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 | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | have hn : n = 0 := by
rw [← le_zero_iff]
apply Nat.le_of_succ_le_succ
apply Nat.le_of_lt_succ
exact hn | 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... | 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.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 →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | simp only [hn, Set.ncard_eq_one] at hsn | 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... | 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.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 →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | obtain ⟨a, hsa⟩ := hsn | 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... | case h.inl.intro
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 →
I... | Please generate a tactic in lean4 to solve the state.
STATE:
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 →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | rw [hsa] at hs_trans | case h.inl.intro
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 →
I... | case h.inl.intro
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 →
I... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inl.intro
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] | rw [stabilizer.isMultiplyPretransitive G α hG.toIsPretransitive] | case h.inl.intro
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 →
I... | case h.inl.intro
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 →
I... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inl.intro
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] | rw [← isPretransitive_iff_is_one_pretransitive] | case h.inl.intro
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 →
I... | case h.inl.intro
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 →
I... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inl.intro
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] | apply isPretransitive.of_surjective_map
(SubMulAction.OfFixingSubgroupOfSingleton.map_bijective G a).surjective hs_trans | case h.inl.intro
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 →
I... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inl.intro
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] | rw [← le_zero_iff] | 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] | apply Nat.le_of_succ_le_succ | 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 ↥(... | case a
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
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] | apply Nat.le_of_lt_succ | case a
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 a.a
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 →
IsPretran... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
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] | exact hn | case a.a
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 →
IsPretran... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
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 : 1 < s.ncard := by rw [hsn]; exact hn | 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... | 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.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 →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | rw [Set.one_lt_ncard] at this | 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... | 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.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 →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | obtain ⟨a, ha, b, hb, hab⟩ := this | 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... | case h.inr.inl.intro.intro.intro.intro
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.ca... | Please generate a tactic in lean4 to solve the state.
STATE:
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 →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | obtain ⟨g, hga, hgb⟩ := Rudio hG s (Set.toFinite s) hs_nonempty hs_ne_top a b hab | case h.inr.inl.intro.intro.intro.intro
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.ca... | case h.inr.inl.intro.intro.intro.intro.intro.intro
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.inl.intro.intro.intro.intro
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.n... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | let t := s ∩ g • s | case h.inr.inl.intro.intro.intro.intro.intro.intro
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 ... | case h.inr.inl.intro.intro.intro.intro.intro.intro
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.inl.intro.intro.intro.intro.intro.intro
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},
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | have ht_trans : IsPretransitive (fixingSubgroup G t)
(SubMulAction.ofFixingSubgroup G t) :=
isPretransitive_ofFixingSubgroup_inter hs_trans (by
apply Set.ncard_pigeonhole_compl'
rw [smul_set_ncard_eq, hsn, ← two_mul]
exact hn1) | case h.inr.inl.intro.intro.intro.intro.intro.intro
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 ... | case h.inr.inl.intro.intro.intro.intro.intro.intro
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.inl.intro.intro.intro.intro.intro.intro
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},
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | suffices ∃ m, m < n ∧ t.ncard = Nat.succ m by
obtain ⟨m, hmn, htm⟩ := this
apply hrec m hmn hG htm _ ht_trans
apply lt_trans _ hsn'
rw [add_lt_add_iff_left, Nat.succ_lt_succ_iff]
exact hmn | case h.inr.inl.intro.intro.intro.intro.intro.intro
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 ... | case h.inr.inl.intro.intro.intro.intro.intro.intro
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.inl.intro.intro.intro.intro.intro.intro
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},
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | use t.ncard.pred | case h.inr.inl.intro.intro.intro.intro.intro.intro
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 ... | 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.inr.inl.intro.intro.intro.intro.intro.intro
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},
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | apply Set.ncard_ne_zero_of_mem (a := a) | 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] | exact ⟨ha, hga⟩ | 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... | no goals | 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] | rw [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 hn | 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] | apply Set.ncard_pigeonhole_compl' | 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 ↥(... | 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
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 [smul_set_ncard_eq, hsn, ← two_mul] | 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] | exact hn1 | 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... | no goals | 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] | obtain ⟨m, hmn, htm⟩ := this | 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 ↥(... | case intro.intro
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 →
I... | 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] | apply hrec m hmn hG htm _ ht_trans | case intro.intro
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 →
I... | 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:
case intro.intro
