url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.of_partition_card | [1348, 1] | [1370, 57] | apply Finset.prod_congr rfl | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
this✝ : ∀ (x : Perm α), x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p
this : Fintype.card ↑{f | f ∈ MulAction.stabilizer (Perm α) p} = Fintype.card ↥(MulAction.stabilizer (Perm α) p)
⊢ (Finset.prod Finset.univ fun a => Fintype.card (Perm { x // p x = a })) =
Finset.prod Finset.univ fun x => Nat.factorial (Fintype.card { x_1 // p x_1 = x }) | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
this✝ : ∀ (x : Perm α), x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p
this : Fintype.card ↑{f | f ∈ MulAction.stabilizer (Perm α) p} = Fintype.card ↥(MulAction.stabilizer (Perm α) p)
⊢ ∀ x ∈ Finset.univ, Fintype.card (Perm { x_1 // p x_1 = x }) = Nat.factorial (Fintype.card { x_1 // p x_1 = x }) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
this✝ : ∀ (x : Perm α), x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p
this : Fintype.card ↑{f | f ∈ MulAction.stabilizer (Perm α) p} = Fintype.card ↥(MulAction.stabilizer (Perm α) p)
⊢ (Finset.prod Finset.univ fun a => Fintype.card (Perm { x // p x = a })) =
Finset.prod Finset.univ fun x => Nat.factorial (Fintype.card { x_1 // p x_1 = x })
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.of_partition_card | [1348, 1] | [1370, 57] | intro i _ | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
this✝ : ∀ (x : Perm α), x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p
this : Fintype.card ↑{f | f ∈ MulAction.stabilizer (Perm α) p} = Fintype.card ↥(MulAction.stabilizer (Perm α) p)
⊢ ∀ x ∈ Finset.univ, Fintype.card (Perm { x_1 // p x_1 = x }) = Nat.factorial (Fintype.card { x_1 // p x_1 = x }) | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
this✝ : ∀ (x : Perm α), x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p
this : Fintype.card ↑{f | f ∈ MulAction.stabilizer (Perm α) p} = Fintype.card ↥(MulAction.stabilizer (Perm α) p)
i : ι
a✝ : i ∈ Finset.univ
⊢ Fintype.card (Perm { x // p x = i }) = Nat.factorial (Fintype.card { x // p x = i }) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
this✝ : ∀ (x : Perm α), x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p
this : Fintype.card ↑{f | f ∈ MulAction.stabilizer (Perm α) p} = Fintype.card ↥(MulAction.stabilizer (Perm α) p)
⊢ ∀ x ∈ Finset.univ, Fintype.card (Perm { x_1 // p x_1 = x }) = Nat.factorial (Fintype.card { x_1 // p x_1 = x })
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.of_partition_card | [1348, 1] | [1370, 57] | exact Fintype.card_perm | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
this✝ : ∀ (x : Perm α), x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p
this : Fintype.card ↑{f | f ∈ MulAction.stabilizer (Perm α) p} = Fintype.card ↥(MulAction.stabilizer (Perm α) p)
i : ι
a✝ : i ∈ Finset.univ
⊢ Fintype.card (Perm { x // p x = i }) = Nat.factorial (Fintype.card { x // p x = i }) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
this✝ : ∀ (x : Perm α), x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p
this : Fintype.card ↑{f | f ∈ MulAction.stabilizer (Perm α) p} = Fintype.card ↥(MulAction.stabilizer (Perm α) p)
i : ι
a✝ : i ∈ Finset.univ
⊢ Fintype.card (Perm { x // p x = i }) = Nat.factorial (Fintype.card { x // p x = i })
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.of_partition_card | [1348, 1] | [1370, 57] | intro x | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
⊢ ∀ (x : Perm α), x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
⊢ x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
⊢ ∀ (x : Perm α), x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.of_partition_card | [1348, 1] | [1370, 57] | simp only [MulAction.mem_stabilizer_iff] | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
⊢ x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
⊢ x • p = p ↔ p ∘ ⇑x = p | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
⊢ x ∈ MulAction.stabilizer (Perm α) p ↔ p ∘ ⇑x = p
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.of_partition_card | [1348, 1] | [1370, 57] | suffices ∀ x : Equiv.Perm α, (x • p = p ↔ p ∘ x = p) by
simp_rw [this] | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
⊢ x • p = p ↔ p ∘ ⇑x = p | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
⊢ ∀ (x : Perm α), x • p = p ↔ p ∘ ⇑x = p | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
⊢ x • p = p ↔ p ∘ ⇑x = p
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.of_partition_card | [1348, 1] | [1370, 57] | intro x | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
⊢ ∀ (x : Perm α), x • p = p ↔ p ∘ ⇑x = p | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x✝ x : Perm α
⊢ x • p = p ↔ p ∘ ⇑x = p | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
⊢ ∀ (x : Perm α), x • p = p ↔ p ∘ ⇑x = p
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.of_partition_card | [1348, 1] | [1370, 57] | change p ∘ (x⁻¹ : Equiv.Perm α) = p ↔ p ∘ x = p | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x✝ x : Perm α
⊢ x • p = p ↔ p ∘ ⇑x = p | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x✝ x : Perm α
⊢ p ∘ ⇑x⁻¹ = p ↔ p ∘ ⇑x = p | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x✝ x : Perm α
⊢ x • p = p ↔ p ∘ ⇑x = p
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.of_partition_card | [1348, 1] | [1370, 57] | rw [Equiv.Perm.inv_def, Equiv.comp_symm_eq, eq_comm] | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x✝ x : Perm α
⊢ p ∘ ⇑x⁻¹ = p ↔ p ∘ ⇑x = p | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x✝ x : Perm α
⊢ p ∘ ⇑x⁻¹ = p ↔ p ∘ ⇑x = p
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.of_partition_card | [1348, 1] | [1370, 57] | simp_rw [this] | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
this : ∀ (x : Perm α), x • p = p ↔ p ∘ ⇑x = p
⊢ x • p = p ↔ p ∘ ⇑x = p | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
p : α → ι
x : Perm α
