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/AlternatingMaximal.lean | alternatingGroup.le_of_isPreprimitive | [290, 1] | [308, 59] | intro hG' | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
⊢ IsPreprimitive (↥G) α → alternatingGroup α ≤ G | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
⊢ alternatingGroup α ≤ G | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
⊢ IsPreprimitive (↥G) α → alternatingGroup α ≤ G
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.le_of_isPreprimitive | [290, 1] | [308, 59] | obtain ⟨g, hg3, hg⟩ := has_three_cycle_of_stabilizer s hα | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
⊢ alternatingGroup α ≤ G | case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsThreeCycle g
hg : g ∈ stabilizer (Equiv.Perm α) s
⊢ alternatingGr... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
⊢ alternatingGroup α ≤ G
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.le_of_isPreprimitive | [290, 1] | [308, 59] | apply jordan_three_cycle hG' hg3 | case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsThreeCycle g
hg : g ∈ stabilizer (Equiv.Perm α) s
⊢ alternatingGr... | case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsThreeCycle g
hg : g ∈ stabilizer (Equiv.Perm α) s
⊢ g ∈ G | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsThre... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.le_of_isPreprimitive | [290, 1] | [308, 59] | apply hG | case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsThreeCycle g
hg : g ∈ stabilizer (Equiv.Perm α) s
⊢ g ∈ G | case intro.intro.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsThreeCycle g
hg : g ∈ stabilizer (Equiv.Perm α) s
⊢ g ∈ stabili... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsThre... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.le_of_isPreprimitive | [290, 1] | [308, 59] | simp only [Subgroup.mem_inf, hg, true_and_iff] | case intro.intro.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsThreeCycle g
hg : g ∈ stabilizer (Equiv.Perm α) s
⊢ g ∈ stabili... | case intro.intro.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsThreeCycle g
hg : g ∈ stabilizer (Equiv.Perm α) s
⊢ g ∈ alterna... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsTh... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.le_of_isPreprimitive | [290, 1] | [308, 59] | exact Equiv.Perm.IsThreeCycle.mem_alternatingGroup hg3 | case intro.intro.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsThreeCycle g
hg : g ∈ stabilizer (Equiv.Perm α) s
⊢ g ∈ alterna... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
hα : 4 < Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G
hG' : IsPreprimitive (↥G) α
g : Equiv.Perm α
hg3 : Equiv.Perm.IsTh... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply IsPreprimitive.mk | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
⊢ IsPreprimitive (... | case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro B hB | case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive ... | case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive ... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | unfold IsTrivialBlock | case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive ... | case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive ... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [or_iff_not_imp_left] | case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive ... | case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive ... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro hB' | case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive ... | case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive ... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | obtain ⟨a, ha, ha'⟩ := Set.not_subset_iff_exists_mem_not_mem.mp
fun h => hB' ((hB_not_le_sc B hB) h) | case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive ... | case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPr... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [Set.not_mem_compl_iff] at ha' | case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPr... | case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPr... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | obtain ⟨b, hb, hb'⟩ := Set.not_subset_iff_exists_mem_not_mem.mp
fun h => hB' ((hB_not_le_s B hB) h) | case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPr... | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← Set.mem_compl_iff] at hb' | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α... | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [eq_top_iff] | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α... | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro x _ | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α... | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | obtain ⟨b, hb⟩ := h1.nonempty | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α... | case has_trivial_blocks'.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingG... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | obtain ⟨⟨g, hg⟩, hgbx : g • b = x⟩ := exists_smul_eq G b x | case has_trivial_blocks'.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingG... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alt... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabil... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | suffices g • B = B by
rw [← hgbx, ← this, Set.smul_mem_smul_set_iff]
exact hsc_le_B hb | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alt... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alt... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply or_iff_not_imp_right.mp (IsBlock.def_one.mp hB ⟨g, hg⟩) | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alt... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alt... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [Set.not_disjoint_iff_nonempty_inter] | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alt... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alt... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | change (g • B ∩ B).Nonempty | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alt... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alt... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Set.ncard_pigeonhole | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alt... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ a... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← Nat.card_eq_fintype_card, ← Set.ncard_add_ncard_compl s] | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ a... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ a... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Nat.lt_of_lt_of_le | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ a... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Nat.add_le_add | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a.h₁
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < ... | 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✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact Set.ncard_le_ncard hsc_le_B | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a.h₂
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < ... | 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.h₂
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | have hG' : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ≤ G :=
le_trans (le_of_lt hG) inf_le_left | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
⊢ IsPretransitive (↥G) α | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alternatingG... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Equiv.Perm.IsPretransitive.of_partition G s | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alternatingG... | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro a ha b hb | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | obtain ⟨g, hg, H⟩ := moves_in h4 s a ha b hb | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | case a.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | use! g | case a.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm ... | case property
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingG... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact hG' hg | case property
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | Please generate a tactic in lean4 to solve the state.
STATE:
case property
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact H | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro a ha b hb | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | obtain ⟨g, hg, H⟩ := moves_in h4 (sᶜ) a ha b hb | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | case a.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | use! g | case a.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm ... | case property
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingG... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply hG' | case property
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ... | case property.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case property
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [stabilizer_compl] at hg | case property.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) ... | case property.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case property.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGrou... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact hg | case property.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) ... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | Please generate a tactic in lean4 to solve the state.
