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.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact hx' | case intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (E... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Pe... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [Equiv.Perm.disjoint_iff_support_disjoint] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [Finset.not_disjoint_iff] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | use a cx | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.suppor... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | apply And.intro (a.mem_support cx) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.suppor... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.suppor... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsF... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [← haτcx_eq_acx] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.suppor... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.suppor... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsF... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact a.mem_support (τ cx) | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.suppor... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsF... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | intro h | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h✝ : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).c... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | simp only [← Subtype.coe_inj, Subtype.coe_mk] at h | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h✝ : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).c... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h✝ : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).c... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h✝ : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact hm' h | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h✝ : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).c... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h✝ : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [← Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff] | case a.mpr.refine_2
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equi... | case a.mpr.refine_2
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equi... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_2
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | cases' hx' with hxc hxd | case a.mpr.refine_2
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equi... | case a.mpr.refine_2.inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_2
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [hxc] | case a.mpr.refine_2.inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (... | case a.mpr.refine_2.inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_2.inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact hc | case a.mpr.refine_2.inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_2.inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [hxd] | case a.mpr.refine_2.inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (... | case a.mpr.refine_2.inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_2.inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact hd | case a.mpr.refine_2.inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_2.inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | simp only [Finset.mem_union] at hx | case a.mpr.refine_1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equi... | case a.mpr.refine_1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equi... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | cases hx with
| inl hx =>
apply Or.intro_left
exact (Equiv.Perm.cycle_is_cycleOf hx hc).symm
| inr hx =>
apply Or.intro_right
exact (Equiv.Perm.cycle_is_cycleOf hx hd).symm | case a.mpr.refine_1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equi... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | apply Or.intro_left | case a.mpr.refine_1.inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (... | case a.mpr.refine_1.inl.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card =... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_1.inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact (Equiv.Perm.cycle_is_cycleOf hx hc).symm | case a.mpr.refine_1.inl.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_1.inl.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | apply Or.intro_right | case a.mpr.refine_1.inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (... | case a.mpr.refine_1.inr.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card =... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_1.inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact (Equiv.Perm.cycle_is_cycleOf hx hd).symm | case a.mpr.refine_1.inr.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.mpr.refine_1.inr.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | apply Equiv.Perm.sum_cycleType | case e_n
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case e_n
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | have hk2' : Nat.Prime (orderOf k) := by
rw [hk2]
exact Nat.prime_two | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | obtain ⟨n, hn⟩ := Equiv.Perm.cycleType_prime_order hk2' | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.su... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | intro i hi | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.su... | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.su... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFact... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [hn, hk2, Multiset.mem_replicate] at hi | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.su... | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.su... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFact... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact hi.right | case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.su... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFact... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [hk2] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact Nat.prime_two | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | ext x | case hg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.suppo... | case hg.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.sup... | Please generate a tactic in lean4 to solve the state.
STATE:
case hg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactors... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | simp only [Equiv.Perm.coe_one, id.def] | case hg.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.sup... | case hg.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.sup... | Please generate a tactic in lean4 to solve the state.