this : ∀ (x : Perm α), x • p = p ↔ p ∘ ⇑x = p
⊢ x • p = p ↔ p ∘ ⇑x = p
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.existsBasis | [1479, 1] | [1485, 96] | suffices hsupp_ne :
∀ c : g.cycleFactorsFinset, (c : Equiv.Perm α).support.Nonempty by
exact ⟨fun c ↦ (hsupp_ne c).choose, fun c ↦ (hsupp_ne c).choose_spec⟩ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Nonempty (Equiv.Perm.Basis g) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑c).Nonempty | 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
⊢ Nonempty (Equiv.Perm.Basis g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.existsBasis | [1479, 1] | [1485, 96] | intro c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑c).Nonempty | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
⊢ (Equiv.Perm.support ↑c).Nonempty | 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
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑c).Nonempty
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.existsBasis | [1479, 1] | [1485, 96] | exact Equiv.Perm.IsCycle.nonempty_support (Equiv.Perm.mem_cycleFactorsFinset_iff.mp c.prop).1 | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
⊢ (Equiv.Perm.support ↑c).Nonempty | 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
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
⊢ (Equiv.Perm.support ↑c).Nonempty
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.existsBasis | [1479, 1] | [1485, 96] | exact ⟨fun c ↦ (hsupp_ne c).choose, fun c ↦ (hsupp_ne c).choose_spec⟩ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
hsupp_ne : ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑c).Nonempty
⊢ Nonempty (Equiv.Perm.Basis 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✝ g : Equiv.Perm α
hsupp_ne : ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑c).Nonempty
⊢ Nonempty (Equiv.Perm.Basis g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Kf_mul_add | [1552, 1] | [1556, 72] | simp only [Kf_def, zpow_add, Equiv.Perm.coe_mul, Function.comp_apply] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i j : ℤ
⊢ Kf a (e' * e) (c, i + j) = (g ^ i) (Kf a e' (e c, j)) | 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
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i j : ℤ
⊢ Kf a (e' * e) (c, i + j) = (g ^ i) (Kf a e' (e c, j))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Kf_add | [1561, 1] | [1565, 29] | rw [← Kf_mul_add, one_mul] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i j : ℤ
⊢ Kf a e (c, i + j) = (g ^ i) (Kf a 1 (e c, j)) | 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
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i j : ℤ
⊢ Kf a e (c, i + j) = (g ^ i) (Kf a 1 (e c, j))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Kf_add' | [1568, 1] | [1573, 6] | rw [← mul_one e, Kf_mul_add, mul_one] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i j : ℤ
⊢ Kf a e (c, i + j) = (g ^ i) (Kf a e (c, j)) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i j : ℤ
⊢ (g ^ i) (Kf a e (1 c, j)) = (g ^ i) (Kf a e (c, j)) | 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
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i j : ℤ
⊢ Kf a e (c, i + j) = (g ^ i) (Kf a e (c, j))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Kf_add' | [1568, 1] | [1573, 6] | rfl | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i j : ℤ
⊢ (g ^ i) (Kf a e (1 c, j)) = (g ^ i) (Kf a e (c, j)) | 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
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i j : ℤ
⊢ (g ^ i) (Kf a e (1 c, j)) = (g ^ i) (Kf a e (c, j))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.eq_cycleOf | [1584, 1] | [1589, 20] | rw [Equiv.Perm.cycleOf_self_apply_zpow] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ↑c = Equiv.Perm.cycleOf g ((g ^ i) (a c)) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ↑c = Equiv.Perm.cycleOf g (a c) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ↑c = Equiv.Perm.cycleOf g ((g ^ i) (a c))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.eq_cycleOf | [1584, 1] | [1589, 20] | rw [a.cycleOf_eq] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ↑c = Equiv.Perm.cycleOf g (a c) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ↑c = Equiv.Perm.cycleOf g (a c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.eq_cycleOf' | [1592, 1] | [1595, 64] | rw [Kf_def, Equiv.Perm.cycleOf_self_apply_zpow, a.cycleOf_eq] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ↑(e c) = Equiv.Perm.cycleOf g (Kf a e (c, i)) | 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
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ↑(e c) = Equiv.Perm.cycleOf g (Kf a e (c, i))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply | [1599, 1] | [1602, 76] | rw [Kf_def, Kf_def, ← Equiv.Perm.mul_apply, ← zpow_one_add, add_comm 1 i] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ g (Kf a e (c, i)) = Kf a e (c, i + 1) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ g (Kf a e (c, i)) = Kf a e (c, i + 1)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply' | [1606, 1] | [1614, 31] | rw [hd] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd : d = e c
⊢ ↑d (Kf a e (c, i)) = Kf a e (c, i + 1) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd : d = e c
⊢ ↑(e c) (Kf a e (c, i)) = Kf a e (c, i + 1) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd : d = e c
⊢ ↑d (Kf a e (c, i)) = Kf a e (c, i + 1)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply' | [1606, 1] | [1614, 31] | rw [Equiv.Perm.Basis.eq_cycleOf', Equiv.Perm.cycleOf_apply_self,
Equiv.Perm.Basis.Kf_apply] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd : d = e c
⊢ ↑(e c) (Kf a e (c, i)) = Kf a e (c, i + 1) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd : d = e c
⊢ ↑(e c) (Kf a e (c, i)) = Kf a e (c, i + 1)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply'' | [1618, 1] | [1630, 12] | suffices hdc : (d : Equiv.Perm α).Disjoint (e c : Equiv.Perm α) by
