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.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← Equiv.Perm.Subtype.image_preimage_of_val hBs] | 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 ... | 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:
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... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Set.Subsingleton.image | 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 ... | case inl.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_... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact hB' | case inl.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_... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.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 ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | have hBs' : B = s := by
apply Set.Subset.antisymm hBs
intro x hx
suffices x = Subtype.val (⟨x, hx⟩ : s) by
rw [this, ← Set.mem_preimage, hB', Set.top_eq_univ]
apply Set.mem_univ
rfl | case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | have : ∃ g' ∈ G, g' • s ≠ s := by
by_contra h
push_neg at h
apply ne_of_lt hG
apply le_antisymm (le_of_lt hG)
intro g' hg'
rw [Subgroup.mem_inf] at hg' ⊢
exact ⟨h g' hg'.left, hg'.right⟩ | case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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', hg's⟩ := this | case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr.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)... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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' IsBlock.def_one.mp hB ⟨g', hg'⟩ with h h | case inr.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)... | case inr.intro.intro.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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.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 ⊓ alternatin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply Set.Subset.antisymm 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] | intro x hx | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 x = Subtype.val (⟨x, hx⟩ : s) by
rw [this, ← Set.mem_preimage, hB', Set.top_eq_univ]
apply Set.mem_univ | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | rfl | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 [this, ← Set.mem_preimage, hB', Set.top_eq_univ] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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.mem_univ | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | by_contra 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
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] | push_neg at 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
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 ne_of_lt 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 : ∀ (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 le_antisymm (le_of_lt 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 : ∀ (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 g' 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 : ∀ (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 [Subgroup.mem_inf] at 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 : ∀ (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] | exact ⟨h g' hg'.left, hg'.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 : 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] | exfalso | case inr.intro.intro.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 ... | case inr.intro.intro.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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.intro.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 ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply hg's | case inr.intro.intro.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 ... | case inr.intro.intro.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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.intro.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 ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [← hBs'] | case inr.intro.intro.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 ... | case inr.intro.intro.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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.intro.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 ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact h | case inr.intro.intro.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 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.intro.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 ⊓ altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | suffices (g' • B).Subsingleton by
apply Set.subsingleton_of_image _ B this
apply Function.Bijective.injective (MulAction.bijective _) | case inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | apply hB_not_le_sc ((⟨g', hg'⟩ : G) • B) (IsBlock_of_block _ hB) | case inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 [← hBs'] | case inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | exact Disjoint.subset_compl_right h | case inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.intro.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | apply Set.subsingleton_of_image _ B 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] | apply Function.Bijective.injective (MulAction.bijective _) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 s → 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' : s →ₑ[φ'] α := {
toFun := Subtype.val
map_smul' := fun ⟨m, _⟩ x => by simp } | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | intro x hx' | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | obtain ⟨⟨k, hk⟩, hkbx : k • b = x⟩ := 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 :... | case 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 ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_n... | 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 k • B = B by
rw [← hkbx, ← this, Set.smul_mem_smul_set_iff]
exact hb | case 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 ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_n... | case 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 ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_n... | Please generate a tactic in lean4 to solve the state.
STATE:
case 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 ... |
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 ⟨k, _⟩) | case 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 ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_n... | case 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 ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_n... | Please generate a tactic in lean4 to solve the state.
STATE:
case 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 ... |
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 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 ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_n... | case 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 ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_n... | Please generate a tactic in lean4 to solve the state.
STATE:
case 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 ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | change (k • B ∩ B).Nonempty | case 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 ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_n... | case 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 ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_n... | Please generate a tactic in lean4 to solve the state.
