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/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [Equiv.Perm.ofSubtype_apply_of_mem] | case h.H.mk.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg : g✝ ∈ G
this : IsPr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.H.mk.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | intro x hx' | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | obtain ⟨⟨k, hk⟩, hkbx : k • b = x⟩ := this | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransitive (↥G)... | case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretr... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | suffices k • B = B by
rw [← hkbx, ← this, Set.smul_mem_smul_set_iff]
exact hb | case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretr... | case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretr... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply or_iff_not_imp_right.mp (IsBlock.def_one.mp hB ⟨k, _⟩) | case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretr... | case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretr... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [← hkbx, ← this, Set.smul_mem_smul_set_iff] | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransitive (↥G)... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransitive (↥G)... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact hb | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransitive (↥G)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [Set.not_disjoint_iff_nonempty_inter] | case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretr... | case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretr... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | change (k • B ∩ B).Nonempty | case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretr... | case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretr... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | use a | case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretr... | case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitiv... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | constructor | case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitiv... | case h.left
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretran... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [mem_fixingSubgroup_iff] at hk | case h.left
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretran... | case h.left
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretran... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [← hk a ha'] | case h.left
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretran... | case h.left
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretran... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact Set.smul_mem_smul_set ha | case h.left
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretran... | case h.right
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretra... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact ha | case h.right
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretra... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.right
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply le_of_lt hG | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitiv... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact fixingSubgroup_le_stabilizer (Equiv.Perm α) s hk | case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitiv... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | suffices
IsPretransitive (fixingSubgroup (Equiv.Perm α) s)
(SubMulAction.ofFixingSubgroup (Equiv.Perm α) s) by
obtain ⟨k, hk⟩ :=
exists_smul_eq (fixingSubgroup (Equiv.Perm α) s)
(⟨b, hb'⟩ : SubMulAction.ofFixingSubgroup (Equiv.Perm α) s) ⟨x, hx'⟩
use k
rw [← Subtype.coe_inj, SubMulAction.val_smul] ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [isPretransitive_iff_is_one_pretransitive] | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply remaining_transitivity' | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitiv... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | simp only [Nat.card_eq_fintype_card, PartENat.card_eq_coe_fintype_card, le_refl] | case hn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransiti... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | obtain ⟨k, hk⟩ :=
exists_smul_eq (fixingSubgroup (Equiv.Perm α) s)
(⟨b, hb'⟩ : SubMulAction.ofFixingSubgroup (Equiv.Perm α) s) ⟨x, hx'⟩ | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransitive (↥G)... | case intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretran... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | use k | case intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretran... | case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransiti... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s <... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [← Subtype.coe_inj, SubMulAction.val_smul] at hk | case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransiti... | case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransiti... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact hk | case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransiti... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact Equiv.Perm.isMultiplyPretransitive α (Nat.card α) | case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitiv... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [add_comm] | case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransit... | case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransit... | Please generate a tactic in lean4 to solve the state.
STATE:
case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [← Set.ncard_add_ncard_compl s] | case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransit... | case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransit... | Please generate a tactic in lean4 to solve the state.
STATE:
case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | simp only [add_le_add_iff_left] | case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransit... | case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransit... | Please generate a tactic in lean4 to solve the state.
STATE:
case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [Nat.succ_le_iff, Set.ncard_pos] | case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransit... | case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransit... | Please generate a tactic in lean4 to solve the state.
