url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | apply Equiv.Perm.mem_cycleFactorsFinset_support_le hx' | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hx : x ∈ Equiv.Perm.support g
... | case mp.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hx : x ∈ Equiv.Perm.support ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | obtain ⟨Hz'⟩ := Hz (g.cycleOf x)
(Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff.mpr hx) | case mp.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hx : x ∈ Equiv.Perm.support ... | case mp.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hx : x ∈ Equiv.Perm.su... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [← Hz' x, Equiv.Perm.mem_support_cycleOf_iff] | case mp.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hx : x ∈ Equiv.Perm.su... | case mp.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hx : x ∈ Equiv.Perm.su... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtyp... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | exact ⟨Equiv.Perm.SameCycle.refl _ _, hx⟩ | case mp.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hx : x ∈ Equiv.Perm.su... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtyp... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | intro hzx | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
⊢ z x ∈ Equiv.Perm.support g ... | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hzx : z x ∈ Equiv.Perm.suppor... | 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 z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | let hzx' := Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff.mpr hzx | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hzx : z x ∈ Equiv.Perm.suppor... | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hzx : z x ∈ Equiv.Perm.suppor... | 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 z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | apply Equiv.Perm.mem_cycleFactorsFinset_support_le hzx' | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hzx : z x ∈ Equiv.Perm.suppor... | case mpr.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hzx : z x ∈ Equiv.Perm.supp... | 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 z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | obtain ⟨Hz'⟩ := Hz (g.cycleOf (z x)) hzx' | case mpr.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hzx : z x ∈ Equiv.Perm.supp... | case mpr.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hzx : z x ∈ Equiv.Per... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [Hz' x, Equiv.Perm.mem_support_cycleOf_iff] | case mpr.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hzx : z x ∈ Equiv.Per... | case mpr.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hzx : z x ∈ Equiv.Per... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subty... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | exact ⟨Equiv.Perm.SameCycle.refl _ _, hzx⟩ | case mpr.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
x : α
hzx : z x ∈ Equiv.Per... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.a.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subty... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [hθ_1 _ x] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | simp only [u, v, Equiv.Perm.subtypePerm_apply] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | simp only [Equiv.Perm.cycleOf_eq_one_iff] at hx | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | exact hx | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [hθ_2 _ x ⟨g.cycleOf x, (Equiv.Perm.cycleOf_ne_one_iff_mem g).mp hx⟩ rfl] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | change (v _ : Equiv.Perm α) x = _ | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [Equiv.Perm.ofSubtype_apply_of_mem] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rfl | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fixedP... | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fix... | 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 z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | simp only [Equiv.Perm.mem_support, Equiv.Perm.cycleOf_apply_self, ne_eq] | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fix... | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fix... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePer... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | simp only [Equiv.Perm.cycleOf_eq_one_iff] at hx | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fix... | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fix... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePer... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | exact hx | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc) ∈ Subgroup.zpowers c
hu : ∀ (x : α), x ∈ Function.fix... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
Hz :
∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z x ∈ Equiv.Perm.support c),
Equiv.Perm.ofSubtype (Equiv.Perm.subtypePer... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rintro ⟨⟨u, v⟩, h⟩ | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
⊢ z ∈ Set.range ⇑(θ g) →
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g)) | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
⊢ ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (Conj... | 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 z : Equiv.Perm α
⊢ z ∈ Set.range ⇑(θ g) →
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [hφ_mem_ker_iff] | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
⊢ ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (Conj... | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
⊢ ∀ t ∈ Equiv.Perm.cycleFactorsFinset g, Commute z t | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
⊢ ConjAct.toConjAct z ∈
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [Equiv.Perm.IsCycle.forall_commute_iff] | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
⊢ ∀ t ∈ Equiv.Perm.cycleFactorsFinset g, Commute z t | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
⊢ ∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
⊢ ∀ t ∈ Equiv.Perm.cycleF... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | intro c hc | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
⊢ ∀ c ∈ Equiv.Perm.cycleFactorsFinset g,
∃ (hc : ∀ (x : α), x ∈ Equiv.Perm.support... | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∃ (hc : ∀ (x : α), x ∈ Equ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
⊢ ∀ c ∈ Equiv.Perm.cycleF... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | intro x | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
