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.isMaximalStab' | [621, 1] | [683, 29] | simp only [Subgroup.mem_map, Subgroup.coeSubtype, exists_prop] | 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... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | use ⟨g, 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 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
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
g : Equiv.Perm α
hg : g ∈ stabilizer (Equiv.Perm α) s
hg' : g ... | 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... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | 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
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 (Equiv.Perm α) s
hg' : g ... | 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
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 (Equiv.Perm α) s
hg'... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s < G'
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | apply le_of_lt hG' | 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
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 (Equiv.Perm α) s
hg'... | case h.left.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'
g : Equiv.Perm α
hg : g ∈ stabilizer (Equiv.Perm α) s
h... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s <... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | simpa only [mem_stabilizer_iff] using hg | case h.left.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'
g : Equiv.Perm α
hg : g ∈ stabilizer (Equiv.Perm α) s
h... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left.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... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rfl | 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
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 (Equiv.Perm α) s
hg... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | intro h | case out.right.a.hG.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'
⊢ ¬Subgroup.map (Subgroup.subtype (alternat... | case out.right.a.hG.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'
h :
Subgroup.map (Subgroup.subtype (alter... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.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 (↥(alternatin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [lt_iff_le_not_le] at hG' | case out.right.a.hG.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'
h :
Subgroup.map (Subgroup.subtype (alter... | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.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 (↥(alternatin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | apply hG'.right | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.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 (↥(alternatin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | intro g' hg' | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.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 (↥(alternatin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [mem_stabilizer_iff] | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.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 (↥(alternatin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | change (g' : Equiv.Perm α) • s = s | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.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 (↥(alternatin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [← mem_stabilizer_iff] | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.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 (↥(alternatin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | apply @inf_le_left (Subgroup (Equiv.Perm α)) _ | case out.right.a.hG.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' ≤ stabilizer (↥(alternatingGroup α)) ... | case out.right.a.hG.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' ∧ ¬G' ≤ stabilizer (↥(alternatingGroup α)... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.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 (↥(alternatin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | apply h | case out.right.a.hG.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' ∧ ¬G' ≤ stabilizer (↥(alternatingGroup α)... | case out.right.a.hG.right.a.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' ∧ ¬G' ≤ stabilizer (↥(alternatingGroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.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 (↥(alternat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [Subgroup.mem_inf] | case out.right.a.hG.right.a.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' ∧ ¬G' ≤ stabilizer (↥(alternatingGroup ... | case out.right.a.hG.right.a.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' ∧ ¬G' ≤ stabilizer (↥(alternatingGroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.right.a.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 (↥(altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | apply And.intro _ g'.prop | case out.right.a.hG.right.a.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' ∧ ¬G' ≤ stabilizer (↥(alternatingGroup ... | 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' ≤ stabilizer (↥(alternatingGroup α)) s
h :
Subgroup.map (Subg... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.a.hG.right.a.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 (↥(altern... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | simp only [Subgroup.mem_map, Subgroup.coeSubtype, SetLike.coe_eq_coe, exists_prop, exists_eq_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' ≤ stabilizer (↥(alternatingGroup α)) s
h :
Subgroup.map (Subg... | 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' ≤ stabilizer (↥(alternatingGroup α)) s
h :
Subgroup.map (Subg... | 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' ∧ ¬G' ≤ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | exact 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' ∧ ¬G' ≤ stabilizer (↥(alternatingGroup α)) s
h :
Subgroup.map (Subg... | 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
hs : Set.ncard s < Set.ncard sᶜ
hα : 4 < Fintype.card α
G' : Subgroup ↥(alternatingGroup α)
hG' : stabilizer (↥(alternatingGroup α)) s ≤ G' ∧ ¬G' ≤ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | rw [Nat.succ_le_iff, Set.one_lt_ncard_iff_nontrivial] | 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
⊢ 2 ≤ Set.ncard 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
⊢ Set.Nontrivial 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