STATE:
case hg.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFacto... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | by_cases hx : x ∈ g.support | case hg.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.sup... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case hg.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFacto... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | obtain ⟨cx, hcx⟩ := Equiv.Perm.sameCycle_of_mem_support hx | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Per... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | obtain ⟨n, _, rfl⟩ := (hcx (a cx) (a.mem_support cx)).exists_pow_eq' | case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Per... | case pos.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycle... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | convert hk_apply cx 2 n | case pos.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card ... | case h.e'_3.h.e'_6.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card =... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | suffices hτ2 : τ ^ 2 = 1 by
rw [hτ2, Equiv.Perm.coe_one, id.def] | case h.e'_3.h.e'_6.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card =... | case h.e'_3.h.e'_6.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card =... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3.h.e'_6.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [pow_two] | case h.e'_3.h.e'_6.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card =... | case h.e'_3.h.e'_6.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card =... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3.h.e'_6.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [Equiv.swap_mul_self] | case h.e'_3.h.e'_6.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3.h.e'_6.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [hτ2, Equiv.Perm.coe_one, id.def] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.support d).ca... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [← Equiv.Perm.not_mem_support] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | intro hx' | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | apply hx | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | apply hksup | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.su... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | apply Equiv.Perm.support_pow_le k 2 | case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.su... | case neg.a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFact... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact hx' | case neg.a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFa... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | intro x | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.su... | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.su... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | by_cases hx : x = ⟨c, hc⟩ | case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.su... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | by_cases hx' : x = ⟨d, hd⟩ | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [hx, Equiv.swap_apply_left] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact hm.symm | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [hx', Equiv.swap_apply_right] | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | exact hm | case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.count_le_one_of_mem_kerφ | [3356, 1] | [3558, 47] | rw [Equiv.swap_apply_of_ne_of_ne hx hx'] | case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactorsFinset g
hm : (Equiv.Perm.support c).card = (Equiv.Perm.supp... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α
c : Equiv.Perm α
hc : c ∈ Equiv.Perm.cycleFactorsFinset g
d : Equiv.Perm α
hd : d ∈ Equiv.Perm.cycleFactor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [SetLike.le_def] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
⊢ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α ↔
(∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧
∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1 | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
⊢ (∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α) ↔
(∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧
∀ (i : ℕ), Mult... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
⊢ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g ≤ alternatingGroup α ↔
(∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | constructor | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
⊢ (∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α) ↔
(∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧
∀ (i : ℕ), Mult... | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
⊢ (∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α) →
(∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧
∀ (i : ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
⊢ (∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α) ↔
(∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multis... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | intro h | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
⊢ (∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α) →
(∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧
∀ (i : ... | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ (∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧
∀ (i : ℕ), Mult... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
⊢ (∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α) →
(∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | constructor | case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ (∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧
∀ (i : ℕ), Mult... | case mp.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ ∀ i ∈ Equiv.Perm.cycleType g, Odd i
case mp.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ (∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Mult... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | exact odd_of_mem_kerφ h | case mp.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ ∀ i ∈ Equiv.Perm.cycleType g, Odd i
case mp.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α... | case mp.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧ ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ ∀ i ∈ Equiv.Perm.cycleType g, Odd i
case mp.right
α : Type ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | constructor | case mp.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧ ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1 | case mp.right.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
case mp.right.right
α : Type u_1
inst✝¹ : DecidableEq α... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | exact card_le_of_mem_kerφ h | case mp.right.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
case mp.right.right
α : Type u_1
inst✝¹ : DecidableEq α... | case mp.right.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.right.left
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g)... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | exact count_le_one_of_mem_kerφ h | case mp.right.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.right.right
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h : ∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (ConjAct (Equiv.Perm α)) g → x ∈ alternatingGroup α
⊢ ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rintro ⟨h_odd, h_fixed, h_count⟩ x hx | case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
