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/Jordan.lean | isPretransitive_ofFixingSubgroup_inter | [98, 1] | [153, 12] | exact hkax | case h
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPretransitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
a : α
ha : a ∈ (s ∪ g • s)ᶜ
ha' : a ∈ (s ∩ g • s)ᶜ
x : α
hx✝ : x ∈ SubMulAction.ofFixingSubgroup G (s ∩ g • s)
hx : x ∉ g • s
hg'x : g⁻¹ • x ∈ SubMulAct... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPretransitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
a : α
ha : a ∈ (s ∪ g • s)ᶜ
ha' : a ∈ (s ∩ g • s)ᶜ
x : α
hx✝ : x ∈ SubMulAction.ofFixingSub... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq | [156, 1] | [169, 37] | rw [SubMulAction.ofStabilizer_carrier] | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 + ↑(Set.encard (SubMulAction.ofStabilizer G a).carrier) = PartENat.card α | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 + ↑(Set.encard {a}ᶜ) = PartENat.card α | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 + ↑(Set.encard (SubMulAction.ofStabilizer G a).carrier) = PartENat.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq | [156, 1] | [169, 37] | rw [← Nat.cast_one] | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 + ↑(Set.encard {a}ᶜ) = PartENat.card α | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ ↑1 + ↑(Set.encard {a}ᶜ) = PartENat.card α | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 + ↑(Set.encard {a}ᶜ) = PartENat.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq | [156, 1] | [169, 37] | apply PartENat.withTopAddEquiv.injective | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ ↑1 + ↑(Set.encard {a}ᶜ) = PartENat.card α | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv (↑1 + ↑(Set.encard {a}ᶜ)) = PartENat.withTopAddEquiv (PartENat.card α) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ ↑1 + ↑(Set.encard {a}ᶜ) = PartENat.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq | [156, 1] | [169, 37] | rw [map_add] | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv (↑1 + ↑(Set.encard {a}ᶜ)) = PartENat.withTopAddEquiv (PartENat.card α) | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑1 + PartENat.withTopAddEquiv ↑(Set.encard {a}ᶜ) = PartENat.withTopAddEquiv (PartENat.card α) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv (↑1 + ↑(Set.encard {a}ᶜ)) = PartENat.withTopAddEquiv (PartENat.card α)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq | [156, 1] | [169, 37] | convert Set.encard_add_encard_compl {a} | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑1 + PartENat.withTopAddEquiv ↑(Set.encard {a}ᶜ) = PartENat.withTopAddEquiv (PartENat.card α) | case h.e'_2.h.e'_5
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑1 = Set.encard {a}
case h.e'_2.h.e'_6
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑(Set.encard {a}ᶜ) = Set.encard {a}ᶜ
case h.e'_3
α : Type u_1
G ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑1 + PartENat.withTopAddEquiv ↑(Set.encard {a}ᶜ) = PartENat.withTopAddEquiv (PartENat.card α)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq | [156, 1] | [169, 37] | rw [Set.encard_singleton] | case h.e'_2.h.e'_5
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑1 = Set.encard {a} | case h.e'_2.h.e'_5
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑1 = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑1 = Set.encard {a}
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq | [156, 1] | [169, 37] | apply PartENat.toWithTop_natCast' | case h.e'_2.h.e'_5
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑1 = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑1 = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq | [156, 1] | [169, 37] | rw [← AddEquiv.eq_symm_apply] | case h.e'_2.h.e'_6
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑(Set.encard {a}ᶜ) = Set.encard {a}ᶜ | case h.e'_2.h.e'_6
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ ↑(Set.encard {a}ᶜ) = (AddEquiv.symm PartENat.withTopAddEquiv) (Set.encard {a}ᶜ) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv ↑(Set.encard {a}ᶜ) = Set.encard {a}ᶜ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq | [156, 1] | [169, 37] | rfl | case h.e'_2.h.e'_6
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ ↑(Set.encard {a}ᶜ) = (AddEquiv.symm PartENat.withTopAddEquiv) (Set.encard {a}ᶜ) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ ↑(Set.encard {a}ᶜ) = (AddEquiv.symm PartENat.withTopAddEquiv) (Set.encard {a}ᶜ)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq | [156, 1] | [169, 37] | convert (Set.encard_univ α).symm | case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv (PartENat.card α) = Set.encard Set.univ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ PartENat.withTopAddEquiv (PartENat.card α) = Set.encard Set.univ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq' | [171, 1] | [177, 35] | rw [SubMulAction.ofStabilizer_carrier] | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 + Set.encard (SubMulAction.ofStabilizer G a).carrier = Set.encard Set.univ | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 + Set.encard {a}ᶜ = Set.encard Set.univ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 + Set.encard (SubMulAction.ofStabilizer G a).carrier = Set.encard Set.univ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq' | [171, 1] | [177, 35] | convert Set.encard_add_encard_compl _ | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 + Set.encard {a}ᶜ = Set.encard Set.univ | case h.e'_2.h.e'_5