⊢ ∀ (x : α), x ∈ Equiv.Perm.... | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ x ∈ Equiv.Perm.suppo... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | simp only [← Equiv.Perm.eq_cycleOf_of_mem_cycleFactorsFinset_iff g c hc] | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ x ∈ Equiv.Perm.suppo... | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ c = Equiv.Perm.cycle... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [← h] | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ c = Equiv.Perm.cycle... | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ c = Equiv.Perm.cycle... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | unfold θ | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ c = Equiv.Perm.cycle... | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ c = Equiv.Perm.cycle... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | unfold θFun | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ c = Equiv.Perm.cycle... | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ c = Equiv.Perm.cycle... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | dsimp only [MonoidHom.coe_mk, OneHom.coe_mk, Equiv.coe_fn_mk] | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ c = Equiv.Perm.cycle... | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ c = Equiv.Perm.cycle... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [θAux_cycleOf_apply_eq] | case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
x : α
⊢ c = Equiv.Perm.cycle... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | use hc' | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ?m.373134
⊢ ∃ (hc : ∀ (x : α), x ∈ Equiv... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.support... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleF... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | suffices Equiv.Perm.ofSubtype (Equiv.Perm.subtypePerm z hc') = v ⟨c, hc⟩ by
rw [this]
exact (v _).prop | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.support... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.support... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | ext x | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.support... | case h.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | by_cases hx : x ∈ c.support | case h.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Pe... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [this] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z ... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleF... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | exact (v _).prop | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.support c ↔ z ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleF... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [Equiv.Perm.ofSubtype_apply_of_mem, Equiv.Perm.subtypePerm_apply] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | 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 z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Pe... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | dsimp | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | 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 z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Pe... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [← h, hθ_2 _ x ⟨c, hc⟩] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | 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 z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Pe... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | exact (Equiv.Perm.cycle_is_cycleOf hx hc).symm | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.su... | 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 z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Pe... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | exact hx | case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.su... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [Equiv.Perm.ofSubtype_apply_of_not_mem] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | 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 z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Pe... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | obtain ⟨m, hm⟩ := (v ⟨c, hc⟩).prop | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.suppo... | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm... | 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 z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Pe... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | dsimp only at hm | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm... | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Eq... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [← hm] | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm... | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Eq... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | apply symm | case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm... | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Pe... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Eq... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | rw [← Equiv.Perm.not_mem_support] | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Pe... | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Pe... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | intro hx' | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Pe... | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Pe... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | apply hx | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Pe... | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Pe... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | exact (Equiv.Perm.support_zpow_le c m) hx' | case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Pe... | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.su... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hφ_ker_eq_θ_range | [2732, 1] | [2812, 31] | exact hx | case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
hc' : ∀ (x : α), x ∈ Equiv.Perm.su... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g z : Equiv.Perm α
u : Equiv.Perm ↑(Function.fixedPoints ⇑g)
v : (c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)
h : (θ g) (u, v) = z
c : Equiv.Perm α
hc : c ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | let u : (Set.range (θ g)) → (φ g).ker := fun ⟨z, hz⟩ => by
rw [← hφ_ker_eq_θ_range] at hz
suffices ConjAct.toConjAct z ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g by
use ⟨ConjAct.toConjAct z, this⟩
have hK : Function.Injective (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g).subtype := by
apply... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card ↑(Set.range ⇑(θ g)) = Fintype.card ↥(MonoidHom.ker (φ g)) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
⊢ Fintype.card ↑(Set.r... | 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
⊢ Fintype.card ↑(Set.range ⇑(θ g)) = Fintype.card ↥(MonoidHom.ker (φ g))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | suffices Function.Bijective u by
exact Fintype.card_of_bijective this | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
⊢ Fintype.card ↑(Set.r... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
⊢ Function.Bijective u | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | constructor | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
⊢ Function.Bijective u | case left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
⊢ Function.I... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | rw [← hφ_ker_eq_θ_range] at hz | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz : z ∈ Set.range ⇑(θ g)