STATE:
case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact h1 | case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransit... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hmn
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [← hgbx, ← this, Set.smul_mem_smul_set_iff] | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact hsc_le_B hb | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact hα | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [MulAction.smul_set_ncard_eq] | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : ... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | simp only [← two_mul] | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : ... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply Nat.mul_le_mul_left | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : ... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a.h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap ... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact Set.ncard_le_ncard hsc_le_B (Set.toFinite B) | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a.h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a.h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | cases' Nat.lt_trichotomy s.ncard sᶜ.ncard with hs hs' | α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s) | case inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s < Set.ncard sᶜ
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s)
case inr
α : Type u_1
inst✝³ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | cases' hs' with hs hs | case inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs' : Set.ncard s = Set.ncard sᶜ ∨ Set.ncard sᶜ < Set.ncard s
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s) | case inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s = Set.ncard sᶜ
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s)
case inr.inr
α : Type u_1
i... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs' : Set.ncard s = Set.ncard sᶜ ∨ Set.ncard sᶜ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | exact Equiv.Perm.isMaximalStab' s h0 h1 hs | case inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s < Set.ncard sᶜ
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s < Set.ncard sᶜ
⊢ Subgroup.IsMax... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | exfalso | case inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s = Set.ncard sᶜ
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s) | case inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s = Set.ncard sᶜ
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s = Set.ncard sᶜ
⊢ Subgroup.I... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | apply hα | case inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s = Set.ncard sᶜ
⊢ False | case inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s = Set.ncard sᶜ
⊢ Fintype.card α = 2 * Set.ncard s | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s = Set.ncard sᶜ
⊢ False
TACT... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | rw [← Nat.card_eq_fintype_card, ← Set.ncard_add_ncard_compl s, two_mul, ← hs] | case inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s = Set.ncard sᶜ
⊢ Fintype.card α = 2 * Set.ncard s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard s = Set.ncard sᶜ
⊢ Fintype.ca... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | rw [← compl_compl s] at h0 | case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s) | case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Subgroup.I... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | rw [← stabilizer_compl] | case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s) | case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Subgroup.IsMaximal (stabilizer (Perm α) sᶜ) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Subgroup... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | apply Equiv.Perm.isMaximalStab' (sᶜ) h1 h0 | case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Subgroup.IsMaximal (stabilizer (Perm α) sᶜ) | case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Set.ncard sᶜ < Set.ncard sᶜᶜ | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Subgroup... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | rw [compl_compl] | case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Set.ncard sᶜ < Set.ncard sᶜᶜ | case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Set.ncard sᶜ < Set.ncard s | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Set.ncar... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab | [578, 1] | [590, 13] | exact hs | case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Set.ncard sᶜ < Set.ncard s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.123924
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty sᶜᶜ
h1 : Set.Nonempty sᶜ
hα : Fintype.card α ≠ 2 * Set.ncard s
hs : Set.ncard sᶜ < Set.ncard s
⊢ Set.ncar... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination.stabilizer_eq | [601, 1] | [608, 75] | ext g | α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
⊢ stabilizer G s = stabilizer G ↑↑s | case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ g ∈ stabilizer G s ↔ g ∈ stabilizer G ↑↑s | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