⊢ 2 ≤ Set.ncard s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.isMaximalStab' | [621, 1] | [683, 29] | 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
⊢ Set.Nontrivial s | 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
hs : Set.ncard s < Set.ncard sᶜ
⊢ Set.Nontrivial s
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.three_le | [686, 1] | [694, 28] | cases' Nat.eq_or_lt_of_le h with h h | α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
⊢ 3 ≤ c | case inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
h : 1 = n
⊢ 3 ≤ c
case inr
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
h : 1 < n
⊢ 3 ≤ c | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
⊢ 3 ≤ c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.three_le | [686, 1] | [694, 28] | rw [Nat.succ_le_iff] | case inr
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
h : 1 < n
⊢ 3 ≤ c | case inr
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
h : 1 < n
⊢ 2 < c | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
h : 1 < n
⊢ 3 ≤ c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.three_le | [686, 1] | [694, 28] | exact lt_of_le_of_lt h h' | case inr
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
h : 1 < n
⊢ 2 < c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
h : 1 < n
⊢ 2 < c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.three_le | [686, 1] | [694, 28] | rw [← h] at h' hh' | case inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
h : 1 = n
⊢ 3 ≤ c | case inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
⊢ 3 ≤ c | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : n < c
hh' : c ≠ 2 * n
h : 1 = n
⊢ 3 ≤ c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.three_le | [686, 1] | [694, 28] | cases' Nat.eq_or_lt_of_le h' with h' h' | case inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
⊢ 3 ≤ c | case inl.inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h'✝ : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
h' : Nat.succ 1 = c
⊢ 3 ≤ c
case inl.inr
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h'✝ : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
h' : Nat.succ 1 < c
⊢ 3 ≤ c | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h' : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
⊢ 3 ≤ c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.three_le | [686, 1] | [694, 28] | exact h' | case inl.inr
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h'✝ : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
h' : Nat.succ 1 < c
⊢ 3 ≤ c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inr
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h'✝ : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
h' : Nat.succ 1 < c
⊢ 3 ≤ c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.three_le | [686, 1] | [694, 28] | exfalso | case inl.inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h'✝ : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
h' : Nat.succ 1 = c
⊢ 3 ≤ c | case inl.inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h'✝ : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
h' : Nat.succ 1 = c
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h'✝ : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
h' : Nat.succ 1 = c
⊢ 3 ≤ c
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.three_le | [686, 1] | [694, 28] | apply hh' h'.symm | case inl.inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h'✝ : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
h' : Nat.succ 1 = c
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inl
α : Type ?u.123292
inst✝¹ : Fintype α
inst✝ : DecidableEq α
c n : ℕ
h✝ : 1 ≤ n
h'✝ : 1 < c
hh' : c ≠ 2 * 1
h : 1 = n
h' : Nat.succ 1 = c
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | have hα : 3 ≤ Fintype.card α := by
rw [← Set.ncard_pos, ← Nat.succ_le_iff] at h0 h1
refine' three_le h0 _ hs
rw [← Nat.card_eq_fintype_card, ← Set.ncard_add_ncard_compl s]
exact Nat.lt_add_of_pos_right h1 | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) s) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ Subgroup.IsMaximal (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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) s)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | have : Nontrivial α := by
rw [← Fintype.one_lt_card_iff_nontrivial]
apply lt_of_lt_of_le _ hα
norm_num | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) s) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
⊢ Subgroup.IsMaximal (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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) s)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | by_cases h0' : Set.Nontrivial s | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
⊢ Subgroup.IsMaxim... | case pos
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaxi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | by_cases h1' : Set.Nontrivial sᶜ | case pos
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | case pos
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgro... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | cases' Nat.lt_trichotomy (Set.ncard s) (Set.ncard (sᶜ : Set α)) with hs' hs' | case pos
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | case pos.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' :... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgro... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | cases' hs' with hs' hs' | case pos.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' :... | case pos.inr.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | rw [← Set.ncard_pos, ← Nat.succ_le_iff] at h0 h1 | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ 3 ≤ Fintype.card α | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Nat.succ 0 ≤ Set.ncard s
h1 : Nat.succ 0 ≤ Set.ncard sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ 3 ≤ 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ 3 ≤ Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | refine' three_le h0 _ hs | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Nat.succ 0 ≤ Set.ncard s
h1 : Nat.succ 0 ≤ Set.ncard sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ 3 ≤ Fintype.card α | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Nat.succ 0 ≤ Set.ncard s
h1 : Nat.succ 0 ≤ Set.ncard sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ Set.ncard s < 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 : Nat.succ 0 ≤ Set.ncard s