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 = Set.encard {a} | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 + Set.encard {a}ᶜ = Set.encard Set.univ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | SubMulAction.add_encard_ofStabilizer_eq' | [171, 1] | [177, 35] | simp only [Set.encard_singleton] | case h.e'_2.h.e'_5
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 = Set.encard {a} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
a : α
⊢ 1 = Set.encard {a}
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | have hG : IsPretransitive G α := by
rw [isPretransitive_iff_is_one_pretransitive]
apply isMultiplyPretransitive_of_higher
exact hG'
norm_num
rw [Nat.cast_two]
exact le_of_lt hsn' | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤ | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | have : Nontrivial α := by
rw [← PartENat.one_lt_card_iff_nontrivial]
refine' lt_trans _ hsn'
rw [← Nat.cast_two, ← Nat.cast_one, PartENat.coe_lt_coe]
norm_num | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤ | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | have hGa : (stabilizer G a).IsMaximal := by
rw [maximal_stabilizer_iff_preprimitive G a]
exact hG'.isPreprimitive_of_two | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤ | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : Subgroup.IsMaximal (stabilizer G a)
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [Subgroup.isMaximal_def] at hGa | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : Subgroup.IsMaximal (stabilizer G a)
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤ | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : Subgroup.IsMaximal (stabilizer G a)
⊢ Subgroup.normalClosure ↑(stabilizer ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | apply hGa.right | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤ | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ stabilizer G a < Subgroup.normalClosure ↑(stabilizer G a) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ Subgroup.normalClosure ↑(stabilizer G a) = ⊤
T... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | constructor | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ stabilizer G a < Subgroup.normalClosure ↑(stabilizer G a) | case a.left
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ ↑(stabilizer G a) ⊆ ↑(Subgroup.normalClosure ↑(stabilizer G a))
case a.right
α : Type u_1
G : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ stabilizer G a < Subgroup.normalClosure... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [isPretransitive_iff_is_one_pretransitive] | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ IsPretransitive G α | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ IsMultiplyPretransitive G α 1 | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ IsPretransitive G α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | apply isMultiplyPretransitive_of_higher | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ IsMultiplyPretransitive G α 1 | case hn
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ IsMultiplyPretransitive G α ?n
case hmn
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ IsMultiplyPretransitive G α 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | exact hG' | case hn
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ IsMultiplyPretransitive G α ?n
case hmn
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢... | case hmn
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ 1 ≤ 2
case hα
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ ↑2 ≤ PartENat.card α | Please generate a tactic in lean4 to solve the state.
STATE:
case hn
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ IsMultiplyPretransitive G α ?n
case hmn
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | norm_num | case hmn
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ 1 ≤ 2
case hα
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ ↑2 ≤ PartENat.card α | case hα
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ ↑2 ≤ PartENat.card α | Please generate a tactic in lean4 to solve the state.
STATE:
case hmn
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ 1 ≤ 2
case hα
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : I... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [Nat.cast_two] | case hα
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ ↑2 ≤ PartENat.card α | case hα
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ 2 ≤ PartENat.card α | Please generate a tactic in lean4 to solve the state.
