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/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | assumption | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | rw [Nat.succ_le_iff, Set.ncard_pos, Set.nonempty_iff_ne_empty] | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | intro h | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | apply ne_top_of_lt hG | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | rw [h, stabilizer_empty_eq_top] | case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_5.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | apply le_antisymm | case h.e'_2.h.e'_6
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ... | case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ st... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | assumption | case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | rw [Nat.succ_le_iff, Set.ncard_pos, Set.nonempty_iff_ne_empty] | case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | intro h | case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | apply ne_top_of_lt hG | case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | rw [← stabilizer_compl, h, stabilizer_empty_eq_top] | case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_6.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | rw [Fintype.card_perm, ← Nat.card_eq_fintype_card, hα] | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤ 1
hα : Nat.card ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤ 1
hα : Nat.card ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | simp | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤ 1
hα : Nat.card ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | exfalso | case inr.inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤... | case inr.inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stab... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | exact ne_bot_of_gt hG h | case inr.inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stab... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | rw [h] | case inr.inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤... | case inr.inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stab... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | rw [← stabilizer_univ_eq_top (Equiv.Perm α) α] | case inr.inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤... | case inr.inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stab... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | apply this | case inr.inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ ≤... | case inr.inr.inr.x
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr.inr
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stab... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | rw [Set.ncard_univ, hα] | case inr.inr.inr.x
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ... | case inr.inr.inr.x
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr.inr.x
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ st... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.has_swap_of_lt_stabilizer | [227, 1] | [274, 13] | norm_num | case inr.inr.inr.x
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ stabilizer (Perm α) t
h1' : Set.ncard s ≤ 1
h1c' : Set.ncard sᶜ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr.inr.x
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.29759
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
this : ∀ (t : Set α), 1 < Set.ncard t → ∃ g, IsSwap g ∧ g ∈ st... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.Subtype.image_preimage_of_val | [277, 1] | [282, 83] | apply Set.Subset.antisymm (Set.image_preimage_subset Subtype.val B) | α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
⊢ Subtype.val '' (Subtype.val ⁻¹' B) = B | α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
⊢ B ⊆ Subtype.val '' (Subtype.val ⁻¹' B) | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
⊢ Subtype.val '' (Subtype.val ⁻¹' B) = B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.Subtype.image_preimage_of_val | [277, 1] | [282, 83] | intro x hx | α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
⊢ B ⊆ Subtype.val '' (Subtype.val ⁻¹' B) | α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
x : α
hx : x ∈ B
⊢ x ∈ Subtype.val '' (Subtype.val ⁻¹' B) | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
⊢ B ⊆ Subtype.val '' (Subtype.val ⁻¹' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.Subtype.image_preimage_of_val | [277, 1] | [282, 83] | use ⟨x, h hx⟩ | α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
x : α
hx : x ∈ B
⊢ x ∈ Subtype.val '' (Subtype.val ⁻¹' B) | case h
α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
x : α
hx : x ∈ B
⊢ { val := x, property := ⋯ } ∈ Subtype.val ⁻¹' B ∧ ↑{ val := x, property := ⋯ } = x | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
x : α
hx : x ∈ B
⊢ x ∈ Subtype.val '' (Subtype.val ⁻¹' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.Subtype.image_preimage_of_val | [277, 1] | [282, 83] | simp only [hx, Set.mem_preimage, Subtype.coe_mk, eq_self_iff_true, and_self_iff] | case h
α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
x : α
hx : x ∈ B
⊢ { val := x, property := ⋯ } ∈ Subtype.val ⁻¹' B ∧ ↑{ val := x, property := ⋯ } = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α✝ : Type ?u.39088
inst✝³ : DecidableEq α✝
G : Type ?u.39100
inst✝² : Group G
inst✝¹ : MulAction G α✝
inst✝ : Fintype α✝
α : Type u_1
s B : Set α
h : B ⊆ s
x : α
hx : x ∈ B
⊢ { val := x, property := ⋯ } ∈ Subtype.val ⁻¹' B ∧ ↑{ val := x, property := ⋯ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | by_cases hBne : Set.Nonempty B | α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
⊢ IsTrivialBlock B ∨ 2 * Set.ncard B ≤ Nat.card α | case pos
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
⊢ IsTrivialBlock B ∨ 2 * Set.ncard B ≤ Nat.card α
case neg
α : T... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
⊢ IsTrivialBlock B ∨ 2 * Set.ncard ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | obtain ⟨m, hm⟩ := ncard_of_block_divides hB hBne | case pos
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
⊢ IsTrivialBlock B ∨ 2 * Set.ncard B ≤ Nat.card α | case pos.intro
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * m