⊢ stabilizer G s = stabilizer G ↑↑s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination.stabilizer_eq | [601, 1] | [608, 75] | simp only [mem_stabilizer_iff] | case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ g ∈ stabilizer G s ↔ g ∈ stabilizer G ↑↑s | case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ g • s = s ↔ g • ↑↑s = ↑↑s | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ g ∈ stabilizer G s ↔ g ∈ stabilizer G ↑↑s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination.stabilizer_eq | [601, 1] | [608, 75] | rw [← Subtype.coe_inj, ← Finset.coe_smul_finset] | case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ g • s = s ↔ g • ↑↑s = ↑↑s | case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ ↑(g • s) = ↑s ↔ ↑(g • ↑s) = ↑↑s | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ g • s = s ↔ g • ↑↑s = ↑↑s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination.stabilizer_eq | [601, 1] | [608, 75] | simp only [← Finset.coe_smul_finset, ← Finset.coe_inj] | case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ ↑(g • s) = ↑s ↔ ↑(g • ↑s) = ↑↑s | case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ ↑↑(g • s) = ↑↑s ↔ ↑(g • ↑s) = ↑↑s | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ ↑(g • s) = ↑s ↔ ↑(g • ↑s) = ↑↑s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination.stabilizer_eq | [601, 1] | [608, 75] | simp only [Nat.combination_mulAction.coe_apply', Finset.coe_smul_finset] | case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ ↑↑(g • s) = ↑↑s ↔ ↑(g • ↑s) = ↑↑s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_2
inst✝³ : DecidableEq α
inst✝² : Fintype α
n : ℕ
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : ↑(Nat.Combination α n)
g : G
⊢ ↑↑(g • s) = ↑↑s ↔ ↑(g • ↑s) = ↑↑s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | cases' Nat.eq_or_lt_of_le h_one_le with h_one h_one_lt | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n) | case inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one : 1 = n
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n)
case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | have : Nontrivial α := by
rw [← Fintype.one_lt_card_iff_nontrivial]
exact lt_trans h_one_lt hn | case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n) | case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this : Nontrivial α
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | haveI ht : IsPretransitive (Equiv.Perm α) (n.Combination α) :=
n.Combination_isPretransitive α | case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this : Nontrivial α
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n) | case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this : Nontrivial α
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | have : Nontrivial (n.Combination α) :=
n.Combination_nontrivial α (lt_trans (Nat.lt_succ_self 0) h_one_lt) hn | case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n) | case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combin... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
⊢ IsPreprimitive (Equiv.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | obtain ⟨sn : n.Combination α⟩ := this.to_nonempty | case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combin... | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
⊢ IsPrepri... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | let s := sn.val | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
⊢ IsPrepri... | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | let hs : s.card = n := sn.prop | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset... | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | rw [← maximal_stabilizer_iff_preprimitive (Equiv.Perm α) sn] | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset... | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | have : stabilizer (Equiv.Perm α) sn =
stabilizer (Equiv.Perm α) (s : Set α) := by
ext g
simp only [mem_stabilizer_iff]
rw [← Subtype.coe_inj]
change g • s = s ↔ _
rw [← Finset.coe_smul_finset, ← Finset.coe_inj] | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset... | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Fins... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | rw [this] | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Fins... | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Fins... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivia... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | apply Equiv.Perm.isMaximalStab (s : Set α) | case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Fins... | case inr.intro.h0
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivia... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | rw [← h_one] | case inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one : 1 = n
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n) | case inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one : 1 = n
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α 1) | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one : 1 = n
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | apply isPreprimitive_of_surjective_map
(Nat.bijective_toCombination_one_equivariant _ α).surjective | case inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one : 1 = n
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α 1) | case inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one : 1 = n
⊢ IsPreprimitive (Equiv.Perm α) α | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one : 1 = n
⊢ IsPreprimitive (Equiv.Perm α) ↑(Nat.Combination α 1)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | exact Equiv.Perm.isPreprimitive α | case inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one : 1 = n
⊢ IsPreprimitive (Equiv.Perm α) α | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one : 1 = n
⊢ IsPreprimitive (Equiv.Perm α) α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | rw [← Fintype.one_lt_card_iff_nontrivial] | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
⊢ Nontrivial α | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
⊢ 1 < Fintype.card α | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
⊢ Nontrivial α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | exact lt_trans h_one_lt hn | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
⊢ 1 < Fintype.card α | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
⊢ 1 < Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | ext g | α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset α := ↑sn