STATE:
case hα
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ ↑2 ≤ PartENat.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | exact le_of_lt hsn' | case hα
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ 2 ≤ PartENat.card α | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hα
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
⊢ 2 ≤ PartENat.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [← PartENat.one_lt_card_iff_nontrivial] | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ Nontrivial α | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ 1 < PartENat.card α | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ Nontrivial α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | refine' lt_trans _ hsn' | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ 1 < PartENat.card α | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ 1 < 2 | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ 1 < PartENat.card α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | norm_num | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ 1 < 2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
⊢ 1 < 2
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [maximal_stabilizer_iff_preprimitive G a] | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
⊢ Subgroup.IsMaximal (stabilizer G a) | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
⊢ IsPreprimitive G α | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
⊢ Subgroup.IsMaximal (stabilizer G a)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | exact hG'.isPreprimitive_of_two | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
⊢ IsPreprimitive G α | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
⊢ IsPreprimitive G α
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | apply Subgroup.le_normalClosure | case a.left
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ ↑(stabilizer G a) ⊆ ↑(Subgroup.normalClosure ↑(stabilizer G a)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.left
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ ↑(stabilizer G a) ⊆ ↑(Subgroup.nor... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | intro hyp | case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ ¬↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a) | case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
⊢ ¬↑(Subgroup.normalClosure ↑(stabi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | have : Nontrivial (SubMulAction.ofStabilizer G a) := by
apply Set.Nontrivial.coe_sort
rw [← Set.one_lt_encard_iff_nontrivial]
rw [← not_le, ← Nat.cast_one, ← WithTop.add_one_le_coe_succ_iff, not_le]
rw [← PartENat.withTopEquiv_lt, ← Set.encard_univ] at hsn'
convert hsn'
simp only [SetLike.coe_sort_coe, Nat.... | case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ False | case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
this : Nontrivial ↥(SubMu... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(st... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [nontrivial_iff] at this | case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
this : Nontrivial ↥(SubMu... | case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
this : ∃ x y, x ≠ y
⊢ Fal... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | obtain ⟨b, c, hbc⟩ := this | case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
this : ∃ x y, x ≠ y
⊢ Fal... | case a.right.intro.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c : ↥(SubMul... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | have : IsPretransitive (stabilizer G a) (SubMulAction.ofStabilizer G a) := by
rw [isPretransitive_iff_is_one_pretransitive]
exact (stabilizer.isMultiplyPretransitive G α hG).mp hG' | case a.right.intro.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c : ↥(SubMul... | case a.right.intro.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c : ↥(SubMu... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normal... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | obtain ⟨⟨g, hg⟩, hgbc⟩ := exists_smul_eq (stabilizer G a) b c | case a.right.intro.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c : ↥(SubMu... | case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.norma... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | apply hbc | case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c ... | case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [← SetLike.coe_eq_coe] | case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c ... | case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [← SetLike.coe_eq_coe] at hgbc | case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c ... | case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | obtain ⟨h, hinvab⟩ := exists_smul_eq G (b : α) a | case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c ... | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [eq_comm, ← inv_smul_eq_iff] at hinvab | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [← hgbc, SetLike.val_smul, ← hinvab] | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [inv_smul_eq_iff, eq_comm] | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | change h • g • h⁻¹ • a = a | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | simp only [smul_smul, ← mul_assoc] | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [← mem_stabilizer_iff] | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | apply hyp | case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a... | case a.right.intro.intro.intro.mk.intro.a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk.intro
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | apply Subgroup.normalClosure_normal.conj_mem | case a.right.intro.intro.intro.mk.intro.a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G... | case a.right.intro.intro.intro.mk.intro.a.a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk.intro.a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp :... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | apply Subgroup.le_normalClosure | case a.right.intro.intro.intro.mk.intro.a.a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer... | case a.right.intro.intro.intro.mk.intro.a.a.a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabiliz... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk.intro.a.a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | exact hg | case a.right.intro.intro.intro.mk.intro.a.a.a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabiliz... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.right.intro.intro.intro.mk.intro.a.a.a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this✝ : Nontrivial α