⊢ IsTrivialBlock B ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
⊢ Is... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | match m with
| 0 =>
left; left
simp only [mul_zero, Finite.card_eq_zero_iff] at hm
exact Set.subsingleton_of_subsingleton
| 1 =>
left; right
simp only [mul_one] at hm
rw [Set.eq_top_iff_ncard, ← hm, Nat.card_eq_fintype_card]
| m + 2 =>
right
rw [hm, mul_comm, add_comm, mul_add]
apply Nat.le_add_right | case pos.intro
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * m
⊢ IsTrivialBlock B ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | left | α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * 0
⊢ IsTrivialBlock B ∨ 2 * Set.ncard... | case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * 0
⊢ IsTrivialBlock B | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Na... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | left | case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * 0
⊢ IsTrivialBlock B | case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * 0
⊢ Set.Subsingleton B | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | simp only [mul_zero, Finite.card_eq_zero_iff] at hm | case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * 0
⊢ Set.Subsingleton B | case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : IsEmpty α
⊢ Set.Subsingleton B | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | exact Set.subsingleton_of_subsingleton | case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : IsEmpty α
⊢ Set.Subsingleton B | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | left | α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * 1
⊢ IsTrivialBlock B ∨ 2 * Set.ncard... | case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * 1
⊢ IsTrivialBlock B | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Na... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | right | case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * 1
⊢ IsTrivialBlock B | case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * 1
⊢ B = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | simp only [mul_one] at hm | case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B * 1
⊢ B = ⊤ | case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B
⊢ B = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | rw [Set.eq_top_iff_ncard, ← hm, Nat.card_eq_fintype_card] | case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ℕ
hm : Nat.card α = Set.ncard B
⊢ B = ⊤ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m : ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | right | α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m✝ m : ℕ
hm : Nat.card α = Set.ncard B * (m + 2)
⊢ IsTrivialBlock B ∨ 2 * ... | case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m✝ m : ℕ
hm : Nat.card α = Set.ncard B * (m + 2)
⊢ 2 * Set.ncard B ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m✝ m : ℕ
hm :... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | rw [hm, mul_comm, add_comm, mul_add] | case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m✝ m : ℕ
hm : Nat.card α = Set.ncard B * (m + 2)
⊢ 2 * Set.ncard B ... | case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m✝ m : ℕ
hm : Nat.card α = Set.ncard B * (m + 2)
⊢ Set.ncard B * 2 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m✝ m :... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | apply Nat.le_add_right | case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m✝ m : ℕ
hm : Nat.card α = Set.ncard B * (m + 2)
⊢ Set.ncard B * 2 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : Set.Nonempty B
m✝ m :... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | simp only [Set.not_nonempty_iff_eq_empty] at hBne | case neg
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : ¬Set.Nonempty B
⊢ IsTrivialBlock B ∨ 2 * Set.ncard B ≤ Nat.card α | case neg
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ IsTrivialBlock B ∨ 2 * Set.ncard B ≤ Nat.card α | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : ¬Set.Nonempty B
⊢ I... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | rw [hBne] | case neg
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ IsTrivialBlock B ∨ 2 * Set.ncard B ≤ Nat.card α | case neg
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ IsTrivialBlock ∅ ∨ 2 * Set.ncard ∅ ≤ Nat.card α | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ IsTrivialBl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | left | case neg
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ IsTrivialBlock ∅ ∨ 2 * Set.ncard ∅ ≤ Nat.card α | case neg.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ IsTrivialBlock ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ IsTrivialBl... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | left | case neg.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ IsTrivialBlock ∅ | case neg.h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ Set.Subsingleton ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ IsTrivial... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | MulAction.isTrivialBlock_or_2_mul_ncard_le_card | [285, 1] | [306, 33] | exact Set.subsingleton_empty | case neg.h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ Set.Subsingleton ∅ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h.h
α : Type u_2
inst✝⁶ : DecidableEq α
G✝ : Type ?u.39967
inst✝⁵ : Group G✝
inst✝⁴ : MulAction G✝ α
inst✝³ : Fintype α
G : Type u_1
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : IsPretransitive G α
B : Set α
hB : IsBlock G B
hBne : B = ∅
⊢ Set.Sub... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | constructor | α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s) | case out
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ IsCoatom (stabilizer (Perm α) s) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ Subgroup.IsMaximal (stabilizer (Perm α) s)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | constructor | case out
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ IsCoatom (stabilizer (Perm α) s) | case out.left
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ stabilizer (Perm α) s ≠ ⊤
case out.right
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Grou... | Please generate a tactic in lean4 to solve the state.