apply Or.resolve_right (Equiv.Perm.disjoint_iff_eq_or_eq.mp hdc (Kf a e ⟨c, i⟩))
rw [Equiv.Perm.Basis.eq_cycleOf', Equiv.Perm.cycleOf_apply_self,
← Equiv.Perm.cycleOf_eq_one_iff, ← Equiv.Perm.Basis.eq_cycleOf']
apply Equiv.Perm.IsCycle.ne_one
exact (Equiv.Perm.mem_cycleFactorsFinset_iff.mp (e c).prop).1 | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ ↑d (Kf a e (c, i)) = Kf a e (c, i) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ Equiv.Perm.Disjoint ↑d ↑(e c) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ ↑d (Kf a e (c, i)) = Kf a e (c, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply'' | [1618, 1] | [1630, 12] | apply g.cycleFactorsFinset_pairwise_disjoint d.prop (e c).prop | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ Equiv.Perm.Disjoint ↑d ↑(e c) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ ↑d ≠ ↑(e c) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ Equiv.Perm.Disjoint ↑d ↑(e c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply'' | [1618, 1] | [1630, 12] | rw [Function.Injective.ne_iff Subtype.coe_injective] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ ↑d ≠ ↑(e c) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ d ≠ e c | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ ↑d ≠ ↑(e c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply'' | [1618, 1] | [1630, 12] | exact hd' | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ d ≠ e c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
⊢ d ≠ e c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply'' | [1618, 1] | [1630, 12] | apply Or.resolve_right (Equiv.Perm.disjoint_iff_eq_or_eq.mp hdc (Kf a e ⟨c, i⟩)) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ ↑d (Kf a e (c, i)) = Kf a e (c, i) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ ¬↑(e c) (Kf a e (c, i)) = Kf a e (c, i) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ ↑d (Kf a e (c, i)) = Kf a e (c, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply'' | [1618, 1] | [1630, 12] | rw [Equiv.Perm.Basis.eq_cycleOf', Equiv.Perm.cycleOf_apply_self,
← Equiv.Perm.cycleOf_eq_one_iff, ← Equiv.Perm.Basis.eq_cycleOf'] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ ¬↑(e c) (Kf a e (c, i)) = Kf a e (c, i) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ ¬↑(e c) = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ ¬↑(e c) (Kf a e (c, i)) = Kf a e (c, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply'' | [1618, 1] | [1630, 12] | apply Equiv.Perm.IsCycle.ne_one | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ ¬↑(e c) = 1 | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ Equiv.Perm.IsCycle ↑(e c) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ ¬↑(e c) = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_apply'' | [1618, 1] | [1630, 12] | exact (Equiv.Perm.mem_cycleFactorsFinset_iff.mp (e c).prop).1 | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ Equiv.Perm.IsCycle ↑(e c) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hd' : d ≠ e c
hdc : Equiv.Perm.Disjoint ↑d ↑(e c)
⊢ Equiv.Perm.IsCycle ↑(e c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | rintro ⟨c, i⟩ ⟨d, j⟩ He | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
⊢ Function.FactorsThrough (Kf a e') (Kf a e) | case mk.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : Kf a e (c, i) = Kf a e (d, j)
⊢ Kf a e' (c, i) = Kf a e' (d, j) | 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
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
⊢ Function.FactorsThrough (Kf a e') (Kf a e)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | simp only [Kf_def] at He ⊢ | case mk.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : Kf a e (c, i) = Kf a e (d, j)
⊢ Kf a e' (c, i) = Kf a e' (d, j) | case mk.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e c)) = (g ^ j) (a (e d))
⊢ (g ^ i) (a (e' c)) = (g ^ j) (a (e' d)) | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : Kf a e (c, i) = Kf a e (d, j)
⊢ Kf a e' (c, i) = Kf a e' (d, j)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | apply Equiv.injective e | case mk.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e c)) = (g ^ j) (a (e d))
⊢ c = d | case mk.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e c)) = (g ^ j) (a (e d))
⊢ e c = e d | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e c)) = (g ^ j) (a (e d))
⊢ c = d
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | rw [← Subtype.coe_inj, Equiv.Perm.Basis.eq_cycleOf, Equiv.Perm.Basis.eq_cycleOf, He] | case mk.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e c)) = (g ^ j) (a (e d))
⊢ e c = e d | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e c)) = (g ^ j) (a (e d))
⊢ e c = e d
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | rw [hcd] at He ⊢ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e c)) = (g ^ j) (a (e d))
hcd : c = d
⊢ (g ^ i) (a (e' c)) = (g ^ j) (a (e' d)) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ (g ^ i) (a (e' d)) = (g ^ j) (a (e' d)) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e c)) = (g ^ j) (a (e d))
hcd : c = d
⊢ (g ^ i) (a (e' c)) = (g ^ j) (a (e' d))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | rw [g.zpow_eq_zpow_on_iff i j,
← Equiv.Perm.cycle_is_cycleOf (a := a (e d)) (a.mem_support _) (e d).prop] at He | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ (g ^ i) (a (e' d)) = (g ^ j) (a (e' d)) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ (g ^ i) (a (e' d)) = (g ^ j) (a (e' d))
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ g (a (e d)) ≠ a (e d) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ (g ^ i) (a (e' d)) = (g ^ j) (a (e' d))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | rw [g.zpow_eq_zpow_on_iff,
← Equiv.Perm.cycle_is_cycleOf (a := a (e' d)) (a.mem_support _) (e' d).prop, ← hee' d] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ (g ^ i) (a (e' d)) = (g ^ j) (a (e' d))
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ g (a (e d)) ≠ a (e d) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ g (a (e' d)) ≠ a (e' d)