⊢ ↥(MonoidHom.ker (φ g)) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
⊢ ↥(MonoidHom.ker (φ g)) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz : z ∈ Set.range ⇑(θ g)
⊢ ↥(MonoidHom.ker (φ g))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | suffices ConjAct.toConjAct z ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g by
use ⟨ConjAct.toConjAct z, this⟩
have hK : Function.Injective (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g).subtype := by
apply Subgroup.subtype_injective
rw [← Subgroup.mem_map_iff_mem hK]
simp only [Subgroup.coeSubtype, S... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
⊢ ↥(MonoidHom.ker (φ g)) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
⊢ ConjAct.toConjAct z ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α... | 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
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
⊢ ↥(Mo... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | obtain ⟨u, ⟨_, hu'⟩⟩ := hz | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
⊢ ConjAct.toConjAct z ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α... | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
u : ↥(MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)
left✝ : u ∈ ↑(MonoidHom.ker (φ g))
hu' : (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) u = ConjAct.toConjAct ... | 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
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
⊢ Conj... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | rw [← hu'] | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
u : ↥(MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)
left✝ : u ∈ ↑(MonoidHom.ker (φ g))
hu' : (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) u = ConjAct.toConjAct ... | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
u : ↥(MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)
left✝ : u ∈ ↑(MonoidHom.ker (φ g))
hu' : (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) u = ConjAct.toConjAct ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
u : ↥(MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)
left✝ : u ∈ ↑(MonoidHom.ker (φ g))
hu' : (Subgroup.subtype (MulAction.s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | exact u.prop | case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
u : ↥(MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)
left✝ : u ∈ ↑(MonoidHom.ker (φ g))
hu' : (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) u = ConjAct.toConjAct ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
u : ↥(MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)
left✝ : u ∈ ↑(MonoidHom.ker (φ g))
hu' : (Subgroup.subtype (MulAction.s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | use ⟨ConjAct.toConjAct z, this⟩ | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this : ConjAct.toConjAct z ∈ MulAction.stabilizer (ConjAct (Equiv.P... | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this : ConjAct.toConjAct z ∈ MulAction.stabilizer (Co... | 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
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this :... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | have hK : Function.Injective (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g).subtype := by
apply Subgroup.subtype_injective | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this : ConjAct.toConjAct z ∈ MulAction.stabilizer (Co... | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this : ConjAct.toConjAct z ∈ MulAction.stabilizer (Co... | Please generate a tactic in lean4 to solve the state.
STATE:
case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | rw [← Subgroup.mem_map_iff_mem hK] | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this : ConjAct.toConjAct z ∈ MulAction.stabilizer (Co... | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this : ConjAct.toConjAct z ∈ MulAction.stabilizer (Co... | Please generate a tactic in lean4 to solve the state.
STATE:
case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | simp only [Subgroup.coeSubtype, Subgroup.coe_mk] | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this : ConjAct.toConjAct z ∈ MulAction.stabilizer (Co... | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this : ConjAct.toConjAct z ∈ MulAction.stabilizer (Co... | Please generate a tactic in lean4 to solve the state.
STATE:
case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | exact hz | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this : ConjAct.toConjAct z ∈ MulAction.stabilizer (Co... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | apply Subgroup.subtype_injective | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this : ConjAct.toConjAct z ∈ MulAction.stabilizer (ConjAct (Equiv.P... | 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
x✝ : ↑(Set.range ⇑(θ g))
z : Equiv.Perm α
hz :
ConjAct.toConjAct z ∈
Subgroup.map (Subgroup.subtype (MulAction.stabilizer (ConjAct (Equiv.Perm α)) g)) (MonoidHom.ker (φ g))
this :... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | exact Fintype.card_of_bijective this | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
this : Function.Biject... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | rintro ⟨z, hz⟩ ⟨w, hw⟩ hzw | case left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
⊢ Function.I... | case left.mk.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
z : Eq... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | simpa only [u, Subtype.mk_eq_mk, MulEquiv.apply_eq_iff_eq] using hzw | case left.mk.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
z : Eq... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left.mk.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := Co... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | rintro ⟨w, hw⟩ | case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
⊢ Function.... | case right.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
w : ↥(Mu... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | use! ConjAct.ofConjAct ((MulAction.stabilizer (ConjAct (Equiv.Perm α)) g).subtype w) | case right.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
w : ↥(Mu... | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
w : ↥(Mu... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := Conj... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | rw [← hφ_ker_eq_θ_range] | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
w : ↥(Mu... | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
w : ↥(Mu... | Please generate a tactic in lean4 to solve the state.
STATE:
case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := Conj... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | simp only [Subgroup.coeSubtype, ConjAct.toConjAct_ofConjAct, Subgroup.mem_map,
SetLike.coe_eq_coe, exists_prop, exists_eq_right, hw] | case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
w : ↥(Mu... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
w : ↥(MulAction... | Please generate a tactic in lean4 to solve the state.
