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_preprimitive_weak_jordan | [455, 1] | [603, 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 →
IsPrepr... | 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_preprimitive_weak_jordan | [455, 1] | [603, 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 →
IsPreprimit... | 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 →
IsPreprimit... | 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_preprimitive_weak_jordan | [455, 1] | [603, 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 →
IsPreprimit... | 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 →
IsPreprim... | 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_preprimitive_weak_jordan | [455, 1] | [603, 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 →
IsPreprim... | 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 →
IsPreprim... | 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_preprimitive_weak_jordan | [455, 1] | [603, 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 →
IsPreprim... | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_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 →
IsPreprimitive ↥(f... | 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_preprimitive_weak_jordan | [455, 1] | [603, 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 →
IsPreprimitive ↥(f... | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_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 →
IsPreprimitive ↥(f... | 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] | 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 →
IsPreprimitive ↥(f... | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_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 →
IsPreprimitive ↥(f... | 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] | 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 →
IsPreprimitive ↥(f... | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_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 →
IsPreprimitive ↥(f... | 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] | 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 →
IsPreprimitive ↥(f... | 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 →
IsPrep... | 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] | 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 →
IsPrep... | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_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 →
IsPreprimitive ↥(f... | 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_preprimitive_weak_jordan | [455, 1] | [603, 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 →
IsPreprimitive ↥(f... | n : ℕ
hrec :
∀ m < n,
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_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 →
IsPreprimitive ↥(f... | 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] | 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 →
IsPreprimitive ↥(f... | 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 | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | revert α G | α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype 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
hprim : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
⊢ IsMultiplyPreprimitive G α (1 + Nat.succ n... | n : ℕ
⊢ ∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s) →
... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype 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
hprim : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | induction' n with n hrec | n : ℕ
⊢ ∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s) →
... | case zero
⊢ ∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ Nat.zero →
1 + Nat.succ Nat.zero < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixing... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
⊢ ∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(f... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | intro α G _ _ _ hG s hsn hα hGs | case succ
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSu... | case succ
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSu... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
I... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [← Set.ncard_pos, hsn] | case succ
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSu... | case succ
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSu... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
I... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply Nat.succ_pos | case succ
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSu... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
I... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | intro α G _ _ _ hG s hsn _ hGs | case zero
⊢ ∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ Nat.zero →
1 + Nat.succ Nat.zero < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixing... | case zero
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn : Set.ncard s = Nat.succ Nat.zero
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
⊢ IsMultiplyPreprimitive G ... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
⊢ ∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ Nat.zero →
1 + Nat.succ Nat.zero < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | haveI : IsPretransitive G α := hG.toIsPretransitive | case zero
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn : Set.ncard s = Nat.succ Nat.zero
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
⊢ IsMultiplyPreprimitive G ... | case zero
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn : Set.ncard s = Nat.succ Nat.zero
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
this : IsPretransitive G α
... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn : Set.ncard s = Nat.succ Nat.zero
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(S... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | simp only [Set.ncard_eq_one] at hsn | case zero
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn : Set.ncard s = Nat.succ Nat.zero
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
this : IsPretransitive G α
... | case zero
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
this : IsPretransitive G α
hsn : ∃ a, s = {a}
⊢ IsMultiplyPreprim... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn : Set.ncard s = Nat.succ Nat.zero
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(S... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | obtain ⟨a, hsa⟩ := hsn | case zero
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
this : IsPretransitive G α
hsn : ∃ a, s = {a}
⊢ IsMultiplyPreprim... | case zero.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
this : IsPretransitive G α
a : α
hsa : s = {a}
⊢ IsMultiply... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
this... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [hsa] at hGs | case zero.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s)
this : IsPretransitive G α
a : α
hsa : s = {a}
⊢ IsMultiply... | case zero.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
⊢ IsMult... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
hGs : IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | constructor | case zero.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
⊢ IsMult... | case zero.intro.left
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
⊢ I... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [stabilizer.isMultiplyPretransitive] | case zero.intro.left
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
⊢ I... | case zero.intro.left
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
⊢ I... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.left
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [← isPretransitive_iff_is_one_pretransitive] | case zero.intro.left
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
⊢ I... | case zero.intro.left
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
