eq... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θAux_inv | [2250, 1] | [2254, 37] | intro x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Function.LeftInverse (θAux g k⁻¹ v⁻¹) (θAux g k v) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x : α
⊢ θAux g k⁻¹ v⁻¹ (θAux g k v x) = x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ Function.LeftInverse (θAux g k⁻¹ v⁻¹) (θAux g k v)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θAux_inv | [2250, 1] | [2254, 37] | rw [θAux_mul] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x : α
⊢ θAux g k⁻¹ v⁻¹ (θAux g k v x) = x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x : α
⊢ θAux g (k⁻¹ * k) (v⁻¹ * v) x = x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x : α
⊢ θAux g k⁻¹ v⁻¹ (θAux g k v x) = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.θAux_inv | [2250, 1] | [2254, 37] | simp only [mul_left_inv, θAux_one] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x : α
⊢ θAux g (k⁻¹ * k) (v⁻¹ * v) x = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
k : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
x : α
⊢ θAux g (k⁻¹ * k) (v⁻¹ * v) x = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_1 | [2402, 1] | [2407, 11] | unfold θ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ((θ g) uv) x = ↑(uv.1 { val := x, property := hx }) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ({ toOneHom := { toFun := fun kv => θFun g kv.1 kv.2, map_one' := ⋯ }, map_mul' := ... | 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
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ((θ g) uv) x = ↑(uv.1 ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_1 | [2402, 1] | [2407, 11] | unfold θFun | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ({ toOneHom := { toFun := fun kv => θFun g kv.1 kv.2, map_one' := ⋯ }, map_mul' := ... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ({
toOneHom :=
{
toFun := fun kv =>
... | 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
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ({ toOneHom := { toFun... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_1 | [2402, 1] | [2407, 11] | simp only [Equiv.coe_fn_mk, MonoidHom.coe_mk, OneHom.coe_mk, Equiv.coe_fn_mk] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ({
toOneHom :=
{
toFun := fun kv =>
... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ θAux g uv.1 uv.2 x = ↑(uv.1 { val := x, property := hx }) | 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
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ({
toOneHom ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_1 | [2402, 1] | [2407, 11] | rw [θAux_apply_of_mem_fixedPoints, Equiv.Perm.ofSubtype_apply_of_mem] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ θAux g uv.1 uv.2 x = ↑(uv.1 { val := x, property := hx }) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x ∈ Function.fixedPoints ⇑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
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ θAux g uv.1 uv.2 x = ↑... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_1 | [2402, 1] | [2407, 11] | exact hx | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x ∈ Function.fixedPoints ⇑g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x ∈ Function.fixedPoin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_2 | [2431, 1] | [2435, 38] | unfold θ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equiv.Perm.cycleOf g x = ↑c
⊢ ((θ g) uv) x = ↑(uv.2 c) x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equiv.Perm.cycleOf g x = ↑c
⊢ ({ toOneHom := { toFun := fun kv =... | 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
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_2 | [2431, 1] | [2435, 38] | unfold θFun | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equiv.Perm.cycleOf g x = ↑c
⊢ ({ toOneHom := { toFun := fun kv =... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equiv.Perm.cycleOf g x = ↑c
⊢ ({
toOneHom :=
... | 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
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_2 | [2431, 1] | [2435, 38] | simp only [MonoidHom.coe_mk, OneHom.coe_mk, Equiv.coe_fn_mk] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equiv.Perm.cycleOf g x = ↑c
⊢ ({
toOneHom :=
... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equiv.Perm.cycleOf g x = ↑c
⊢ θAux g uv.1 uv.2 x = ↑(uv.2 c) x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_2 | [2431, 1] | [2435, 38] | exact θAux_apply_of_cycleOf_eq c hx | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equiv.Perm.cycleOf g x = ↑c
⊢ θAux g uv.1 uv.2 x = ↑(uv.2 c) x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
uv :
Equiv.Perm ↑(Function.fixedPoints ⇑g) × ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))
x : α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hx : Equ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | ext x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
⊢ (θ g) (1, Pi.mulSingle c { val := ↑c, property := ⋯ }) = ↑c | case H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
⊢ ((θ g) (1, Pi.mulSingle c { val := ↑c, property := ⋯ })) x = ↑c x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
⊢ (θ g) (1, Pi.mulSingle c { val := ↑c, property := ⋯ }) = ↑c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | by_cases hx : x ∈ Function.fixedPoints g | case H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
⊢ ((θ g) (1, Pi.mulSingle c { val := ↑c, property := ⋯ })) x = ↑c x | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ((θ g) (1, Pi.mulSingle c { val := ↑c, property := ⋯ })) x = ↑c x
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c :... | Please generate a tactic in lean4 to solve the state.