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ g (a (e d)) ≠ a (e d) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ (g ^ i) (a (e' d)) = (g ^ j) (a (e' d))
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ g (a (e d)) ≠ a (e d)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | exact He | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ g (a (e' d)) ≠ a (e' d)
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ g (a (e d)) ≠ a (e d) | case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ g (a (e' d)) ≠ a (e' d)
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ g (a (e d)) ≠ a (e d) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ g (a (e' d)) ≠ a (e' d)
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ g (a (e d)) ≠ a (e d)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | rw [← Equiv.Perm.mem_support, ← Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff,
← Equiv.Perm.cycle_is_cycleOf (a := a (e' d)) (a.mem_support _) (e' d).prop] | case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ g (a (e' d)) ≠ a (e' d) | case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ ↑(e' d) ∈ Equiv.Perm.cycleFactorsFinset g | Please generate a tactic in lean4 to solve the state.
STATE:
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ g (a (e' d)) ≠ a (e' d)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | exact (e' d).prop | case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ ↑(e' d) ∈ Equiv.Perm.cycleFactorsFinset g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : i % ↑(Equiv.Perm.support ↑(e d)).card = j % ↑(Equiv.Perm.support ↑(e d)).card
hcd : c = d
⊢ ↑(e' d) ∈ Equiv.Perm.cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | rw [← Equiv.Perm.mem_support, ← Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff,
← Equiv.Perm.cycle_is_cycleOf (a := a (e d)) (a.mem_support _) (e d).prop] | case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ g (a (e d)) ≠ a (e d) | case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ ↑(e d) ∈ Equiv.Perm.cycleFactorsFinset g | Please generate a tactic in lean4 to solve the state.
STATE:
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ g (a (e d)) ≠ a (e d)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | Equiv.Perm.Basis.Kf_factorsThrough | [1653, 1] | [1675, 87] | exact (e d).prop | case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ ↑(e d) ∈ Equiv.Perm.cycleFactorsFinset g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
e e' : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hee' :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(e c)).card = (Equiv.Perm.support ↑(e' c)).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
j : ℤ
He : (g ^ i) (a (e d)) = (g ^ j) (a (e d))
hcd : c = d
⊢ ↑(e d) ∈ Equiv.Perm.cycleFactorsFinset g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply | [1685, 1] | [1691, 60] | simp only [k] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ (Kf a 1 (c, i)) = Kf a τ (c, i) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ Function.extend (Kf a 1) (Kf a τ) id (Kf a 1 (c, i)) = Kf a τ (c, i) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ (Kf a 1 (c, i)) = Kf a τ (c, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply | [1685, 1] | [1691, 60] | rw [Function.FactorsThrough.extend_apply (Equiv.Perm.Basis.Kf_factorsThrough a _) id ⟨c, i⟩] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ Function.extend (Kf a 1) (Kf a τ) id (Kf a 1 (c, i)) = Kf a τ (c, i) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(1 c)).card = (Equiv.Perm.support ↑(τ c)).card | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ Function.extend (Kf a 1) (Kf a τ) id (Kf a 1 (c, i)) = Kf a τ (c, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply | [1685, 1] | [1691, 60] | intro c | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(1 c)).card = (Equiv.Perm.support ↑(τ c)).card | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c✝ : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
⊢ (Equiv.Perm.support ↑(1 c)).card = (Equiv.Perm.support ↑(τ c)).card | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑(1 c)).card = (Equiv.Perm.support ↑(τ c)).card
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply | [1685, 1] | [1691, 60] | simp only [← hτ c, Equiv.Perm.coe_one, id.def] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c✝ : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
⊢ (Equiv.Perm.support ↑(1 c)).card = (Equiv.Perm.support ↑(τ c)).card | 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
a : Equiv.Perm.Basis g
c✝ : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
⊢ (Equiv.Perm.support ↑(1 c)).card = (Equiv.Perm.support ↑(τ c)).card
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_of_not_mem_support | [1702, 1] | [1711, 38] | simp only [k] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ k a τ x = x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ Function.extend (Kf a 1) (Kf a τ) id 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
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ k a τ x = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_of_not_mem_support | [1702, 1] | [1711, 38] | rw [Function.extend_apply'] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ Function.extend (Kf a 1) (Kf a τ) id x = x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ id x = x
case hb
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ ¬∃ a_1, Kf a 1 a_1 = 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
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ Function.extend (Kf a 1) (Kf a τ) id x = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_of_not_mem_support | [1702, 1] | [1711, 38] | simp only [id.def] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ id x = x
case hb
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ ¬∃ a_1, Kf a 1 a_1 = x | case hb