hGa : IsCoatom (stabilizer G a)
h... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | apply Set.Nontrivial.coe_sort | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ Nontrivial ↥(SubMulAction.ofStabilize... | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ Set.Nontrivial ↑(SubMulAction.... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [← Set.one_lt_encard_iff_nontrivial] | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ Set.Nontrivial ↑(SubMulAction.... | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ 1 < Set.encard ↑(SubMulAction.... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabiliz... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [← not_le, ← Nat.cast_one, ← WithTop.add_one_le_coe_succ_iff, not_le] | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ 1 < Set.encard ↑(SubMulAction.... | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ ↑(Nat.succ 1) < Set.encard ↑(S... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabiliz... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [← PartENat.withTopEquiv_lt, ← Set.encard_univ] at hsn' | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ ↑(Nat.succ 1) < Set.encard ↑(S... | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ ↑(Na... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabiliz... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | convert hsn' | case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢ ↑(Na... | case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgrou... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | simp only [SetLike.coe_sort_coe, Nat.cast_succ, Nat.cast_one] | case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [← Nat.cast_two] | case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [← PartENat.withTopEquiv.symm_apply_eq] | case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rfl | case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | case h.e'_4
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [add_comm] | case h.e'_4
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | case h.e'_4
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | exact SubMulAction.add_encard_ofStabilizer_eq' a | case h.e'_4
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
⊢... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : PartENat.withTopEquiv 2 < Set.encard Set.univ
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Su... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | rw [isPretransitive_iff_is_one_pretransitive] | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c : ↥(SubMulAction.ofStabilizer G a)
... | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c : ↥(SubMulAction.ofStabilizer G a)
... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | normalClosure_of_stabilizer_eq_top | [186, 1] | [242, 13] | exact (stabilizer.isMultiplyPretransitive G α hG).mp hG' | α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)) ⊆ ↑(stabilizer G a)
b c : ↥(SubMulAction.ofStabilizer G a)
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝¹ : Group G
inst✝ : MulAction G α
hsn' : 2 < PartENat.card α
hG' : IsMultiplyPretransitive G α 2
a : α
hG : IsPretransitive G α
this : Nontrivial α
hGa : IsCoatom (stabilizer G a)
hyp : ↑(Subgroup.normalClosure ↑(stabilizer G a)... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | have hts : s ∩ g • s ≤ s := Set.inter_subset_left s _ | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
⊢ IsPreprimitive ↥(fixingSubgroup G (s ∩ g • s)) ↥(SubMulAct... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
⊢ IsPreprimitive ↥(fixingSubgroup G (s ∩... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | have this : IsPretransitive (fixingSubgroup G (s ∩ g • s))
(SubMulAction.ofFixingSubgroup G (s ∩ g • s)) :=
isPretransitive_ofFixingSubgroup_inter hs.toIsPretransitive ha | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
⊢ IsPreprimitive ↥(fixingSubgroup G (s ∩... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | apply isPreprimitive_of_large_image (f := SubMulAction.ofFixingSubgroup.mapOfInclusion G hts) hs | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [← Set.image_univ,
Set.ncard_image_of_injective _ (SubMulAction.ofFixingSubgroup.mapOfInclusion_injective G _)] | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | have this : Set.ncard (s ∩ g • s)ᶜ < 2 * Set.ncard (sᶜ) := by
rw [Set.compl_inter, ← Nat.add_lt_add_iff_right, Set.ncard_union_add_ncard_inter]
rw [← Set.compl_union, two_mul, add_assoc]
simp only [add_lt_add_iff_left]
rw [← add_lt_add_iff_left, Set.ncard_add_ncard_compl]
rw [MulAction.smul_set_ncard_eq, ← a... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransitive ↥(fixingSubgroup... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | convert this | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransitive ↥(fixingSubgroup... | case h.e'_3
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransitive ↥(fi... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [Set.compl_inter, ← Nat.add_lt_add_iff_right, Set.ncard_union_add_ncard_inter] | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [← Set.compl_union, two_mul, add_assoc] | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | simp only [add_lt_add_iff_left] | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [← add_lt_add_iff_left, Set.ncard_add_ncard_compl] | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [MulAction.smul_set_ncard_eq, ← add_assoc, Set.ncard_add_ncard_compl] | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | simp only [lt_add_iff_pos_right] | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [Set.ncard_pos] | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [Set.nonempty_compl] | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | exact ha | α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this : IsPretransitive ↥(fixingSubgroup ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [← Nat.card_eq_fintype_card, ← Set.Nat.card_coe_set_eq] | case h.e'_3