STATE:
case H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
⊢ ((θ g) (1, Pi.mulSingle c { val := ↑c, property := ⋯ })) x = ↑c x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | rw [← Equiv.Perm.cycleOf_ne_one_iff_mem, ne_eq, Equiv.Perm.cycleOf_eq_one_iff] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
⊢ Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
⊢ ¬g x = 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 }
x : α
hx : x ∉ Function.fixedPoints ⇑g
⊢ Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | simpa [Function.mem_fixedPoints_iff] using 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 }
x : α
hx : x ∉ Function.fixedPoints ⇑g
⊢ ¬g x = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
⊢ ¬g x = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | simp only [hθ_1 _ x hx, Equiv.Perm.coe_one, id_eq] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ((θ g) (1, Pi.mulSingle c { val := ↑c, property := ⋯ })) x = ↑c x | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x = ↑c x | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ((θ g) (1, Pi.mulSingle c { val := ↑c, property := ⋯ })) x = ↑c x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | apply symm | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x = ↑c x | case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑c x = x | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x = ↑c x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | rw [← Equiv.Perm.not_mem_support] | case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑c x = x | case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x ∉ Equiv.Perm.support ↑c | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑c x = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | simp only [Function.mem_fixedPoints, Function.IsFixedPt, ← Equiv.Perm.not_mem_support] at hx | case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x ∉ Equiv.Perm.support ↑c | case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ x ∉ Equiv.Perm.support ↑c | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x ∉ Equiv.Perm.support ↑c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | intro hx' | case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ x ∉ Equiv.Perm.support ↑c | case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
hx' : x ∈ Equiv.Perm.support ↑c
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ x ∉ Equiv.Perm.support ↑c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | apply hx | case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
hx' : x ∈ Equiv.Perm.support ↑c
⊢ False | case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
hx' : x ∈ Equiv.Perm.support ↑c
⊢ x ∈ Equiv.Perm.support g | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
hx' : x ∈ Equiv.Perm.support ↑c
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | apply Equiv.Perm.mem_cycleFactorsFinset_support_le c.prop hx' | case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
hx' : x ∈ Equiv.Perm.support ↑c
⊢ x ∈ Equiv.Perm.support g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
hx' : x ∈ Equiv.Perm.support ↑c
⊢ x ∈ Equiv.Perm.support g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | rw [hθ_2 _ x ⟨g.cycleOf x, hx'⟩ rfl] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ((θ g) (1, Pi.mulSingle c { val := ↑c, property := ⋯ })) x = ↑c x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ↑((1, Pi.mulSingle c { val := ↑c, property := ⋯ }).2 { val := Equiv.Perm.cycleOf g x, property :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ((θ g) (1, Pi.mulSingle c { val := ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | dsimp only | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ↑((1, Pi.mulSingle c { val := ↑c, property := ⋯ }).2 { val := Equiv.Perm.cycleOf g x, property :... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ↑(Pi.mulSingle c { val := ↑c, property := ⋯ } { val := Equiv.Perm.cycleOf g x, property := hx' }... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ↑((1, Pi.mulSingle c { val := ↑c, p... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | by_cases hc : c = ⟨Equiv.Perm.cycleOf g x, hx'⟩ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ↑(Pi.mulSingle c { val := ↑c, property := ⋯ } { val := Equiv.Perm.cycleOf g x, property := hx' }... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ ↑(Pi.mulSingle c { 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
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ↑(Pi.mulSingle c { val := ↑c, prope... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | rw [hc, Pi.mulSingle_eq_same, Equiv.Perm.cycleOf_apply_self] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ ↑(Pi.mulSingle c { val := ↑... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : c = { val := Equiv.Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | rw [Pi.mulSingle_eq_of_ne' hc] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ ↑(Pi.mulSingle c { val := ... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ ↑1 x = ↑c 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 }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | simp only [OneMemClass.coe_one, 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 }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ ↑1 x = ↑c 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 }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ x = ↑c 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 }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | apply symm | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ x = ↑c x | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ ↑c x = 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 }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | rw [← Equiv.Perm.not_mem_support] | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ ↑c x = x | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ x ∉ Equiv.Perm.support ↑... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | intro hxc | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
⊢ x ∉ Equiv.Perm.support ↑... | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
hxc : x ∈ Equiv.Perm.suppo... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | apply hc | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
hxc : x ∈ Equiv.Perm.suppo... | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
hxc : x ∈ Equiv.Perm.suppo... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | rw [← Subtype.coe_inj] | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
hxc : x ∈ Equiv.Perm.suppo... | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
hxc : x ∈ Equiv.Perm.suppo... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_single | [2437, 1] | [2462, 48] | exact Equiv.Perm.cycle_is_cycleOf hxc c.prop | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.Perm.cycleOf g x, property := hx' }
hxc : x ∈ Equiv.Perm.suppo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Function.fixedPoints ⇑g