STATE:
case 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 ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | use a | case 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 ⊓ alternatingGroup α
this : IsPretransitive (↥G) α
hB_n... | 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
this : IsPretransitive (↥G) α
hB_ne_sc : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case 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 ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | constructor | 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
this : IsPretransitive (↥G) α
hB_ne_sc : ... | case h.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 : IsPretransitive (↥G) α
hB_ne_... | 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] | rw [← hkbx, ← this, Set.smul_mem_smul_set_iff] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | exact 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] | rw [mem_fixingSubgroup_iff] at hk | case h.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 : IsPretransitive (↥G) α
hB_ne_... | case h.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 : IsPretransitive (↥G) α
hB_ne_... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.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 [← hk a ha'] | case h.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 : IsPretransitive (↥G) α
hB_ne_... | case h.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 : IsPretransitive (↥G) α
hB_ne_... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.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] | exact Set.smul_mem_smul_set ha | case h.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 : IsPretransitive (↥G) α
hB_ne_... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.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] | exact ha | case h.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 : IsPretransitive (↥G) α
hB_ne... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.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] | apply le_trans (le_of_lt 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 : ∀ (B : ... | 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
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] | exact inf_le_left | 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
this : IsPretransitive (↥G) α
hB_ne_sc : ... | 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
this : IsPretransitive (↥G) α
hB_ne_sc : ... | 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 [Subgroup.mem_inf] | 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
this : IsPretransitive (↥G) α
hB_ne_sc : ... | 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
this : IsPretransitive (↥G) α
hB_ne_sc : ... | 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
this : IsPretransitive (↥G) α
hB_ne_sc : ... | 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
this : IsPretransitive (↥G) α
hB_ne_... | 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] | suffices hk' : k ∈ stabilizer (alternatingGroup α) s by
simpa [mem_stabilizer_iff] using hk' | 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
this : IsPretransitive (↥G) α
hB_ne_... | 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
this : IsPretransitive (↥G) α
hB_ne_... | 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] | apply MulAction.fixingSubgroup_le_stabilizer | 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
this : IsPretransitive (↥G) α
hB_ne_... | case a.left.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
this : IsPretransitive (↥G) α
hB_n... | 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] | exact hk | case a.left.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
this : IsPretransitive (↥G) α
hB_n... | 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
this : IsPretransitive (↥G) α
hB_ne... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.left.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 ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | exact k.prop | 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
this : IsPretransitive (↥G) α
hB_ne... | 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] | simpa [mem_stabilizer_iff] using hk' | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | haveI : IsPretransitive (fixingSubgroup (alternatingGroup α) s)
(SubMulAction.ofFixingSubgroup (alternatingGroup α) s) :=
isPretransitive_ofFixingSubgroup s h0 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
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] | obtain ⟨k, hk⟩ :=
exists_smul_eq (fixingSubgroup (alternatingGroup α) s)
(⟨b, hb'⟩ : SubMulAction.ofFixingSubgroup (alternatingGroup α) s) ⟨x, hx'⟩ | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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 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
hB_ne_... | 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] | use k | 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
hB_ne_... | 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
this✝ : IsPretransitive (↥G) α
hB_ne_sc :... | 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] | rw [← Subtype.coe_inj, SubMulAction.val_smul] at hk | 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
this✝ : IsPretransitive (↥G) α
hB_ne_sc :... | 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
this✝ : IsPretransitive (↥G) α
hB_ne_sc :... | 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] | exact hk | 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
this✝ : IsPretransitive (↥G) α
hB_ne_sc :... | 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] | rw [← hgbx, ← this, Set.smul_mem_smul_set_iff] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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] | exact hsc_le_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 :... | 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] | apply Nat.add_lt_add_right _ (Set.ncard (sᶜ : Set α)) | 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 ⊓... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nontrivial 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:
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] | use Set.ncard (sᶜ : Set 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
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] | 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
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] | apply le_trans (Set.ncard_le_ncard hsc_le_B) | 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 < ... | 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.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.Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | apply le_of_eq | 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 < ... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a.h₁.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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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.Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isPreprimitive_of_stabilizer_lt | [413, 2] | [618, 36] | rw [MulAction.smul_set_ncard_eq] | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a.h₁.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 ... | 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.h₁.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.P... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | have h0 : 2 ≤ Set.ncard s := by
rw [Nat.succ_le_iff, Set.one_lt_ncard_iff_nontrivial]
exact h0' | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
⊢ 4 < Fintype.card α | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 4 < Fintype.card α | 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
hs : Set.ncard s < Set.ncard sᶜ
⊢ 4 < Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [← Nat.card_eq_fintype_card, ← Set.ncard_add_ncard_compl s] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 4 < Fintype.card α | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 4 < Set.ncard s + Set.ncard 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
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 4 < Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | change 2 + 2 < _ | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 4 < Set.ncard s + Set.ncard sᶜ | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 2 + 2 < Set.ncard s + Set.ncard 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
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 4 < Set.ncard s + Set.ncard sᶜ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | apply lt_of_le_of_lt | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 2 + 2 < Set.ncard s + Set.ncard sᶜ | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 2 + 2 ≤ ?b
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s ... | 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
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 2 + 2 < Set.ncard s + Set.ncard sᶜ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | exact Nat.add_le_add_right h0 2 | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 2 + 2 ≤ ?b
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s ... | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ Set.ncard s + 2 < Set.ncard s + Set.ncard sᶜ | 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
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 2 + 2 ≤ ?b
case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0'... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | apply Nat.add_lt_add_left | case a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ Set.ncard s + 2 < Set.ncard s + Set.ncard sᶜ | case a.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 2 < Set.ncard sᶜ | 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
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ Set.ncard s + 2 < Set.ncard s + Set.ncard sᶜ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | exact lt_of_le_of_lt h0 hs | case a.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 2 < Set.ncard sᶜ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
h0 : 2 ≤ Set.ncard s
⊢ 2 < Set.ncard sᶜ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | constructor | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
⊢ Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) s) | case out
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
⊢ IsCoatom (stabilizer (↥(alternatingGroup α)) s) | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
⊢ Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) s)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | constructor | case out
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
⊢ IsCoatom (stabilizer (↥(alternatingGroup α)) s) | case out.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
⊢ stabilizer (↥(alternatingGroup α)) s ≠ ⊤
case out.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontri... | Please generate a tactic in lean4 to solve the state.