⊢ I... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.left
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply isPretransitive.of_surjective_map
(SubMulAction.OfFixingSubgroupOfSingleton.map_bijective G a).surjective
hGs.toIsPretransitive | case zero.intro.left
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
⊢ I... | case zero.intro.left.hα'
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.left
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | exact hG.toIsPretransitive | case zero.intro.left.hα'
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.left.hα'
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgrou... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | intro t h | case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
⊢ ... | case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
t ... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | simp only [Nat.zero_eq, Nat.cast_add, Nat.cast_one] at h | case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
t ... | case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
t ... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [← Nat.cast_one, WithTop.add_eq_add_iff, Nat.cast_one] at h | case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
t ... | case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
t ... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | obtain ⟨b, htb⟩ := Set.encard_eq_one.mp h | case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
t ... | case zero.intro.right.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = ... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.right
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | obtain ⟨g, hg⟩ := exists_smul_eq G a b | case zero.intro.right.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = ... | case zero.intro.right.intro.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa ... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.right.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubg... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | have hst : g • ({a} : Set α) = ({b} : Set α) := by
change (fun x => g • x) '' {a} = {b}
rw [Set.image_singleton, hg] | case zero.intro.right.intro.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa ... | case zero.intro.right.intro.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa ... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.right.intro.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [htb] | case zero.intro.right.intro.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa ... | case zero.intro.right.intro.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa ... | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.right.intro.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | refine' isPreprimitive_of_surjective_map
(SubMulAction.conjMap_ofFixingSubgroup_bijective G hst).surjective hGs | case zero.intro.right.intro.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case zero.intro.right.intro.intro
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | change (fun x => g • x) '' {a} = {b} | α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
t : Set α
h : Set.encard... | α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
t : Set α
h : Set.encard... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.o... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [Set.image_singleton, hg] | α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.ofFixingSubgroup G {a})
hsa : s = {a}
t : Set α
h : Set.encard... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
hG : IsPreprimitive G α
s : Set α
hsn'✝ : 1 + Nat.succ Nat.zero < Fintype.card α
this : IsPretransitive G α
a : α
hGs : IsPreprimitive ↥(fixingSubgroup G {a}) ↥(SubMulAction.o... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | obtain ⟨a, t, _, hst⟩ := this | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | have ha' : a ∉ Subtype.val '' t := by
intro h; rw [Set.mem_image] at h ; obtain ⟨x, hx⟩ := h
apply x.prop; rw [hx.right]; exact Set.mem_singleton a | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | have ht_prim : IsPreprimitive (stabilizer G a) (SubMulAction.ofStabilizer G a) := by
rw [isPreprimitive_iff_is_one_preprimitive]
rw [← stabilizer.isMultiplyPreprimitive G α (Nat.le_refl 1) hG.toIsPretransitive]
apply is_two_preprimitive_weak_jordan hG hsn hα hGs | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | have hGs' : IsPreprimitive (fixingSubgroup (stabilizer G a) t)
(SubMulAction.ofFixingSubgroup (stabilizer G a) t) := by
apply isPreprimitive_of_surjective_map
(SubMulAction.equivariantMap_ofFixingSubgroup_to_ofStabilizer_bijective G a t).surjective
apply isPreprimitive_of_surjective_map
(SubMulAction.OfF... | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [← Nat.succ_eq_one_add] | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [stabilizer.isMultiplyPreprimitive G α _ hG.toIsPretransitive] | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | intro h | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [Set.mem_image] at h | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | obtain ⟨x, hx⟩ := h | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingS... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply x.prop | case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingS... | case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingS... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [hx.right] | case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingS... | case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingS... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | exact Set.mem_singleton a | case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingS... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [isPreprimitive_iff_is_one_preprimitive] | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [← stabilizer.isMultiplyPreprimitive G α (Nat.le_refl 1) hG.toIsPretransitive] | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply is_two_preprimitive_weak_jordan hG hsn hα hGs | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply isPreprimitive_of_surjective_map
(SubMulAction.equivariantMap_ofFixingSubgroup_to_ofStabilizer_bijective G a t).surjective | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply isPreprimitive_of_surjective_map
(SubMulAction.OfFixingSubgroupOfEq.map_bijective G hst).surjective | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | exact hGs | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [this] | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | refine' hrec ht_prim _ _ hGs' | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | case refine'_1
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [← Set.ncard_image_of_injective t Subtype.val_injective] | case refine'_1
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | case refine'_1
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply Nat.add_right_cancel | case refine'_1