STATE:
case out
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ IsCoatom (stabilizer (Perm α) s)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact stabilizer_ne_top s h0 h1 | case out.left
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ stabilizer (Perm α) s ≠ ⊤
case out.right
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Grou... | case out.right
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ ∀ (b : Subgroup (Perm α)), stabilizer (Perm α) s < b → b = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
case out.left
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ stabilizer (Perm α) s ≠ ⊤
case out.right
α : Ty... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | intro G hG | case out.right
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ ∀ (b : Subgroup (Perm α)), stabilizer (Perm α) s < b → b = ⊤ | case out.right
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
⊢ G = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right
α : Type u_1
inst✝³ : DecidableEq α
G : Type ?u.45087
inst✝² : Group G
inst✝¹ : MulAction G α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
⊢ ∀ (b : Subgroup (Perm α)), stabilizer (Perm α) ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | obtain ⟨g, hg_swap, hg⟩ := has_swap_of_lt_stabilizer s G hG | case out.right
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
⊢ G = ⊤ | case out.right.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α)... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply jordan_swap _ g hg_swap hg | case out.right.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ IsPreprimitive (↥G) α | Please generate a tactic in lean4 to solve the state.
STATE:
case out.right.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabili... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply IsPreprimitive.mk | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | have hB_ne_sc : ∀ (B : Set α) (_ : IsBlock G B), ¬B = sᶜ := by
intro B hB hBsc
cases MulAction.isTrivialBlock_or_2_mul_ncard_le_card hB with
| inl hB_triv =>
cases hB_triv with
| inl hB_subsingleton =>
have : Set.ncard B ≤ 1 := by
rw [Set.ncard_le_one_iff_eq]
apply Set.Subsingleton.e... | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilize... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | intro B hB | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilize... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | unfold IsTrivialBlock | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilize... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [or_iff_not_imp_left] | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilize... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | intro hB' | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilize... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | obtain ⟨a, ha, ha'⟩ :=
Set.not_subset_iff_exists_mem_not_mem.mp fun h => hB' ((hB_not_le_sc B hB) h) | case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
thi... | case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilize... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [Set.not_mem_compl_iff] at ha' | case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg... | case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | obtain ⟨b, hb, hb'⟩ :=
Set.not_subset_iff_exists_mem_not_mem.mp fun h => hB' ((hB_not_le_s B hB) h) | case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg... | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap :... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [← Set.mem_compl_iff] at hb' | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap :... | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap :... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [eq_top_iff] | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap :... | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap :... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | intro x _ | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap :... | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap :... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | obtain ⟨b, hb⟩ := h1 | case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap :... | case has_trivial_blocks'.intro.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | obtain ⟨⟨g, hg⟩, hgbx : g • b = x⟩ := exists_smul_eq G b x | case has_trivial_blocks'.intro.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : ... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSw... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | suffices g • B = B by
rw [← hgbx, ← this, Set.smul_mem_smul_set_iff]
exact hsc_le_B hb | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSw... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSw... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply or_iff_not_imp_right.mp (IsBlock.def_one.mp hB ⟨g, hg⟩) | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSw... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSw... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [Set.not_disjoint_iff_nonempty_inter] | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSw... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSw... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | change (g • B ∩ B).Nonempty | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSw... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSw... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply Set.ncard_pigeonhole | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSw... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : Is... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [← Nat.card_eq_fintype_card, ← Set.ncard_add_ncard_compl s] | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : Is... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : Is... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Pe... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply Nat.lt_of_lt_of_le | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : Is... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Pe... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [Nat.add_lt_add_iff_right] | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : ... | case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case has_trivial_blocks'.intro.intro.intro.intro.intro.intro.mk.h.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply IsPretransitive.of_partition G s | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ IsPretransitive (↥G) α | case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ ∀ a ∈ s, ∀ b ∈ s, ∃... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply moves_in | case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ ∀ a ∈ s, ∀ b ∈ s, ∃... | case a.hGt