h1 : Nat.succ 0 ≤ Set.ncard sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ 3 ≤ Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | 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 : Nat.succ 0 ≤ Set.ncard s
h1 : Nat.succ 0 ≤ Set.ncard sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ Set.ncard s < Fintype.card α | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Nat.succ 0 ≤ Set.ncard s
h1 : Nat.succ 0 ≤ Set.ncard sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ Set.ncard s < 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 : Nat.succ 0 ≤ Set.ncard s
h1 : Nat.succ 0 ≤ Set.ncard sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ Set.ncard s < Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | exact Nat.lt_add_of_pos_right h1 | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Nat.succ 0 ≤ Set.ncard s
h1 : Nat.succ 0 ≤ Set.ncard sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ Set.ncard s < Set.ncard s + Set.ncard sᶜ | 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 : Nat.succ 0 ≤ Set.ncard s
h1 : Nat.succ 0 ≤ Set.ncard sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
⊢ Set.ncard s < Set.ncard s + Set.ncard sᶜ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | rw [← Fintype.one_lt_card_iff_nontrivial] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ Nontrivial α | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ 1 < 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ Nontrivial α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | apply lt_of_lt_of_le _ hα | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ 1 < Fintype.card α | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ 1 < 3 | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ 1 < Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | norm_num | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ 1 < 3 | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
⊢ 1 < 3
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | intro t ht ht' | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
⊢ ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht : Set.Nonempty t
ht' : Set.Subsingleton t
⊢ Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t) | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
⊢ ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaxima... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | suffices ∃ a : α, t = ({a} : Set α) by
obtain ⟨a, rfl⟩ := this
have : stabilizer (alternatingGroup α) ({a} : Set α) = stabilizer (alternatingGroup α) a := by
ext
simp only [mem_stabilizer_iff, Set.smul_set_singleton, Set.singleton_eq_singleton_iff]
rw [this]
apply hasMaximalStabilizersOfPreprimitive
a... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht : Set.Nonempty t
ht' : Set.Subsingleton t
⊢ Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht : Set.Nonempty t
ht' : Set.Subsingleton t
⊢ ∃ a, t = {a} | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht : Set.Nonempty t
ht' : Set.Subsingleton t
⊢ Subgroup.IsMaxi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | obtain ⟨a, rfl⟩ := this | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
t : Set α
ht : Set.Nonempty t
ht' : Set.Subsingleton t
this : ∃ a, t = {a}
⊢ Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) ... | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
⊢ Subgroup.IsMaximal (stabilizer ↥(alternatingGroup α) {a}) | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
t : Set α
ht : Set.Nonempty t
ht' : Set.Subsingleton t
this : ∃ a, t = ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | have : stabilizer (alternatingGroup α) ({a} : Set α) = stabilizer (alternatingGroup α) a := by
ext
simp only [mem_stabilizer_iff, Set.smul_set_singleton, Set.singleton_eq_singleton_iff] | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
⊢ Subgroup.IsMaximal (stabilizer ↥(alternatingGroup α) {a}) | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
this : stabilizer ↥(alternatingGroup α) {a} = stabilizer (↥(altern... | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
⊢ Subg... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | rw [this] | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
this : stabilizer ↥(alternatingGroup α) {a} = stabilizer (↥(altern... | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
this : stabilizer ↥(alternatingGroup α) {a} = stabilizer (↥(altern... | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
this ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | apply hasMaximalStabilizersOfPreprimitive | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
this : stabilizer ↥(alternatingGroup α) {a} = stabilizer (↥(altern... | case intro.hpGX
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
this : stabilizer ↥(alternatingGroup α) {a} = stabilizer (↥(a... | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
this ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | apply AlternatingGroup.isPreprimitive hα | case intro.hpGX
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
this : stabilizer ↥(alternatingGroup α) {a} = stabilizer (↥(a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hpGX
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this✝ : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | ext | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
⊢ stabilizer ↥(alternatingGroup α) {a} = stabilizer (↥(alternatingGroup α)) a | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
x✝ : ↥(alternatingGroup α)
⊢ x✝ ∈ stabilizer ↥(alternatingGroup α) {a} ... | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
⊢ stabilizer ↥(al... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | simp only [mem_stabilizer_iff, Set.smul_set_singleton, Set.singleton_eq_singleton_iff] | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
x✝ : ↥(alternatingGroup α)
⊢ x✝ ∈ stabilizer ↥(alternatingGroup α) {a} ... | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
a : α
ht : Set.Nonempty {a}
ht' : Set.Subsingleton {a}
x✝ : ↥(alt... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | obtain ⟨a, ha⟩ := ht | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht : Set.Nonempty t
ht' : Set.Subsingleton t
⊢ ∃ a, t = {a} | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht' : Set.Subsingleton t
a : α
ha : a ∈ t
⊢ ∃ a, t = {a} | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht : Set.Nonempty t
ht' : Set.Subsingleton t
⊢ ∃ a, t = {a}
TA... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | use a | case intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht' : Set.Subsingleton t