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | case refine'_1.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [← Set.ncard_insert_of_not_mem ha', ← hst, hsn] | case refine'_1.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | change _ < Fintype.card (SubMulAction.ofStabilizer G a).carrier | case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [← Nat.card_eq_fintype_card, Set.Nat.card_coe_set_eq] | case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [SubMulAction.ofStabilizer_carrier] | case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [← Nat.succ_eq_one_add] | case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply Nat.lt_of_add_lt_add_left | case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFix... | case refine'_2.a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [Set.ncard_add_ncard_compl] | case refine'_2.a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | case refine'_2.a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2.a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | simp only [Set.ncard_singleton, Nat.card_eq_fintype_card] | case refine'_2.a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | case refine'_2.a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2.a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | exact hα | case refine'_2.a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2.a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | exact Nat.succ_eq_one_add (n + 1) | case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulActi... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply Nat.succ_le_succ | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | case a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply Nat.zero_le | case a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | obtain ⟨a, ha⟩ := this | n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s... | case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingS... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimit... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | use a | case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingS... | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | use Subtype.val ⁻¹' s | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply And.intro ha | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [Set.image_preimage_eq_inter_range] | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [Set.insert_eq] | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | simp only [Subtype.range_coe_subtype, Set.singleton_union, Set.mem_inter_iff, Set.mem_setOf_eq] | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | simp_rw [SubMulAction.mem_ofStabilizer_iff] | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | simp only [Ne.def] | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | ext x | case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgr... | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [Set.mem_insert_iff] | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
Is... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | simp | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
Is... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [or_and_left] | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
Is... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | simp_rw [or_not] | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
Is... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [and_true_iff] | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
Is... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | constructor | case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSub... | case h.h.mp
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixing... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
Is... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | intro hx | case h.h.mp
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixing... | case h.h.mp
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixing... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mp
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | apply Or.intro_right _ hx | case h.h.mp
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixing... | case h.h.mpr
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixin... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mp
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | intro hx | case h.h.mpr
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixin... | case h.h.mpr
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixin... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mpr
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | cases' hx with hx hx | case h.h.mpr
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixin... | case h.h.mpr.inl
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mpr
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | rw [hx] | case h.h.mpr.inl
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | case h.h.mpr.inl
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mpr.inl
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | exact ha | case h.h.mpr.inl
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | case h.h.mpr.inr
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mpr.inl
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | isMultiplyPreprimitive_jordan | [640, 1] | [740, 21] | exact hx | case h.h.mpr.inr
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
IsPreprimitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofF... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mpr.inr
n : ℕ
hrec :
∀ {α : Type u_2} {G : Type u_1} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : Fintype α],
IsPreprimitive G α →
∀ {s : Set α},
Set.ncard s = Nat.succ n →
1 + Nat.succ n < Fintype.card α →
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | eq_s2_of_nontrivial | [751, 1] | [763, 11] | classical
apply Subgroup.eq_top_of_card_eq
apply le_antisymm
apply Fintype.card_subtype_le
rw [Fintype.card_equiv (Equiv.cast rfl)]
refine' le_trans _ _
exact (2 : ℕ).factorial
exact Nat.factorial_le hα
rw [Nat.factorial_two]
rw [← Fintype.one_lt_card_iff_nontrivial] at hG
exact hG | α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ G = ⊤ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ G = ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | eq_s2_of_nontrivial | [751, 1] | [763, 11] | apply Subgroup.eq_top_of_card_eq | α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ G = ⊤ | case h
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card ↥G = Fintype.card (Equiv.Perm α) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ G = ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | eq_s2_of_nontrivial | [751, 1] | [763, 11] | apply le_antisymm | case h
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card ↥G = Fintype.card (Equiv.Perm α) | case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card ↥G ≤ Fintype.card (Equiv.Perm α)
case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card (Equiv.Perm α) ≤ Fintype.card ↥G | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card ↥G = Fintype.card (Equiv.Perm α)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | eq_s2_of_nontrivial | [751, 1] | [763, 11] | apply Fintype.card_subtype_le | case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card ↥G ≤ Fintype.card (Equiv.Perm α)
case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card (Equiv.Perm α) ≤ Fintype.card ↥G | case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card (Equiv.Perm α) ≤ Fintype.card ↥G | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card ↥G ≤ Fintype.card (Equiv.Perm α)
case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : No... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | eq_s2_of_nontrivial | [751, 1] | [763, 11] | rw [Fintype.card_equiv (Equiv.cast rfl)] | case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card (Equiv.Perm α) ≤ Fintype.card ↥G | case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Nat.factorial (Fintype.card α) ≤ Fintype.card ↥G | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Fintype.card (Equiv.Perm α) ≤ Fintype.card ↥G
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Jordan.lean | eq_s2_of_nontrivial | [751, 1] | [763, 11] | refine' le_trans _ _ | case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Nat.factorial (Fintype.card α) ≤ Fintype.card ↥G | case h.a.refine'_1
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ ℕ
case h.a.refine'_2
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Nat.factorial (Fintype.card α) ≤ ?h.a.refine'_1
case h.a.refine'_3
α :... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
α : Type u_1
inst✝ : Fintype α
G : Subgroup (Equiv.Perm α)
hα : Fintype.card α ≤ 2
hG : Nontrivial ↥G
⊢ Nat.factorial (Fintype.card α) ≤ Fintype.card ↥G
TACTIC:
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.