STATE:
case property
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := Conj... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card' | [2896, 1] | [2923, 99] | simp only [u, Subgroup.coeSubtype, ConjAct.toConjAct_ofConjAct, Subtype.mk_eq_mk, SetLike.eta] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toConjAct z, property := this }, property := ⋯ }
w : ↥(MulAction... | 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✝ g : Equiv.Perm α
u : ↑(Set.range ⇑(θ g)) → ↥(MonoidHom.ker (φ g)) :=
fun x =>
match x with
| { val := z, property := hz } =>
let_fun this := ⋯;
{ val := { val := ConjAct.toC... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Equiv.Perm.card_fixedBy | [2926, 1] | [2935, 79] | rw [Equiv.Perm.sum_cycleType, ← Finset.card_compl] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card ↑(MulAction.fixedBy α g) = Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card ↑(MulAction.fixedBy α g) = (Equiv.Perm.support g)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✝ g : Equiv.Perm α
⊢ Fintype.card ↑(MulAction.fixedBy α g) = Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Equiv.Perm.card_fixedBy | [2926, 1] | [2935, 79] | simp only [Fintype.card_ofFinset, Set.mem_compl_iff, Finset.mem_coe,
Equiv.Perm.mem_support, Classical.not_not] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card ↑(MulAction.fixedBy α g) = (Equiv.Perm.support g)ᶜ.card | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.filter (fun x => x ∈ MulAction.fixedBy α g) Finset.univ).card = (Equiv.Perm.support g)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✝ g : Equiv.Perm α
⊢ Fintype.card ↑(MulAction.fixedBy α g) = (Equiv.Perm.support g)ᶜ.card
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Equiv.Perm.card_fixedBy | [2926, 1] | [2935, 79] | apply congr_arg | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.filter (fun x => x ∈ MulAction.fixedBy α g) Finset.univ).card = (Equiv.Perm.support g)ᶜ.card | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Finset.filter (fun x => x ∈ MulAction.fixedBy α g) Finset.univ = (Equiv.Perm.support g)ᶜ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.filter (fun x => x ∈ MulAction.fixedBy α g) Finset.univ).card = (Equiv.Perm.support g)ᶜ.card
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Equiv.Perm.card_fixedBy | [2926, 1] | [2935, 79] | ext x | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Finset.filter (fun x => x ∈ MulAction.fixedBy α g) Finset.univ = (Equiv.Perm.support g)ᶜ | case h.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x : α
⊢ x ∈ Finset.filter (fun x => x ∈ MulAction.fixedBy α g) Finset.univ ↔ x ∈ (Equiv.Perm.support g)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✝ g : Equiv.Perm α
⊢ Finset.filter (fun x => x ∈ MulAction.fixedBy α g) Finset.univ = (Equiv.Perm.support g)ᶜ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Equiv.Perm.card_fixedBy | [2926, 1] | [2935, 79] | simp only [MulAction.mem_fixedBy, Equiv.Perm.smul_def, Finset.mem_filter, Finset.mem_univ,
true_and_iff, Finset.mem_compl, Equiv.Perm.mem_support, Classical.not_not] | case h.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x : α
⊢ x ∈ Finset.filter (fun x => x ∈ MulAction.fixedBy α g) Finset.univ ↔ x ∈ (Equiv.Perm.support g)ᶜ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
x : α
⊢ x ∈ Finset.filter (fun x => x ∈ MulAction.fixedBy α g) Finset.univ ↔ x ∈ (Equiv.Perm.support g)ᶜ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | by_cases hp : p | α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
⊢ Fintype.card ((hp : p) → β hp) = if h : p then Fintype.card (β h) else 1 | case pos
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : p
⊢ Fintype.card ((hp : p) → β hp) = if h : p then Fintype.card (β h) else 1
case neg
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
⊢ Fintype.card ((hp : p) → β hp) = if h : p then Fintype.card (β h) else 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | simp only [dif_pos hp] | case pos
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : p
⊢ Fintype.card ((hp : p) → β hp) = if h : p then Fintype.card (β h) else 1 | case pos
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : p
⊢ Fintype.card ((hp : p) → β hp) = Fintype.card (β hp) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : p
⊢ Fintype.card ((hp : p) → β hp) = if h : p then Fintype.card (β h) else 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | rw [Fintype.card_eq] | case pos
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : p
⊢ Fintype.card ((hp : p) → β hp) = Fintype.card (β hp) | case pos
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : p
⊢ Nonempty (((hp : p) → β hp) ≃ β hp) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : p