hs : ... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset α := ↑s... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combinati... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | simp only [mem_stabilizer_iff] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset α := ↑s... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset α := ↑s... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Co... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | rw [← Subtype.coe_inj] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset α := ↑s... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset α := ↑s... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Co... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | change g • s = s ↔ _ | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset α := ↑s... | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset α := ↑s... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Co... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | rw [← Finset.coe_smul_finset, ← Finset.coe_inj] | case h
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : Finset α := ↑s... | 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
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Co... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | simp only [Finset.coe_nonempty, ← Finset.card_pos, hs] | case inr.intro.h0
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | case inr.intro.h0
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.h0
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontri... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | apply lt_trans one_pos h_one_lt | case inr.intro.h0
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.h0
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontri... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | simp only [← Finset.coe_compl, Finset.coe_nonempty,
← Finset.card_compl_lt_iff_nonempty, compl_compl, hs] | case inr.intro.h1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | case inr.intro.h1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.h1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontri... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | exact hn | case inr.intro.h1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.h1
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontri... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | simp only [Set.ncard_coe_Finset, ne_eq] | case inr.intro.hα
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | case inr.intro.hα
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.hα
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontri... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | simp only [Finset.coe_sort_coe, Fintype.card_coe, hs] | case inr.intro.hα
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | case inr.intro.hα
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.hα
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontri... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.Nat.Combination_isPreprimitive | [612, 1] | [655, 13] | exact hα | case inr.intro.hα
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combination α n)
s : F... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.hα
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
h_one_lt : 1 < n
this✝¹ : Nontrivial α
ht : IsPretransitive (Equiv.Perm α) ↑(Nat.Combination α n)
this✝ : Nontri... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | cases' subsingleton_or_nontrivial α with hα hα | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
⊢ Subgroup.Characteristic (alternatingGroup α) | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Subsingleton α
⊢ Subgroup.Characteristic (alternatingGroup α)
case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
⊢ Subgroup.Characteristic (alternatingGroup α) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
⊢ Subgroup.Characteristic (alternatingGroup α)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | apply Subgroup.Characteristic.mk | case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
⊢ Subgroup.Characteristic (alternatingGroup α) | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
⊢ ∀ (ϕ : Equiv.Perm α ≃* Equiv.Perm α),
Subgroup.comap (MulEquiv.toMonoidHom ϕ) (alternatingGroup α) = alternatingGroup α | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
⊢ Subgroup.Characteristic (alternatingGroup α)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | intro φ | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
⊢ ∀ (ϕ : Equiv.Perm α ≃* Equiv.Perm α),
Subgroup.comap (MulEquiv.toMonoidHom ϕ) (alternatingGroup α) = alternatingGroup α | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
⊢ Subgroup.comap (MulEquiv.toMonoidHom φ) (alternatingGroup α) = alternatingGroup α | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
⊢ ∀ (ϕ : Equiv.Perm α ≃* Equiv.Perm α),
Subgroup.comap (MulEquiv.toMonoidHom ϕ) (alternatingGroup α) = alternatingGroup α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | rw [alternatingGroup_eq_sign_ker] | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
⊢ Subgroup.comap (MulEquiv.toMonoidHom φ) (alternatingGroup α) = alternatingGroup α | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
⊢ Subgroup.comap (MulEquiv.toMonoidHom φ) (MonoidHom.ker Equiv.Perm.sign) = MonoidHom.ker Equiv.Perm.sign | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
⊢ Subgroup.comap (MulEquiv.toMonoidHom φ) (alternatingGroup α) = alternatingGroup α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | rw [MonoidHom.comap_ker] | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
⊢ Subgroup.comap (MulEquiv.toMonoidHom φ) (MonoidHom.ker Equiv.Perm.sign) = MonoidHom.ker Equiv.Perm.sign | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
⊢ MonoidHom.ker (MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)) = MonoidHom.ker Equiv.Perm.sign | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