hx' : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
hc : ¬c = { val := Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | rw [← MonoidHom.ker_eq_bot_iff, eq_bot_iff] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Function.Injective ⇑(θ g) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ MonoidHom.ker (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✝ g : Equiv.Perm α
⊢ Function.Injective ⇑(θ g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | rintro ⟨u, v⟩ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ MonoidHom.ker (θ g) ≤ ⊥ | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (u, v) ∈ MonoidHom.ker (θ g) → (u, v) ∈ ⊥ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ MonoidHom.ker (θ g) ≤ ⊥
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | unfold θ | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (u, v) ∈ MonoidHom.ker (θ g) → (u, v) ∈ ⊥ | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (u, v) ∈ MonoidHom.ker { toOneHom := { toFun := fun kv => θFun g kv.1 kv.2, map_one' := ⋯ }, map_mul' := ⋯ } →
... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (u, v) ∈ MonoidHom.ker (θ g) → (u, v) ∈ ⊥
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | unfold θFun | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (u, v) ∈ MonoidHom.ker { toOneHom := { toFun := fun kv => θFun g kv.1 kv.2, map_one' := ⋯ }, map_mul' := ⋯ } →
... | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (u, v) ∈
MonoidHom.ker
{
toOneHom :=
{
toFun := fun kv =>
... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (u, v) ∈ MonoidHom.ker { toOneHom := { toFun := fun k... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | simp only [MonoidHom.coe_mk, OneHom.coe_mk, MonoidHom.mem_ker, Equiv.Perm.ext_iff] | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (u, v) ∈
MonoidHom.ker
{
toOneHom :=
{
toFun := fun kv =>
... | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (∀ (x : α), { toFun := θAux g u v, invFun := θAux g u⁻¹ v⁻¹, left_inv := ⋯, right_inv := ⋯ } x = 1 x) → (u, v) ∈ ⊥ | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (u, v) ∈
MonoidHom.ker
{
toOn... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | simp only [Equiv.coe_fn_mk, Equiv.Perm.coe_one, id_eq] | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (∀ (x : α), { toFun := θAux g u v, invFun := θAux g u⁻¹ v⁻¹, left_inv := ⋯, right_inv := ⋯ } x = 1 x) → (u, v) ∈ ⊥ | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (∀ (x : α), θAux g u v x = x) → (u, v) ∈ ⊥ | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (∀ (x : α), { toFun := θAux g u v, invFun := θAux g u... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | intro huv | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (∀ (x : α), θAux g u v x = x) → (u, v) ∈ ⊥ | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ (u, v) ∈ ⊥ | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
⊢ (∀ (x : α), θAux g u v x = x) → (u, v) ∈ ⊥
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | simp only [Subgroup.mem_bot, Prod.mk_eq_one, MonoidHom.mem_ker] | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ (u, v) ∈ ⊥ | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ u = 1 ∧ v = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ (u, v) ∈ ⊥
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | constructor | case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ u = 1 ∧ v = 1 | case mk.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ u = 1
case mk.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ u = 1 ∧ v = 1
TACTI... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | ext ⟨x, hx⟩ | case mk.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ u = 1 | case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑(u { val := x, property := h... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ u = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | simp only [Equiv.Perm.coe_one, id_eq] | case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑(u { val := x, property := h... | case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑(u { val := x, property := h... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | conv_rhs => rw [← huv x] | case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑(u { val := x, property := h... | case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑(u { val := x, property := h... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | rw [θAux_apply_of_mem_fixedPoints, Equiv.Perm.ofSubtype_apply_of_mem] | case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ ↑(u { val := x, property := h... | case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x ∈ Function.fixedPoints ⇑g | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | exact hx | case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx : x ∈ Function.fixedPoints ⇑g
⊢ x ∈ Function.fixedPoints ⇑g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.left.H.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
x : α
hx ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | ext c x | case mk.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ v = 1 | case mk.right.h.a.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
⊢ ↑(v c) x = ↑(... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
⊢ v = 1
TACTIC:... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | by_cases hx : g.cycleOf x = 1 | case mk.right.h.a.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
⊢ ↑(v c) x = ↑(... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.right.h.a.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x /... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | rw [← ne_eq, Equiv.Perm.cycleOf_ne_one_iff_mem] at hx | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : ¬Equiv.Perm.cycleOf g... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g ... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | simp only [Pi.one_apply, OneMemClass.coe_one, Equiv.Perm.coe_one, id_eq] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g ... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g ... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | by_cases hc : g.cycleOf x = ↑c | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g ... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g ... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | simp only [Equiv.Perm.cycleOf_eq_one_iff, ← Equiv.Perm.not_mem_support] at hx | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g ... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.suppor... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | simp only [Pi.one_apply, OneMemClass.coe_one, Equiv.Perm.coe_one, id_eq] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.suppor... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.suppor... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | obtain ⟨m, hm⟩ := (v c).prop | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.suppor... | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | rw [← hm] | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | dsimp | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | rw [← Equiv.Perm.not_mem_support] | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | intro hx' | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | suffices ¬ x ∈ Equiv.Perm.support c by