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ ¬∃ a_1, Kf a 1 a_1 = 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
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ id x = x
case hb
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ ¬∃ a_1, Kf a 1 a_1 = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_of_not_mem_support | [1702, 1] | [1711, 38] | intro hyp | case hb
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ ¬∃ a_1, Kf a 1 a_1 = x | case hb
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
hyp : ∃ a_1, Kf a 1 a_1 = x
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case hb
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
⊢ ¬∃ a_1, Kf a 1 a_1 = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_of_not_mem_support | [1702, 1] | [1711, 38] | obtain ⟨⟨c, i⟩, rfl⟩ := hyp | case hb
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
hyp : ∃ a_1, Kf a 1 a_1 = x
⊢ False | case hb.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hx : Kf a 1 (c, i) ∉ Equiv.Perm.support g
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case hb
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
x : α
hx : x ∉ Equiv.Perm.support g
hyp : ∃ a_1, Kf a 1 a_1 = x
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_of_not_mem_support | [1702, 1] | [1711, 38] | apply hx | case hb.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hx : Kf a 1 (c, i) ∉ Equiv.Perm.support g
⊢ False | case hb.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hx : Kf a 1 (c, i) ∉ Equiv.Perm.support g
⊢ Kf a 1 (c, i) ∈ Equiv.Perm.support g | Please generate a tactic in lean4 to solve the state.
STATE:
case hb.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hx : Kf a 1 (c, i) ∉ Equiv.Perm.support g
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_of_not_mem_support | [1702, 1] | [1711, 38] | rw [Kf_def, Equiv.Perm.zpow_apply_mem_support] | case hb.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hx : Kf a 1 (c, i) ∉ Equiv.Perm.support g
⊢ Kf a 1 (c, i) ∈ Equiv.Perm.support g | case hb.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hx : Kf a 1 (c, i) ∉ Equiv.Perm.support g
⊢ a (1 c) ∈ Equiv.Perm.support g | Please generate a tactic in lean4 to solve the state.
STATE:
case hb.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hx : Kf a 1 (c, i) ∉ Equiv.Perm.support g
⊢ Kf a 1 (c, i) ∈ Equiv.Perm.support g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_of_not_mem_support | [1702, 1] | [1711, 38] | apply Equiv.Perm.Basis.mem_support' | case hb.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hx : Kf a 1 (c, i) ∉ Equiv.Perm.support g
⊢ a (1 c) ∈ Equiv.Perm.support g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hb.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
hx : Kf a 1 (c, i) ∉ Equiv.Perm.support g
⊢ a (1 c) ∈ Equiv.Perm.support g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | constructor | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
⊢ x ∈ Equiv.Perm.support g ↔ ∃ c i, x = Kf a 1 (c, i) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
⊢ x ∈ Equiv.Perm.support g → ∃ c i, x = Kf a 1 (c, i)
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
⊢ (∃ c i, x = Kf a 1 (c, i)) → 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 : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
⊢ x ∈ Equiv.Perm.support g ↔ ∃ c i, x = Kf a 1 (c, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | intro hx | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
⊢ x ∈ Equiv.Perm.support g → ∃ c i, x = Kf a 1 (c, i) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : x ∈ Equiv.Perm.support g
⊢ ∃ c i, x = Kf a 1 (c, i) | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
⊢ x ∈ Equiv.Perm.support g → ∃ c i, x = Kf a 1 (c, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | rw [← Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff] at hx | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : x ∈ Equiv.Perm.support g
⊢ ∃ c i, x = Kf a 1 (c, i) | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∃ c i, x = Kf a 1 (c, i) | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : x ∈ Equiv.Perm.support g
⊢ ∃ c i, x = Kf a 1 (c, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | use ⟨g.cycleOf x, hx⟩ | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∃ c i, x = Kf a 1 (c, i) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∃ i, x = Kf a 1 ({ val := Equiv.Perm.cycleOf g x, property := hx }, i) | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∃ c i, x = Kf a 1 (c, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | simp only [Kf_def, Equiv.Perm.coe_one, id.def] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∃ i, x = Kf a 1 ({ val := Equiv.Perm.cycleOf g x, property := hx }, i) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx }) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∃ i, x = Kf a 1 ({ val := Equiv.Perm.cycleOf g x, property := hx }, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | let ha := a.mem_support ⟨g.cycleOf x, hx⟩ | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx }) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
ha : Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx } ∈
Equiv.Perm.support ↑{ val := Equiv.Perm.cycleOf g x, property := hx } :=
Equiv.Perm.Basis.mem_support { val := Equiv.Perm.cycleOf g x, property := hx }
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx }) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx })
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | simp only [Subtype.coe_mk, Equiv.Perm.mem_support_cycleOf_iff] at ha | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
ha : Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx } ∈
Equiv.Perm.support ↑{ val := Equiv.Perm.cycleOf g x, property := hx } :=
Equiv.Perm.Basis.mem_support { val := Equiv.Perm.cycleOf g x, property := hx }
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx }) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
ha :