⊢ Subgroup.comap (MulEquiv.toMonoidHom φ) (MonoidHom.ker Equiv.Perm.sign) = MonoidHom.ker Equiv.Perm.sign
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | let s := Equiv.Perm.sign.comp φ.toMonoidHom | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
⊢ MonoidHom.ker (MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)) = MonoidHom.ker Equiv.Perm.sign | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
⊢ MonoidHom.ker (MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)) = MonoidHom.ker Equiv.Perm.sign | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
⊢ MonoidHom.ker (MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)) = MonoidHom.ker Equiv.Perm.sign
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | have hs : Function.Surjective s := by
change Function.Surjective (Equiv.Perm.sign ∘ φ)
rw [Function.Surjective.of_comp_iff _]
exact Equiv.Perm.sign_surjective α
exact MulEquiv.surjective φ | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
⊢ MonoidHom.ker (MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)) = MonoidHom.ker Equiv.Perm.sign | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
⊢ MonoidHom.ker (MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)) = MonoidHom.ker ... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
⊢ MonoidHom.ker (MonoidHom.comp Equiv.Perm.sign (MulEquiv... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | obtain ⟨g', hg'⟩ := hs (-1) | case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
⊢ MonoidHom.ker (MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)) = MonoidHom.ker ... | case inr.fixed.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg' : s g' = -1
⊢ MonoidHom.ker (MonoidHom.comp Equiv.Perm.sign (M... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
⊢ MonoidHom.ker (MonoidHom.co... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | have hg' : s g' ≠ 1 := by
rw [hg', ← bne_iff_ne]
rfl | case inr.fixed.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg' : s g' = -1
⊢ MonoidHom.ker (MonoidHom.comp Equiv.Perm.sign (M... | case inr.fixed.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
⊢ MonoidHom.ker (MonoidHom.comp Eq... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg' :... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | apply congr_arg | case inr.fixed.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
⊢ MonoidHom.ker (MonoidHom.comp Eq... | case inr.fixed.intro.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
⊢ MonoidHom.comp Equiv.Perm.sign... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | ext g | case inr.fixed.intro.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
⊢ MonoidHom.comp Equiv.Perm.sign... | case inr.fixed.intro.h.h.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
g : Equiv.Perm α
⊢ ↑((Monoid... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed.intro.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | simp only [MonoidHom.coe_comp, MulEquiv.coe_toMonoidHom, Function.comp_apply] | case inr.fixed.intro.h.h.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
g : Equiv.Perm α
⊢ ↑((Monoid... | case inr.fixed.intro.h.h.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
g : Equiv.Perm α
⊢ ↑(Equiv.P... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed.intro.h.h.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | apply congr_arg | case inr.fixed.intro.h.h.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
g : Equiv.Perm α
⊢ ↑(Equiv.P... | case inr.fixed.intro.h.h.a.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
g : Equiv.Perm α
⊢ Equiv.P... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed.intro.h.h.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | refine' Equiv.Perm.swap_induction_on g _ _ | case inr.fixed.intro.h.h.a.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
g : Equiv.Perm α
⊢ Equiv.P... | case inr.fixed.intro.h.h.a.h.refine'_1
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm α
hg'✝ : s g' = -1
hg' : s g' ≠ 1
g : Equiv.Perm α... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.fixed.intro.h.h.a.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
hs : Function.Surjective ⇑s
g' : Equiv.Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | rw [alternatingGroup_of_subsingleton] | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Subsingleton α
⊢ Subgroup.Characteristic (alternatingGroup α) | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Subsingleton α
⊢ Subgroup.Characteristic ⊥ | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Subsingleton α
⊢ Subgroup.Characteristic (alternatingGroup α)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | exact Subgroup.botCharacteristic | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Subsingleton α
⊢ Subgroup.Characteristic ⊥ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Subsingleton α
⊢ Subgroup.Characteristic ⊥
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | change Function.Surjective (Equiv.Perm.sign ∘ φ) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
⊢ Function.Surjective ⇑s | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
⊢ Function.Surjective (⇑Equiv.Perm.sign ∘ ⇑φ) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
⊢ Function.Surjective ⇑s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/IndexNormal.lean | alternatingGroup_is_characteristic | [37, 1] | [79, 72] | rw [Function.Surjective.of_comp_iff _] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
⊢ Function.Surjective (⇑Equiv.Perm.sign ∘ ⇑φ) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
⊢ Function.Surjective ⇑Equiv.Perm.sign
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* E... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hα : Nontrivial α
φ : Equiv.Perm α ≃* Equiv.Perm α
s : Equiv.Perm α →* ℤˣ := MonoidHom.comp Equiv.Perm.sign (MulEquiv.toMonoidHom φ)
⊢ Function.Surjective (⇑Equiv.Perm.sign ∘ ⇑φ)
TACTIC:
|
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