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] | apply lt_trans _ 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 [add_lt_add_iff_left, Nat.succ_lt_succ_iff] | 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 hmn | 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 [← Nat.succ_lt_succ_iff, ← hsn, Nat.succ_pred this] | 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] | constructor | 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 ↥(... | case left
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 →
IsPretra... | 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] | apply Set.ncard_lt_ncard _ (Set.toFinite s) | case left
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 →
IsPretra... | 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:
case left
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] | constructor | 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 ↥(... | case left
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 →
IsPretra... | 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] | apply Set.inter_subset_left | case left
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 →
IsPretra... | case right
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 left
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 h | case right
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 right
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 right
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] | apply hgb | case right
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 right
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 right
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] | apply Set.inter_subset_right | case right
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 right.a
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 →
IsPre... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
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] | apply h | case right.a
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 →
IsPre... | case right.a.a
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 right.a
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] | exact hb | case right.a.a
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.a.a
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] | rfl | case right
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
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 : Set.Nontrivial sᶜ := by
rw [← Set.one_lt_ncard_iff_nontrivial]
rw [← Nat.add_lt_add_iff_left, Set.ncard_add_ncard_compl]
rw [Nat.card_eq_fintype_card, add_comm, hsn]
exact hsn' | case h.inr.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 →
IsP... | case h.inr.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 →
IsP... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.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] | obtain ⟨a, ha : a ∈ sᶜ, b, hb : b ∈ sᶜ, hab⟩ := this | case h.inr.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 →
IsP... | case h.inr.inr.intro.intro.intro.intro
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.ca... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.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] | obtain ⟨g, hga, hgb⟩ := Rudio hG sᶜ (Set.toFinite sᶜ)
(Set.nonempty_of_mem ha)
(by intro h
simp only [Set.top_eq_univ, Set.compl_univ_iff] at h
simp only [h, Set.not_nonempty_empty] at hs_nonempty)
a b hab | case h.inr.inr.intro.intro.intro.intro
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.ca... | case h.inr.inr.intro.intro.intro.intro.intro.intro
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.inr.intro.intro.intro.intro
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.n... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | let t := s ∩ g • s | case h.inr.inr.intro.intro.intro.intro.intro.intro
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 ... | case h.inr.inr.intro.intro.intro.intro.intro.intro
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.inr.intro.intro.intro.intro.intro.intro
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},
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | have : a ∉ s ∪ g • s := by
rw [Set.mem_union]
intro h
cases' h with h h
exact ha h
rw [Set.mem_smul_set_iff_inv_smul_mem] at hga h
exact hga h | case h.inr.inr.intro.intro.intro.intro.intro.intro
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 ... | case h.inr.inr.intro.intro.intro.intro.intro.intro
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.inr.intro.intro.intro.intro.intro.intro
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},
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | have ht_trans : IsPretransitive (fixingSubgroup G t)
(SubMulAction.ofFixingSubgroup G t) :=
isPretransitive_ofFixingSubgroup_inter hs_trans
(by intro h; apply this; rw [h]; trivial) | case h.inr.inr.intro.intro.intro.intro.intro.intro
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 ... | case h.inr.inr.intro.intro.intro.intro.intro.intro
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.inr.intro.intro.intro.intro.intro.intro
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},
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | suffices ∃ m : ℕ, m < n ∧ t.ncard = Nat.succ m by
obtain ⟨m, hmn, htm⟩ := this
refine' hrec m hmn hG htm (by
apply lt_trans _ hsn'
rw [add_lt_add_iff_left, Nat.succ_lt_succ_iff]
exact hmn) ht_trans | case h.inr.inr.intro.intro.intro.intro.intro.intro
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 ... | case h.inr.inr.intro.intro.intro.intro.intro.intro
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.inr.inr.intro.intro.intro.intro.intro.intro
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},
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | use t.ncard.pred | case h.inr.inr.intro.intro.intro.intro.intro.intro
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 ... | 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.inr.inr.intro.intro.intro.intro.intro.intro
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},
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | rw [← Set.one_lt_ncard_iff_nontrivial] | 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 [← Nat.add_lt_add_iff_left, Set.ncard_add_ncard_compl] | 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 [Nat.card_eq_fintype_card, add_comm, 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 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 ↥(... | 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] | intro 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 →
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] | simp only [Set.top_eq_univ, Set.compl_univ_iff] at 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 →
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] | simp only [h, Set.not_nonempty_empty] at hs_nonempty | 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.mem_union] | 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] | intro 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 →
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] | cases' h with h 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 →
IsPretransitive ↥(... | case 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 →
IsPretran... | 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 ha h | case 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 →
IsPretran... | case 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 →
IsPretran... | Please generate a tactic in lean4 to solve the state.