⊢ Fintype.card ((hp : p) → β hp) = Fintype.card (β hp)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | exact ⟨@Equiv.funUnique p (β hp) (uniqueProp hp)⟩ | case pos
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : p
⊢ Nonempty (((hp : p) → β hp) ≃ β hp) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : p
⊢ Nonempty (((hp : p) → β hp) ≃ β hp)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | simp only [dif_neg hp] | case neg
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ Fintype.card ((hp : p) → β hp) = if h : p then Fintype.card (β h) else 1 | case neg
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ Fintype.card ((hp : p) → β hp) = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ Fintype.card ((hp : p) → β hp) = if h : p then Fintype.card (β h) else 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | rw [Fintype.card_eq_one_iff] | case neg
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ Fintype.card ((hp : p) → β hp) = 1 | case neg
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ ∃ x, ∀ (y : (hp : p) → β hp), y = x | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ Fintype.card ((hp : p) → β hp) = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | use (fun h => False.elim (hp h)) | case neg
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ ∃ x, ∀ (y : (hp : p) → β hp), y = x | case h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ ∀ (y : (hp : p) → β hp), y = fun h => ⋯.elim | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ ∃ x, ∀ (y : (hp : p) → β hp), y = x
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | intro u | case h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ ∀ (y : (hp : p) → β hp), y = fun h => ⋯.elim | case h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
u : (hp : p) → β hp
⊢ u = fun h => ⋯.elim | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
⊢ ∀ (y : (hp : p) → β hp), y = fun h => ⋯.elim
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | ext h | case h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
u : (hp : p) → β hp
⊢ u = fun h => ⋯.elim | case h.h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
u : (hp : p) → β hp
h : p
⊢ u h = ⋯.elim | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
u : (hp : p) → β hp
⊢ u = fun h => ⋯.elim
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | exfalso | case h.h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
u : (hp : p) → β hp
h : p
⊢ u h = ⋯.elim | case h.h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
u : (hp : p) → β hp
h : p
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
u : (hp : p) → β hp
h : p
⊢ u h = ⋯.elim
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.Fintype.card_pfun | [2938, 1] | [2947, 40] | exact hp h | case h.h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
u : (hp : p) → β hp
h : p
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
α : Type ?u.398702
inst✝³ : DecidableEq α
inst✝² : Fintype α
g : Equiv.Perm α
p : Prop
inst✝¹ : Decidable p
β : p → Type u_1
inst✝ : (hp : p) → Fintype (β hp)
hp : ¬p
u : (hp : p) → β hp
h : p
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card | [2950, 1] | [2970, 18] | rw [Set.card_range_of_injective (hθ_injective g)] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card ↑(Set.range ⇑(θ g)) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)) * Multiset.prod (Equiv.Perm.cycleType g) | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card
(Equiv.Perm ↑(Function.fixedPoints ⇑g) ×
((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)) * Multiset.prod (Equ... | 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
⊢ Fintype.card ↑(Set.range ⇑(θ g)) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)) * Multiset.prod (Equiv.Perm.cycleType g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card | [2950, 1] | [2970, 18] | rw [Fintype.card_prod] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card
(Equiv.Perm ↑(Function.fixedPoints ⇑g) ×
((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)) * Multiset.prod (Equ... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card (Equiv.Perm ↑(Function.fixedPoints ⇑g)) *
Fintype.card ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)) * Multiset.prod... | 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
⊢ Fintype.card
(Equiv.Perm ↑(Function.fixedPoints ⇑g) ×
((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c))) =
Nat.factorial (Fintype.card α ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card | [2950, 1] | [2970, 18] | rw [Fintype.card_perm] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card (Equiv.Perm ↑(Function.fixedPoints ⇑g)) *
Fintype.card ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)) * Multiset.prod... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Nat.factorial (Fintype.card ↑(Function.fixedPoints ⇑g)) *