a : α
ha : a ∈ t
⊢ ∃ a, t = {a} | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht' : Set.Subsingleton t
a : α
ha : a ∈ t
⊢ t = {a} | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht' : Set.Subsingleton t
a : α
ha : a ∈ t
⊢ ∃ a, t ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | exact Set.Subsingleton.eq_singleton_of_mem ht' ha | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht' : Set.Subsingleton t
a : α
ha : a ∈ t
⊢ t = {a} | 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.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
t : Set α
ht' : Set.Subsingleton t
a : α
ha : a ∈ t
⊢ t = {a}
TAC... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | exact isMaximalStab' s h0' h1' hs' | case pos.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | exfalso | case pos.inr.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | case pos.inr.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.inr.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | apply hs | case pos.inr.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | case pos.inr.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.inr.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | rw [← Nat.card_eq_fintype_card, ← Set.ncard_add_ncard_compl s, ← hs', ← two_mul] | case pos.inr.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.inr.inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | rw [← compl_compl s] at h0' | case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | rw [← stabilizer_compl] | case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | apply isMaximalStab' (sᶜ) h1' h0' | case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | simp_rw [compl_compl s] | case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | convert hs' | case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.inr.inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | simp only [Set.not_nontrivial_iff] at h1' | case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgro... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | rw [← stabilizer_compl] | case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgro... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | exact h (sᶜ) h1 h1' | case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgro... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | simp only [Set.not_nontrivial_iff] at h0' | case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : ¬Se... | case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgro... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Stabilizer.isMaximal | [699, 1] | [745, 21] | exact h s h0 h0' | case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgroup.IsMaximal (stabilizer (↥(alternatingGroup α)) t)
h0' : Set... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hs : Fintype.card α ≠ 2 * Set.ncard s
hα : 3 ≤ Fintype.card α
this : Nontrivial α
h : ∀ (t : Set α), Set.Nonempty t → Set.Subsingleton t → Subgro... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | have hα' : 3 ≤ Fintype.card α := three_le h_one_le hn hα | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | have : Nontrivial α := by
rw [← Fintype.one_lt_card_iff_nontrivial];
exact lt_of_le_of_lt h_one_le hn | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | cases' Nat.eq_or_lt_of_le h_one_le with h_one h_one_lt | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n) | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one : 1 = n
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | have : Nontrivial (n.Combination α) :=
Nat.Combination_nontrivial α (lt_trans (Nat.lt_succ_self 0) h_one_lt) hn | case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combinati... | case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
⊢ IsPreprimi... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combinatio... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | obtain ⟨sn⟩ := Nontrivial.to_nonempty (α := n.Combination α) | case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
⊢ IsPreprimi... | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combinati... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | let s := sn.val | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑... | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Com... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | let hs : s.card = n := sn.prop | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑... | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Com... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | rw [← maximal_stabilizer_iff_preprimitive (alternatingGroup α) sn] | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑... | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Com... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | have : stabilizer (alternatingGroup α) sn =
stabilizer (alternatingGroup α) (s : Set α) := by
ext g
simp only [mem_stabilizer_iff]
rw [← Subtype.coe_inj]
change g • s = s ↔ _
rw [← Finset.coe_smul_finset, ← Finset.coe_inj] | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑... | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn :... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Com... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | rw [this] | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn :... | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn :... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Co... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | apply Stabilizer.isMaximal (s : Set α) | case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
sn :... | case inr.intro.h0
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
s... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Co... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | rw [← Fintype.one_lt_card_iff_nontrivial] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
⊢ Nontrivial α | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
⊢ 1 < 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
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
⊢ Nontrivial α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | exact lt_of_le_of_lt h_one_le hn | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
⊢ 1 < Fintype.card α | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
⊢ 1 < Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | rw [← h_one] | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one : 1 = n