STATE:
case 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 →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | is_two_pretransitive_weak_jordan | [298, 1] | [445, 14] | rw [Set.mem_smul_set_iff_inv_smul_mem] at hga h | case 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 →
IsPretran... | case 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 →
IsPretran... | Please generate a tactic in lean4 to solve the state.
STATE:
case 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] | exact hga h | case 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 →
IsPretran... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case 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 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 →
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] | apply this | 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 [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 →
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] | trivial | 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] | obtain ⟨m, hmn, htm⟩ := this | 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 ↥(... | case intro.intro
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 →
I... | 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] | refine' hrec m hmn hG htm (by
apply lt_trans _ hsn'
rw [add_lt_add_iff_left, Nat.succ_lt_succ_iff]
exact hmn) ht_trans | case intro.intro
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 →
I... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
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] | apply lt_trans _ 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 [add_lt_add_iff_left, Nat.succ_lt_succ_iff] | 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 hmn | 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 [← Nat.succ_lt_succ_iff, ← hsn, Nat.succ_pred this] | 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] | constructor | 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 ↥(... | case left
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 →
IsPretra... | 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] | apply Set.ncard_lt_ncard _ (Set.toFinite s) | case left
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 →
IsPretra... | 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:
case left
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] | constructor | 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 ↥(... | case left
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 →
IsPretra... | 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] | apply Set.inter_subset_left | case left
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 →
IsPretra... | case right
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 left
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 h | case right
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 right
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 right
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] | suffices s = g • s by
apply hb
rw [this]
simp only [smul_compl_set, Set.mem_compl_iff, Set.not_not_mem] at hgb
exact hgb | case right
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 right
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 right
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] | apply Set.eq_of_subset_of_ncard_le | case right
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 right.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 →
IsPre... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
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] | exact Set.toFinite (g • s) | case right.ht
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 →
IsPr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.ht
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] | apply hb | 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 [this] | 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] | simp only [smul_compl_set, Set.mem_compl_iff, Set.not_not_mem] at hgb | 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 hgb | 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] | exact subset_trans h (Set.inter_subset_right _ _) | case right.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 →
IsPre... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.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] | rw [smul_set_ncard_eq] | case right.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 →
IsPr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.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] | rfl | case right
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
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] | rw [← Nat.pos_iff_ne_zero] | 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] | apply Nat.lt_of_add_lt_add_right | 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.a
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 →
IsPretran... | 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] | rw [Set.ncard_inter_add_ncard_union, zero_add, smul_set_ncard_eq,
hsn, ← two_mul] | case h.a
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 →
IsPretran... | case h.a
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 →
IsPretran... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
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] | apply lt_of_lt_of_le _ hn2 | case h.a
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 →
IsPretran... | 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:
case h.a
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] | rw [← not_le] | 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] | intro 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 →
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] | apply this | 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] | convert Set.mem_univ a | 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 ↥(... | case h.e'_5
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 →
IsPret... | 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] | apply Set.eq_of_subset_of_ncard_le (Set.subset_univ _) _ Set.finite_univ | case h.e'_5
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 →
IsPret... | 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:
case h.e'_5
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] | simp only [Set.ncard_univ, Nat.card_eq_fintype_card] | 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 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 →
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_preprimitive_weak_jordan | [455, 1] | [603, 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_prim : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
⊢ IsMultiplyPreprim... | 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 →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActio... | 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_prim : IsPreprimitive ↥(fixingSubgroup ... |
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