STATE:
case property.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGrou... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact H | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro h | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply (lt_iff_le_not_le.mp hG).right | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [le_inf_iff] | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | constructor | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ alter... | case a.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro g | case a.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ ... | case a.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [Subgroup.mem_inf, mem_stabilizer_iff] | case a.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ ... | case a.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rintro ⟨hg, _⟩ | case a.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓ ... | case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← Subgroup.coe_mk G g hg] | case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α... | case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | change (⟨g, hg⟩ : ↥G) • s = s | case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α... | case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← mem_stabilizer_iff, h] | case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α... | case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact Subgroup.mem_top _ | case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact inf_le_right | case a.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
hG' : stabilizer (Equiv.Perm α) s ⊓... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro B hB hBsc | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
⊢ ∀ (B : Set α), I... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
B : Set α
hB : IsB... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | obtain ⟨b, hb⟩ := h1.nonempty | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
B : Set α
hB : IsB... | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
B : Set... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← hBsc] at hb | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
B : Set... | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
B : Set... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α <... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | obtain ⟨a, ha⟩ := h0.nonempty | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
B : Set... | case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
B... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α <... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | obtain ⟨k, hk⟩ := exists_smul_eq G b a | case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
B... | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGro... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | suffices Set.ncard (B : Set α) ≤ Set.ncard s by
apply Nat.lt_irrefl (Set.ncard B)
apply lt_of_le_of_lt this
simp_rw [hBsc]; exact hα | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← smul_set_ncard_eq k B] | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Set.ncard_le_ncard (ht := Set.toFinite s) | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← Set.disjoint_compl_right_iff_subset, ← hBsc] | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply or_iff_not_imp_left.mp (IsBlock.def_one.mp hB k) | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro h | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Set.not_mem_empty a | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← Set.inter_compl_self s] | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | constructor | case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥... | case intro.intro.intro.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransiti... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Nat.lt_irrefl (Set.ncard B) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
B : Set α
hB : Is... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
B : Set α
hB : Is... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply lt_of_le_of_lt this | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
B : Set α
hB : Is... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
B : Set α
hB : Is... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | simp_rw [hBsc] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
B : Set α
hB : Is... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
B : Set α
hB : Is... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact hα | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
B : Set α
hB : Is... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact ha | case intro.intro.intro.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransiti... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alt... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← hk, ← hBsc, ← h, Set.smul_mem_smul_set_iff] | case intro.intro.intro.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransit... | case intro.intro.intro.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransit... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ al... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact hb | case intro.intro.intro.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransit... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ al... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro B hB hBsc | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B : ... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B : ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← Equiv.Perm.Subtype.image_preimage_of_val hBsc] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B : ... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B : ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Set.Subsingleton.image | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B : ... | case hs
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | suffices IsTrivialBlock (Subtype.val ⁻¹' B : Set (sᶜ : Set α)) by
apply Or.resolve_right this
intro hB'
apply hB_ne_sc B hB
simp only [Set.top_eq_univ, Set.preimage_eq_univ_iff, Subtype.range_coe_subtype] at hB'
apply Set.Subset.antisymm hBsc hB' | case hs
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc :... | case hs
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc :... | Please generate a tactic in lean4 to solve the state.
STATE:
case hs
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | suffices IsPreprimitive (stabilizer G (sᶜ : Set α)) (sᶜ : Set α) by
refine' IsPreprimitive.has_trivial_blocks this _
let φ' : stabilizer G (sᶜ : Set α) → G := Subtype.val
let f' : (sᶜ : Set α) →ₑ[φ'] α := {
toFun := Subtype.val
map_smul' := fun m x => by simp only [SMul.smul_stabilizer_def] }
apply MulA... | case hs
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc :... | case hs
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc :... | Please generate a tactic in lean4 to solve the state.
STATE:
case hs
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply stabilizer.isPreprimitive' | case hs
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc :... | case hs.hsc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_... | Please generate a tactic in lean4 to solve the state.
STATE:
case hs
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Or.resolve_right this | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro hB' | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply hB_ne_sc B hB | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | simp only [Set.top_eq_univ, Set.preimage_eq_univ_iff, Subtype.range_coe_subtype] at hB' | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Set.Subset.antisymm hBsc hB' | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | refine' IsPreprimitive.has_trivial_blocks this _ | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | let φ' : stabilizer G (sᶜ : Set α) → G := Subtype.val | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | let f' : (sᶜ : Set α) →ₑ[φ'] α := {
toFun := Subtype.val
map_smul' := fun m x => by simp only [SMul.smul_stabilizer_def] } | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply MulAction.IsBlock_preimage f' hB | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | simp only [SMul.smul_stabilizer_def] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [compl_compl] | case hs.hsc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_... | case hs.hsc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_... | Please generate a tactic in lean4 to solve the state.
STATE:
case hs.hsc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact h0 | case hs.hsc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hs.hsc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [stabilizer_compl] | case hs.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_s... | case hs.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_s... | Please generate a tactic in lean4 to solve the state.
STATE:
case hs.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α <... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact le_trans (le_of_lt hG) inf_le_left | case hs.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_s... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hs.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α <... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | intro B hB hBs | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B : ... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B : ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | suffices IsPreprimitive (stabilizer G s) (s : Set α) by
refine' IsPreprimitive.has_trivial_blocks this _
let φ' : stabilizer G s → G := Subtype.val
let f' : s →ₑ[φ'] α := {
toFun := Subtype.val
map_smul' := fun ⟨m, _⟩ x => by simp }
apply MulAction.IsBlock_preimage f' hB | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B : ... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B : ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply stabilizer.isPreprimitive' s h1 | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B : ... | case hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply le_trans (le_of_lt hG) inf_le_left | case hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | cases' this with hB' hB' | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this✝ : IsPretransitive (↥G) α
hB_ne_sc : ∀ (B :... | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_ne_sc ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial s
h1 : Set.Nontrivial sᶜ
hα : Set.ncard s < Set.ncard sᶜ
h4 : 4 ≤ Fintype.card α
G : Subgroup (Equiv.Perm α)
hG : stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α < G ⊓ altern... |
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