apply this
apply Equiv.Perm.support_zpow_le _ _ hx' | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | intro hx' | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | apply hx | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | apply Equiv.Perm.mem_cycleFactorsFinset_support_le c.prop hx' | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | apply this | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cyc... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | apply Equiv.Perm.support_zpow_le _ _ hx' | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
m : ℤ... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cyc... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | rw [← θAux_apply_of_cycleOf_eq c hc, huv] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | obtain ⟨m, hm⟩ := (v c).prop | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g ... | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | rw [← hm] | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | dsimp | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | rw [← Equiv.Perm.not_mem_support] | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | intro hx' | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | suffices ¬ x ∈ Equiv.Perm.support c by
apply this
apply Equiv.Perm.support_zpow_le _ _ hx' | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | intro h | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | exact hc (Equiv.Perm.cycle_is_cycleOf h c.prop).symm | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycl... | no goals | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | apply this | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cyc... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hθ_injective | [2580, 1] | [2622, 59] | apply Equiv.Perm.support_zpow_le _ _ hx' | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv... | 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✝ g : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
huv : ∀ (x : α), θAux g u v x = x
c : { x // x ∈ Equiv.Perm.cyc... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | constructor | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
⊢ ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g)) ↔
z ∈ Set.range ⇑(θ g) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
⊢ ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g)) →
z ∈ Set.range ⇑(θ g)
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Pe... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
⊢ ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g)) ↔
z ∈ Set.range ⇑(θ g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [hφ_mem_ker_iff, Equiv.Perm.IsCycle.forall_commute_iff, Set.mem_range] | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
⊢ ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g)) →
z ∈ Set.range ⇑(θ g) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
⊢ (∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c) →
∃ y, (θ g) y = z | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
⊢ ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g)) →
z ∈ Set.range ⇑(θ g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | intro Hz | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
⊢ (∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c) →
∃ y, (θ g) y = z | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
⊢ ∃ y, (θ g) y = z | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
⊢ (∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | let u := Equiv.Perm.subtypePerm z hu | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedPo... | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedPo... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | let v : (c : g.cycleFactorsFinset) → (Subgroup.zpowers (c : Equiv.Perm α)) :=
fun c => ⟨Equiv.Perm.ofSubtype
(z.subtypePerm (Classical.choose (Hz c.val c.prop))),
Classical.choose_spec (Hz c.val c.prop)⟩ | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedPo... | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedPo... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | use ⟨u, v⟩ | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedPo... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedPoi... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | ext x | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedPoi... | case h.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | 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 z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z h... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | by_cases hx : g.cycleOf x = 1 | case h.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | intro x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
⊢ ∀ (x : α), x ∈ Function.fixedPoints ⇑g ↔ z... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ x ∈ Function.fixedPoints ⇑g ↔ z x ∈ ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | simp only [Function.fixedPoints, Equiv.Perm.smul_def, Function.IsFixedPt] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ x ∈ Function.fixedPoints ⇑g ↔ z x ∈ ... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ x ∈ {x | g x = x} ↔ z x ∈ {x | g x =... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | simp only [← Equiv.Perm.not_mem_support] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ x ∈ {x | g x = x} ↔ z x ∈ {x | g x =... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ x ∈ {x | x ∉ Equiv.Perm.support g} ↔... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | simp only [Set.mem_setOf_eq, not_iff_not] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ x ∈ {x | x ∉ Equiv.Perm.support g} ↔... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ x ∈ Equiv.Perm.support g ↔ z x ∈ Equ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | constructor | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ x ∈ Equiv.Perm.support g ↔ z x ∈ Equ... | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ x ∈ Equiv.Perm.support g → z... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | intro hx | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ x ∈ Equiv.Perm.support g → z... | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hx : x ∈ Equiv.Perm.support g
... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | let hx' := Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff.mpr hx | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hx : x ∈ Equiv.Perm.support g
... | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hx : x ∈ Equiv.Perm.support g
... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z ... |
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