⊢ ((∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧
∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1) →
∀ ⦃x : ConjAct (Equiv.Perm α)⦄, x ∈ MulAction.stabilizer (... | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
⊢ ((∀ i ∈ Equiv.Perm.cycleType g, Odd i) ∧
Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1 ∧
∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1) →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | suffices (OnCycleFactors.φ g).ker = ⊤ by
rw [← OnCycleFactors.hφ_ker_eq_θ_range, this]
simp only [Subgroup.coeSubtype, Subgroup.mem_map, Subgroup.mem_top, true_and]
exact ⟨⟨x, hx⟩, rfl⟩ | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [eq_top_iff] | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | intro y _ | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | suffices (OnCycleFactors.φ g).range = ⊥ by
rw [MonoidHom.mem_ker, ← Subgroup.mem_bot, ← this, MonoidHom.mem_range]
exact ⟨y, rfl⟩ | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [eq_bot_iff] | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | intro z | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [← OnCycleFactors.Iφ_eq_range, Subgroup.mem_bot] | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | intro hz | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | apply Equiv.ext | case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.st... | case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | intro c | case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.... | case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cy... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [← Multiset.nodup_iff_count_le_one, Equiv.Perm.cycleType_def,
Multiset.nodup_map_iff_inj_on (Equiv.Perm.cycleFactorsFinset g).nodup]
at h_count | case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.... | case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count :
∀ x ∈ (Equiv.Perm.cycleFactorsFinset g).val,
∀ y ∈ (Equiv.Perm.cycleFactorsFinset g).val,
(... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cy... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [Equiv.Perm.coe_one, id.def, ← Subtype.coe_inj] | case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count :
∀ x ∈ (Equiv.Perm.cycleFactorsFinset g).val,
∀ y ∈ (Equiv.Perm.cycleFactorsFinset g).val,
(... | case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count :
∀ x ∈ (Equiv.Perm.cycleFactorsFinset g).val,
∀ y ∈ (Equiv.Perm.cycleFactorsFinset g).val,
(... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count :
∀ x ∈ (Equiv.Perm.cycleFactorsFinset g).... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | exact h_count (z c) (z c).prop c c.prop (hz c) | case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count :
∀ x ∈ (Equiv.Perm.cycleFactorsFinset g).val,
∀ y ∈ (Equiv.Perm.cycleFactorsFinset g).val,
(... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro.H
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count :
∀ x ∈ (Equiv.Perm.cycleFactorsFinset g).... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | obtain ⟨⟨y, uv⟩, rfl⟩ := Set.mem_range.mp hx' | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.stabilizer (ConjAct (Eq... | case intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c : { x... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : Conj... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [Equiv.Perm.mem_alternatingGroup, OnCycleFactors.sign_ψ] | case intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c : { x... | case intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c : { x... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | convert mul_one _ | case intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c : { x... | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | apply Finset.prod_eq_one | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | case h.e'_2.h.e'_6.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rintro ⟨c, hc⟩ _ | case h.e'_2.h.e'_6.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (... | case h.e'_2.h.e'_6.h.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6.h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | obtain ⟨k, hk⟩ := (uv _).prop | case h.e'_2.h.e'_6.h.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv ... | case h.e'_2.h.e'_6.h.mk.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6.h.mk
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.c... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [← hk, map_zpow] | case h.e'_2.h.e'_6.h.mk.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑... | case h.e'_2.h.e'_6.h.mk.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6.h.mk.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | convert one_zpow k | case h.e'_2.h.e'_6.h.mk.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑... | case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6.h.mk.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | simp only | case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [Equiv.Perm.IsCycle.sign, Odd.neg_one_pow, neg_neg] | case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | apply h_odd | case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [Equiv.Perm.cycleType_def, Multiset.mem_map] | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (... | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | use c | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c : { x // x ∈... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | exact ⟨hc, rfl⟩ | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c : { x // x ∈... | case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [Equiv.Perm.mem_cycleFactorsFinset_iff] at hc | case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | exact hc.left | case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | apply symm | case h.e'_3
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c : { x /... | case h.e'_3.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c : { x... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | convert Equiv.Perm.sign_one | case h.e'_3.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c : { x... | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [← Equiv.Perm.card_support_le_one] | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | apply le_trans (Finset.card_le_univ _) | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | change Fintype.card (MulAction.fixedBy α g) ≤ 1 | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [OnCycleFactors.Equiv.Perm.card_fixedBy g, tsub_le_iff_left] | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | exact h_fixed | case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
y : Equiv.Perm ↑(Function.fixedPoints ⇑g)
uv : (c ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/ConjClassCount.lean | OnCycleFactors.kerφ_le_alternating_iff | [3560, 1] | [3620, 51] | rw [← OnCycleFactors.hφ_ker_eq_θ_range, this] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.stabilizer (ConjAct (Eq... | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : ConjAct (Equiv.Perm α)
hx : x ∈ MulAction.stabilizer (ConjAct (Eq... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
g : Equiv.Perm α
h_odd : ∀ i ∈ Equiv.Perm.cycleType g, Odd i
h_fixed : Fintype.card α ≤ Multiset.sum (Equiv.Perm.cycleType g) + 1
h_count : ∀ (i : ℕ), Multiset.count i (Equiv.Perm.cycleType g) ≤ 1
x : Conj... |
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