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransitive ↥(fi... | case h.e'_3
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransitive ↥(fi... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rfl | case h.e'_3
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransitive ↥(fi... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [← SubMulAction.ofFixingSubgroup_carrier G] | case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransiti... | case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransiti... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [← Set.ncard_image_of_injective (Set.univ) (SubMulAction.ofFixingSubgroup G s).inclusion_injective] | case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransiti... | case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransiti... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | rw [← SubMulAction.image_inclusion] | case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransiti... | case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransiti... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | congr | case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretransiti... | case h.e'_4.h.e'_6.e_s
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretran... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.h.e'_6
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter | [248, 1] | [282, 31] | simp only [Set.image_univ] | case h.e'_4.h.e'_6.e_s
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g : G
ha : s ∪ g • s ≠ ⊤
hts : s ∩ g • s ≤ s
this✝ : IsPretran... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.h.e'_6.e_s
α : Type u_2
G✝ : Type ?u.115687
inst✝⁴ : Group G✝
inst✝³ : MulAction G✝ α
inst✝² : Fintype α
G : Type u_1
inst✝¹ : Group G
inst✝ : MulAction G α
s : Set α
hs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | revert α G | α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hG : IsPreprimitive G α
s : Set α
n : ℕ
hsn : Set.ncard s = Nat.succ n
hsn' : 1 + Nat.succ n < Fintype.card α
hs_trans : IsPretransitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
⊢ IsMultiplyPretr... | n : ℕ
⊢ ∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPretransitive ↥(fixingSubgroup G s) ↥(SubMulActi... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
inst✝¹ : Fintype α
inst✝ : DecidableEq α
hG : IsPreprimitive G α
s : Set α
n : ℕ
hsn : Set.ncard s = Nat.succ n
hsn' : 1 + Nat.succ n < Fintype.card α
hs_trans : IsPretransitive ↥(fixingSubgrou... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | induction' n using Nat.strong_induction_on with n hrec | n : ℕ
⊢ ∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPretransitive ↥(fixingSubgroup G s) ↥(SubMulActi... | case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransi... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
⊢ ∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | intro α G _ _ _ _ hG s hsn hsn' hs_trans | case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransi... | case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransi... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | have hs_ne_top : s ≠ ⊤ := by
intro hs
rw [hs, Set.top_eq_univ, Set.ncard_univ] at hsn
rw [← hsn, Nat.card_eq_fintype_card, add_lt_iff_neg_right] at hsn'
contradiction | case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransi... | case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransi... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | have hs_nonempty : s.Nonempty := by
rw [← Set.ncard_pos, hsn]
exact Nat.succ_pos n | case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransi... | case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransi... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | cases' Nat.lt_or_ge n.succ 2 with hn hn | case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransi... | case h.inl
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretr... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | cases' Nat.lt_or_ge (2 * n.succ) (Fintype.card α) with hn1 hn2 | case h.inr
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretr... | case h.inr.inl
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsP... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | intro hs | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransitive ↥(... | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransitive ↥(... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + N... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | rw [hs, Set.top_eq_univ, Set.ncard_univ] at hsn | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransitive ↥(... | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransitive ↥(... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + N... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | rw [← hsn, Nat.card_eq_fintype_card, add_lt_iff_neg_right] at hsn' | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransitive ↥(... | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransitive ↥(... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + N... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | contradiction | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransitive ↥(... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + N... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | rw [← Set.ncard_pos, hsn] | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransitive ↥(... | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransitive ↥(... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + N... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | exact Nat.succ_pos n | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + Nat.succ m < Fintype.card α →
IsPretransitive ↥(... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α]
[inst_3 : DecidableEq α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ m →
1 + N... |
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