Equiv.Perm.SameCycle g x (Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx }) ∧
x ∈ Equiv.Perm.support g
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx }) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
ha : Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx } ∈
Equiv.Perm.support ↑{ val := Equiv.Perm.cycleOf g x, property := hx } :=
Equiv.Perm.Basis.mem_support { val := Equiv.Perm.cycleOf g x, property := hx }
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx })
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | obtain ⟨i, hi⟩ := ha.1.symm | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
ha :
Equiv.Perm.SameCycle g x (Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx }) ∧
x ∈ Equiv.Perm.support g
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx }) | case h.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
ha :
Equiv.Perm.SameCycle g x (Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx }) ∧
x ∈ Equiv.Perm.support g
i : ℤ
hi : (g ^ i) (Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx }) = x
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx }) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
ha :
Equiv.Perm.SameCycle g x (Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx }) ∧
x ∈ Equiv.Perm.support g
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx })
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | exact ⟨i, hi.symm⟩ | case h.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
ha :
Equiv.Perm.SameCycle g x (Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx }) ∧
x ∈ Equiv.Perm.support g
i : ℤ
hi : (g ^ i) (Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx }) = x
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx }) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
hx : Equiv.Perm.cycleOf g x ∈ Equiv.Perm.cycleFactorsFinset g
ha :
Equiv.Perm.SameCycle g x (Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx }) ∧
x ∈ Equiv.Perm.support g
i : ℤ
hi : (g ^ i) (Equiv.Perm.Basis.toFun { val := Equiv.Perm.cycleOf g x, property := hx }) = x
⊢ ∃ i, x = (g ^ i) (a { val := Equiv.Perm.cycleOf g x, property := hx })
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | rintro ⟨c, i, rfl⟩ | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
⊢ (∃ c i, x = Kf a 1 (c, i)) → x ∈ Equiv.Perm.support g | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a 1 (c, i) ∈ Equiv.Perm.support g | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
x : α
⊢ (∃ c i, x = Kf a 1 (c, i)) → x ∈ Equiv.Perm.support g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | simp only [Kf_def, Equiv.Perm.zpow_apply_mem_support, Equiv.Perm.coe_one, id.def] | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a 1 (c, i) ∈ Equiv.Perm.support g | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ a c ∈ Equiv.Perm.support g | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a 1 (c, i) ∈ Equiv.Perm.support g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | apply Equiv.Perm.mem_cycleFactorsFinset_support_le c.prop | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ a c ∈ Equiv.Perm.support g | case mpr.intro.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ a c ∈ Equiv.Perm.support ↑c | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ a c ∈ Equiv.Perm.support g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.mem_support_iff_exists_Kf | [1715, 1] | [1730, 24] | apply a.mem_support | case mpr.intro.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ a c ∈ Equiv.Perm.support ↑c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ a c ∈ Equiv.Perm.support ↑c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | ext x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
⊢ k a τ ∘ ⇑(g ^ j) = ⇑(g ^ j) ∘ k a τ | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
⊢ (k a τ ∘ ⇑(g ^ j)) x = (⇑(g ^ j) ∘ k a τ) 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
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
⊢ k a τ ∘ ⇑(g ^ j) = ⇑(g ^ j) ∘ k a τ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | simp only [Function.comp_apply] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
⊢ (k a τ ∘ ⇑(g ^ j)) x = (⇑(g ^ j) ∘ k a τ) x | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
⊢ (k a τ ∘ ⇑(g ^ j)) x = (⇑(g ^ j) ∘ k a τ) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | by_cases hx : x ∈ g.support | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x) | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∈ Equiv.Perm.support g
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x)
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | rw [mem_support_iff_exists_Kf a] at hx | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∈ Equiv.Perm.support g
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x) | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : ∃ c i, x = Kf a 1 (c, i)
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ 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
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∈ Equiv.Perm.support g
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | obtain ⟨c, i, rfl⟩ := hx | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : ∃ c i, x = Kf a 1 (c, i)
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x) | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ k a τ ((g ^ j) (Kf a 1 (c, i))) = (g ^ j) (k a τ (Kf a 1 (c, i))) | 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
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : ∃ c i, x = Kf a 1 (c, i)