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ stabilizer (Per... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact hG | case a.hGt
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ stabilizer (Per... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.hGt
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s <... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply moves_in | case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ ∀ a ∈ sᶜ, ∀ b ∈ sᶜ,... | case a.hGt
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ stabilizer (Per... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [stabilizer_compl] | case a.hGt
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ stabilizer (Per... | case a.hGt
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ stabilizer (Per... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.hGt
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s <... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | intro h | case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
⊢ stabilizer (↥G) s ≠... | case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
h : stabilizer (↥G) s... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply lt_irrefl G | case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
h : stabilizer (↥G) s... | case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
h : stabilizer (↥G) s... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply lt_of_le_of_lt _ hG | case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
h : stabilizer (↥G) s... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
h : stabilizer (↥G) s = ⊤
⊢ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | intro g hg | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
h : stabilizer (↥G) s = ⊤
⊢ ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [mem_stabilizer_iff] | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [← Subgroup.coe_mk G g hg] | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | change (⟨g, hg⟩ : ↥G) • s = s | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [← mem_stabilizer_iff] | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [h] | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | trivial | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Perm α
hg_swap : IsSwap g✝
hg✝ : g✝ ∈ G
h : stabilizer (↥G) s = ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g✝ : Per... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | intro B hB hBsc | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | cases MulAction.isTrivialBlock_or_2_mul_ncard_le_card hB with
| inl hB_triv =>
cases hB_triv with
| inl hB_subsingleton =>
have : Set.ncard B ≤ 1 := by
rw [Set.ncard_le_one_iff_eq]
apply Set.Subsingleton.eq_empty_or_singleton
exact hB_subsingleton
apply not_lt.mpr this
rw [hBsc]
ap... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | cases hB_triv with
| inl hB_subsingleton =>
have : Set.ncard B ≤ 1 := by
rw [Set.ncard_le_one_iff_eq]
apply Set.Subsingleton.eq_empty_or_singleton
exact hB_subsingleton
apply not_lt.mpr this
rw [hBsc]
apply lt_of_le_of_lt _ hα
rw [Nat.succ_le_iff, Set.ncard_pos]
exact h0
| inr hB_top =>
apply ... | case inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransit... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | have : Set.ncard B ≤ 1 := by
rw [Set.ncard_le_one_iff_eq]
apply Set.Subsingleton.eq_empty_or_singleton
exact hB_subsingleton | case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretra... | case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretr... | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply not_lt.mpr this | case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretr... | case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretr... | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [hBsc] | case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretr... | case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretr... | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply lt_of_le_of_lt _ hα | case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretr... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransitive (↥G)... | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inl
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [Nat.succ_le_iff, Set.ncard_pos] | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransitive (↥G)... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransitive (↥G)... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact h0 | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this✝ : IsPretransitive (↥G)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | rw [Set.ncard_le_one_iff_eq] | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply Set.Subsingleton.eq_empty_or_singleton | α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransitive (↥G) ... | case hs
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransiti... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | exact hB_subsingleton | case hs
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretransiti... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hs
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | apply Set.not_nonempty_empty | case inl.inr
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPretra... | case inl.inr.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPret... | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inr
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/PermMaximal.lean | Equiv.Perm.isMaximalStab' | [308, 1] | [572, 55] | simp only [hBsc, Set.top_eq_univ, Set.compl_univ_iff] at hB_top | case inl.inr.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPret... | case inl.inr.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α) s < G
g : Perm α
hg_swap : IsSwap g
hg : g ∈ G
this : IsPret... | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inr.a
α : Type u_1
inst✝³ : DecidableEq α
G✝ : Type ?u.45087
inst✝² : Group G✝
inst✝¹ : MulAction G✝ α
inst✝ : Fintype α
s : Set α
h0 : Set.Nonempty s
h1 : Set.Nonempty sᶜ
hα : Set.ncard s < Set.ncard sᶜ
G : Subgroup (Perm α)
hG : stabilizer (Perm α)... |
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