STATE:
case out
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
⊢ IsCoatom (stabilizer (↥(alternatingGroup α)) s)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | exact stabilizer_ne_top' s h0'.nonempty h1' | case out.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
⊢ stabilizer (↥(alternatingGroup α)) s ≠ ⊤ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case out.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
⊢ stabilizer (↥(alternatingGroup α)) s ≠ ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | intro G' hG' | case out.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
⊢ ∀ (b : Subgroup ↥(alternatingGroup α)), stabilizer (↥(alternatingGroup α)) s < b → b = ⊤ | case out.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ G' = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
⊢ ∀ (b : Subgroup ↥(alternatingGroup α)), stabilizer (↥(alternatingGroup α)) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | suffices alternatingGroup α ≤ G'.map (alternatingGroup α).subtype by
rw [eq_top_iff]; intro g _
obtain ⟨g', hg', hgg'⟩ := this g.prop
simp only [Subgroup.coeSubtype, SetLike.coe_eq_coe] at hgg'
rw [← hgg']; exact hg' | case out.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ G' = ⊤ | case out.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ alternatingGroup α ≤ Subgroup.map (Subgroup.subtype ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | apply le_of_isPreprimitive s hα | case out.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ alternatingGroup α ≤ Subgroup.map (Subgroup.subtype ... | case out.right.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [eq_top_iff] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.subtype (alternati... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.subtype (alternati... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : a... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | intro g _ | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.subtype (alternati... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.subtype (alternati... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : a... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | obtain ⟨g', hg', hgg'⟩ := this g.prop | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.subtype (alternati... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.s... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : a... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | simp only [Subgroup.coeSubtype, SetLike.coe_eq_coe] at hgg' | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.s... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.s... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [← hgg'] | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.s... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.s... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | exact hg' | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
this : alternatingGroup α ≤ Subgroup.map (Subgroup.s... | no goals | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [← Subgroup.subgroupOf_map_subtype, Subgroup.map_subtype_le_map_subtype] | case out.right.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ stabilizer (Equiv.Perm α) s ⊓ alternatingGroup α ... | case out.right.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ Subgroup.subgroupOf (stabilizer (Equiv.Perm α) s)... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [MulAction.stabilizer_subgroupOf_eq] at hG' | case out.right.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ Subgroup.subgroupOf (stabilizer (Equiv.Perm α) s)... | case out.right.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : Subgroup.subgroupOf (stabilizer (Equiv.Perm α) s) (alternatingGroup α) < G'
⊢ Subgroup.subgro... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | exact le_of_lt hG' | case out.right.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : Subgroup.subgroupOf (stabilizer (Equiv.Perm α) s) (alternatingGroup α) < G'
⊢ Subgroup.subgro... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : Subgroup.subgroupOf (stabilizer ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | apply isPreprimitive_of_stabilizer_lt s h0' h1' hs (le_of_lt hα) | case out.right.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ IsPreprimitive (↥(Subgroup.map (Subgroup.subtype (... | case out.right.a.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ stabilizer (Equiv.Perm α) s ⊓ alternatingGroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [lt_iff_le_not_le] | case out.right.a.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ stabilizer (Equiv.Perm α) s ⊓ alternatingGroup ... | case out.right.a.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ stabilizer (Equiv.Perm α) s ⊓ alternatingGroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | constructor | case out.right.a.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ stabilizer (Equiv.Perm α) s ⊓ alternatingGroup ... | case out.right.a.hG.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ stabilizer (Equiv.Perm α) s ⊓ alternatingG... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | intro g | case out.right.a.hG.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
⊢ stabilizer (Equiv.Perm α) s ⊓ alternatingG... | case out.right.a.hG.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
g : Equiv.Perm α
⊢ g ∈ stabilizer (Equiv.Per... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternating... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | simp only [Subgroup.mem_inf] | case out.right.a.hG.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
g : Equiv.Perm α
⊢ g ∈ stabilizer (Equiv.Per... | case out.right.a.hG.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
g : Equiv.Perm α
⊢ g ∈ stabilizer (Equiv.Per... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternating... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rintro ⟨hg, hg'⟩ | case out.right.a.hG.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
g : Equiv.Perm α
⊢ g ∈ stabilizer (Equiv.Per... | case out.right.a.hG.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
g : Equiv.Perm α
hg : g ∈ stabilizer (... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.left
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternating... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | refine' And.intro _ hg' | case out.right.a.hG.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
g : Equiv.Perm α
hg : g ∈ stabilizer (... | case out.right.a.hG.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
g : Equiv.Perm α
hg : g ∈ stabilizer (... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.left.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0' : Set.Nontrivial s
h1' : Set.Nontrivial sᶜ
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alter... |
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