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | rw [← Kf_add'] | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ k a τ ((g ^ j) (Kf a 1 (c, i))) = (g ^ j) (k a τ (Kf a 1 (c, i))) | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ k a τ (Kf a 1 (c, j + i)) = (g ^ j) (k a τ (Kf a 1 (c, i))) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ k a τ ((g ^ j) (Kf a 1 (c, i))) = (g ^ j) (k a τ (Kf a 1 (c, i)))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | rw [k_apply a c (j + i) hτ] | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ k a τ (Kf a 1 (c, j + i)) = (g ^ j) (k a τ (Kf a 1 (c, i))) | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a τ (c, j + i) = (g ^ j) (k a τ (Kf a 1 (c, i))) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ k a τ (Kf a 1 (c, j + i)) = (g ^ j) (k a τ (Kf a 1 (c, i)))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | rw [k_apply a c i hτ] | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a τ (c, j + i) = (g ^ j) (k a τ (Kf a 1 (c, i))) | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a τ (c, j + i) = (g ^ j) (Kf a τ (c, i)) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a τ (c, j + i) = (g ^ j) (k a τ (Kf a 1 (c, i)))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | rw [Kf_add'] | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a τ (c, j + i) = (g ^ j) (Kf a τ (c, i)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a τ (c, j + i) = (g ^ j) (Kf a τ (c, i))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | rw [k_apply_of_not_mem_support x hx] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x) | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ k a τ ((g ^ j) x) = (g ^ j) 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
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ k a τ ((g ^ j) x) = (g ^ j) (k a τ x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | rw [k_apply_of_not_mem_support ((g ^ j : Equiv.Perm α) x) _] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ k a τ ((g ^ j) x) = (g ^ j) x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ (g ^ j) x ∉ Equiv.Perm.support 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 : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ k a τ ((g ^ j) x) = (g ^ j) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | rw [Equiv.Perm.zpow_apply_mem_support] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ (g ^ j) x ∉ Equiv.Perm.support g | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ 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 : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ (g ^ j) x ∉ Equiv.Perm.support g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute_zpow | [1734, 1] | [1749, 13] | exact hx | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ x ∉ Equiv.Perm.support 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
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
j : ℤ
x : α
hx : x ∉ Equiv.Perm.support g
⊢ x ∉ Equiv.Perm.support g
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_commute | [1752, 1] | [1755, 50] | simpa only [zpow_one] using k_commute_zpow hτ 1 | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ ∘ ⇑g = ⇑g ∘ k a τ | 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
a : Equiv.Perm.Basis g
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ ∘ ⇑g = ⇑g ∘ k a τ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_gen | [1758, 1] | [1772, 6] | simp only [Kf_def] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ (Kf a σ (c, i)) = Kf a (τ * σ) (c, i) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ ((g ^ i) (a (σ c))) = (g ^ i) (a ((τ * σ) c)) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ (Kf a σ (c, i)) = Kf a (τ * σ) (c, i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_gen | [1758, 1] | [1772, 6] | rw [← Function.comp_apply (f := k a τ), k_commute_zpow hτ, Function.comp_apply] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ ((g ^ i) (a (σ c))) = (g ^ i) (a ((τ * σ) c)) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ (g ^ i) (k a τ (a (σ c))) = (g ^ i) (a ((τ * σ) c)) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ ((g ^ i) (a (σ c))) = (g ^ i) (a ((τ * σ) c))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_gen | [1758, 1] | [1772, 6] | apply congr_arg | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ (g ^ i) (k a τ (a (σ c))) = (g ^ i) (a ((τ * σ) c)) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ (a (σ c)) = a ((τ * σ) c) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ (g ^ i) (k a τ (a (σ c))) = (g ^ i) (a ((τ * σ) c))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_gen | [1758, 1] | [1772, 6] | dsimp | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ (a (σ c)) = a ((τ * σ) c) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ (a (σ c)) = a (τ (σ 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
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ (a (σ c)) = a ((τ * σ) c)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_gen | [1758, 1] | [1772, 6] | have : ∀ (d) (τ : Equiv.Perm g.cycleFactorsFinset),
a (τ d) = Kf a 1 (τ d, 0) :=
fun d τ ↦ rfl | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ (a (σ c)) = a (τ (σ c)) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
this :
∀ (d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) (τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
a (τ d) = Kf a 1 (τ d, 0)
⊢ k a τ (a (σ c)) = a (τ (σ 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
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a τ (a (σ c)) = a (τ (σ c))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_gen | [1758, 1] | [1772, 6] | rw [this _ σ,
k_apply a (σ c) 0 hτ, ← Function.comp_apply (f := τ), ← Equiv.Perm.coe_mul,
this _ (τ * σ)] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
this :
∀ (d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) (τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
a (τ d) = Kf a 1 (τ d, 0)
⊢ k a τ (a (σ c)) = a (τ (σ c)) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
this :
∀ (d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) (τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
a (τ d) = Kf a 1 (τ d, 0)
⊢ Kf a τ (σ c, 0) = Kf a 1 ((τ * σ) c, 0) | 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
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
this :