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n) | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one : 1 = n
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α 1) | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one : 1 = n
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | apply isPreprimitive_of_surjective_map
(Nat.bijective_toCombination_one_equivariant _ α).surjective | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one : 1 = n
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α 1) | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one : 1 = n
⊢ IsPreprimitive (↥(alternatingGroup α)) α | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one : 1 = n
⊢ IsPreprimitive ↥(alternatingGroup α) ↑(Nat.Combination α 1)
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | exact AlternatingGroup.isPreprimitive hα' | case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one : 1 = n
⊢ IsPreprimitive (↥(alternatingGroup α)) α | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one : 1 = n
⊢ IsPreprimitive (↥(alternatingGroup α)) α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | have : Fintype.card α - n + n = Fintype.card α := by apply Nat.sub_add_cancel; exact le_of_lt hn | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one_lt : 1 < n
⊢ IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one_lt : 1 < n
⊢ IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
TACTI... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | rw [isPretransitive.of_bijective_map_iff Function.surjective_id
(Nat.Combination_compl_bijective (alternatingGroup α) α this)] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α (Fintype.card α - n)) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsPretransitive ↥(... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | apply Nat.Combination_isPretransitive_of_IsMultiplyPretransitive | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α (Fintype.card α - n)) | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsMultiplyPretransitive (↥(alternatingGroup α)) α (Fintype.card α - n) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsPretransitive ↥(... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | apply isMultiplyPretransitive_of_higher (alternatingGroup α) α _
(Nat.sub_le_sub_left h_one_lt _) | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsMultiplyPretransitive (↥(alternatingGroup α)) α (Fintype.card α - n) | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ ↑(Fintype.card α - Nat.succ 1) ≤ PartENat.card α
α : Type u_1
inst✝¹ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsMultiplyP... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | apply Nat.sub_add_cancel | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one_lt : 1 < n
⊢ Fintype.card α - n + n = Fintype.card α | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one_lt : 1 < n
⊢ n ≤ 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
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one_lt : 1 < n
⊢ Fintype.card α - n + n = Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | exact le_of_lt hn | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one_lt : 1 < n
⊢ n ≤ Fintype.card α | 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
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this : Nontrivial α
h_one_lt : 1 < n
⊢ n ≤ Fintype.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | rw [PartENat.card_eq_coe_fintype_card] | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ ↑(Fintype.card α - Nat.succ 1) ≤ PartENat.card α | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ ↑(Fintype.card α - Nat.succ 1) ≤ ↑(Fintype.card α) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ ↑(Fintype.c... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | simp only [PartENat.coe_le_coe, tsub_le_self] | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ ↑(Fintype.card α - Nat.succ 1) ≤ ↑(Fintype.card α) | 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
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ ↑(Fintype.c... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | apply IsMultiplyPretransitive.alternatingGroup_of_sub_two | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsMultiplyPretransitive (↥(alternatingGroup α)) α (Fintype.card α - Nat.succ 1) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
this : Fintype.card α - n + n = Fintype.card α
⊢ IsMultiplyPretrans... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | ext g | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Combinatio... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Com... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
t... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | simp only [mem_stabilizer_iff] | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Com... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Com... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | rw [← Subtype.coe_inj] | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Com... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Com... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | change g • s = s ↔ _ | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Com... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Com... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | rw [← Finset.coe_smul_finset, ← Finset.coe_inj] | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this : Nontrivial ↑(Nat.Combination α n)
sn : ↑(Nat.Com... | 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
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | simp only [Finset.coe_nonempty, ← Finset.card_pos, hs] | case inr.intro.h0
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
s... | case inr.intro.h0
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
s... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.h0
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/AlternatingMaximal.lean | alternatingGroup.Nat.Combination.isPreprimitive_of_alt | [750, 1] | [797, 13] | apply lt_trans one_pos h_one_lt | case inr.intro.h0
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat.Combination α n)
this✝ : Nontrivial ↑(Nat.Combination α n)
s... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.h0
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
n : ℕ
h_one_le : 1 ≤ n
hn : n < Fintype.card α
hα : Fintype.card α ≠ 2 * n
hα' : 3 ≤ Fintype.card α
this✝¹ : Nontrivial α
h_one_lt : 1 < n
ht : IsPretransitive ↥(alternatingGroup α) ↑(Nat... |
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