Fintype.card ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)) * Multiset.p... | 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
⊢ Fintype.card (Equiv.Perm ↑(Function.fixedPoints ⇑g)) *
Fintype.card ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)) =
Nat.factorial (Fintype.ca... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card | [2950, 1] | [2970, 18] | rw [Fintype.card_pi] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Nat.factorial (Fintype.card ↑(Function.fixedPoints ⇑g)) *
Fintype.card ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)) * Multiset.p... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Nat.factorial (Fintype.card ↑(Function.fixedPoints ⇑g)) *
Finset.prod Finset.univ fun a => Fintype.card ↥(Subgroup.zpowers ↑a)) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)) * Multiset.prod (Equiv.Perm.cycl... | 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
⊢ Nat.factorial (Fintype.card ↑(Function.fixedPoints ⇑g)) *
Fintype.card ((c : { x // x ∈ Equiv.Perm.cycleFactorsFinset g }) → ↥(Subgroup.zpowers ↑c)) =
Nat.factorial (Fintype... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card | [2950, 1] | [2970, 18] | apply congr_arg | case hx
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Nat.factorial (Fintype.card ↑(Function.fixedPoints ⇑g)) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)) | case hx.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card ↑(Function.fixedPoints ⇑g) = Fintype.card α - Multiset.sum (Equiv.Perm.cycleType 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✝ g : Equiv.Perm α
⊢ Nat.factorial (Fintype.card ↑(Function.fixedPoints ⇑g)) =
Nat.factorial (Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card | [2950, 1] | [2970, 18] | exact Equiv.Perm.card_fixedBy g | case hx.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card ↑(Function.fixedPoints ⇑g) = Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hx.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ Fintype.card ↑(Function.fixedPoints ⇑g) = Fintype.card α - Multiset.sum (Equiv.Perm.cycleType g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card | [2950, 1] | [2970, 18] | rw [Equiv.Perm.cycleType] | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.prod Finset.univ fun a => Fintype.card ↥(Subgroup.zpowers ↑a)) = Multiset.prod (Equiv.Perm.cycleType g) | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.prod Finset.univ fun a => Fintype.card ↥(Subgroup.zpowers ↑a)) =
Multiset.prod (Multiset.map (Finset.card ∘ Equiv.Perm.support) (Equiv.Perm.cycleFactorsFinset g).val) | Please generate a tactic in lean4 to solve the state.
STATE:
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.prod Finset.univ fun a => Fintype.card ↥(Subgroup.zpowers ↑a)) = Multiset.prod (Equiv.Perm.cycleType g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card | [2950, 1] | [2970, 18] | simp only [Finset.univ_eq_attach, Finset.attach_val, Function.comp_apply] | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.prod Finset.univ fun a => Fintype.card ↥(Subgroup.zpowers ↑a)) =
Multiset.prod (Multiset.map (Finset.card ∘ Equiv.Perm.support) (Equiv.Perm.cycleFactorsFinset g).val) | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.prod (Finset.attach (Equiv.Perm.cycleFactorsFinset g)) fun a => Fintype.card ↥(Subgroup.zpowers ↑a)) =
Multiset.prod (Multiset.map (fun x => (Equiv.Perm.support x).card) (Equiv.Perm.cycleFactorsFinset g).val) | Please generate a tactic in lean4 to solve the state.
STATE:
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.prod Finset.univ fun a => Fintype.card ↥(Subgroup.zpowers ↑a)) =
Multiset.prod (Multiset.map (Finset.card ∘ Equiv.Perm.support) (Equiv.Perm.cycleFactorsFinset g).v... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.hψ_range_card | [2950, 1] | [2970, 18] | rw [Finset.prod_attach (s := g.cycleFactorsFinset) (f := fun a ↦ Fintype.card (Subgroup.zpowers (a : Equiv.Perm α)))] | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.prod (Finset.attach (Equiv.Perm.cycleFactorsFinset g)) fun a => Fintype.card ↥(Subgroup.zpowers ↑a)) =
Multiset.prod (Multiset.map (fun x => (Equiv.Perm.support x).card) (Equiv.Perm.cycleFactorsFinset g).val) | case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.prod (Equiv.Perm.cycleFactorsFinset g) fun x => Fintype.card ↥(Subgroup.zpowers x)) =
Multiset.prod (Multiset.map (fun x => (Equiv.Perm.support x).card) (Equiv.Perm.cycleFactorsFinset g).val) | Please generate a tactic in lean4 to solve the state.
STATE:
case hy
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g✝ g : Equiv.Perm α
⊢ (Finset.prod (Finset.attach (Equiv.Perm.cycleFactorsFinset g)) fun a => Fintype.card ↥(Subgroup.zpowers ↑a)) =
Multiset.prod (Multiset.map (fun x => (Equiv.Perm.support x)... |
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