∀ (d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) (τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
a (τ d) = Kf a 1 (τ d, 0)
⊢ k a τ (a (σ c)) = a (τ (σ c))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_apply_gen | [1758, 1] | [1772, 6] | rfl | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
this :
∀ (d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) (τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
a (τ d) = Kf a 1 (τ d, 0)
⊢ Kf a τ (σ c, 0) = Kf a 1 ((τ * σ) c, 0) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
σ τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
this :
∀ (d : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) (τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
a (τ d) = Kf a 1 (τ d, 0)
⊢ Kf a τ (σ c, 0) = Kf a 1 ((τ * σ) c, 0)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_mul | [1775, 1] | [1791, 48] | ext x | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a σ ∘ k a τ = k a (σ * τ) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
⊢ (k a σ ∘ k a τ) x = k a (σ * τ) 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
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
⊢ k a σ ∘ k a τ = k a (σ * τ)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_mul | [1775, 1] | [1791, 48] | simp only [Function.comp_apply] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
⊢ (k a σ ∘ k a τ) x = k a (σ * τ) x | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
⊢ k a σ (k a τ x) = k a (σ * τ) x | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
⊢ (k a σ ∘ k a τ) x = k a (σ * τ) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_mul | [1775, 1] | [1791, 48] | by_cases hx : x ∈ g.support | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
⊢ k a σ (k a τ x) = k a (σ * τ) x | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
hx : x ∈ Equiv.Perm.support g
⊢ k a σ (k a τ x) = k a (σ * τ) x
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
hx : x ∉ Equiv.Perm.support g
⊢ k a σ (k a τ x) = k a (σ * τ) x | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
⊢ k a σ (k a τ x) = k a (σ * τ) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_mul | [1775, 1] | [1791, 48] | simp only [mem_support_iff_exists_Kf a] at hx | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
hx : x ∈ Equiv.Perm.support g
⊢ k a σ (k a τ x) = k a (σ * τ) x | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
hx : ∃ c i, x = Kf a 1 (c, i)
⊢ k a σ (k a τ x) = k a (σ * τ) 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
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
hx : x ∈ Equiv.Perm.support g
⊢ k a σ (k a τ x) = k a (σ * τ) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_mul | [1775, 1] | [1791, 48] | obtain ⟨c, i, rfl⟩ := hx | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
hx : ∃ c i, x = Kf a 1 (c, i)
⊢ k a σ (k a τ x) = k a (σ * τ) x | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ k a σ (k a τ (Kf a 1 (c, i))) = k a (σ * τ) (Kf a 1 (c, i)) | 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
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
x : α
hx : ∃ c i, x = Kf a 1 (c, i)
⊢ k a σ (k a τ x) = k a (σ * τ) x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_mul | [1775, 1] | [1791, 48] | rw [k_apply a c i hτ, k_apply_gen _] | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ k a σ (k a τ (Kf a 1 (c, i))) = k a (σ * τ) (Kf a 1 (c, i)) | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a (σ * τ) (c, i) = k a (σ * τ) (Kf a 1 (c, i))
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ k a σ (k a τ (Kf a 1 (c, i))) = k a (σ * τ) (Kf a 1 (c, i))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_mul | [1775, 1] | [1791, 48] | rw [k_apply_gen] | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a (σ * τ) (c, i) = k a (σ * τ) (Kf a 1 (c, i))
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a (σ * τ) (c, i) = Kf a (σ * τ * 1) (c, i)
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑((σ * τ) c)).card = (Equiv.Perm.support ↑c).card
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a (σ * τ) (c, i) = k a (σ * τ) (Kf a 1 (c, i))
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_mul | [1775, 1] | [1791, 48] | simp only [mul_one] | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a (σ * τ) (c, i) = Kf a (σ * τ * 1) (c, i)
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑((σ * τ) c)).card = (Equiv.Perm.support ↑c).card
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑((σ * τ) c)).card = (Equiv.Perm.support ↑c).card
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ Kf a (σ * τ) (c, i) = Kf a (σ * τ * 1) (c, i)
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑((σ * τ) c)).card = (Equiv.Perm.support ↑c).card
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_mul | [1775, 1] | [1791, 48] | exact hσ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card | 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
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.k_mul | [1775, 1] | [1791, 48] | intro c | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑((σ * τ) c)).card = (Equiv.Perm.support ↑c).card | case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c✝ : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
⊢ (Equiv.Perm.support ↑((σ * τ) c)).card = (Equiv.Perm.support ↑c).card | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
a : Equiv.Perm.Basis g
σ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hσ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(σ c)).card = (Equiv.Perm.support ↑c).card
τ : Equiv.Perm { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
hτ :
∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }), (Equiv.Perm.support ↑(τ c)).card = (Equiv.Perm.support ↑c).card
c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }
i : ℤ
⊢ ∀ (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }),
(Equiv.Perm.support ↑((σ * τ) c)).card = (Equiv.Perm.support ↑c).card
TACTIC:
|
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