| import Mathlib | |
| namespace OAI | |
| namespace SnakyConditional | |
| variable {α : Type*} [DecidableEq α] | |
| inductive WinsIn (win : Finset α → Prop) : ℕ → Finset α → Finset α → Prop | |
| | done {n M B} : win M → WinsIn win n M B | |
| | move {n M B} (x : α) (hxM : x ∉ M) (hxB : x ∉ B) | |
| (next : ∀ b, b ∉ insert x M → b ∉ B → | |
| WinsIn win n (insert x M) (insert b B)) : | |
| WinsIn win (n + 1) M B | |
| def Template (win : Finset α → Prop) (n : ℕ) (A H : Finset α) : Prop := | |
| ∀ M B, Disjoint M B → A ⊆ M → Disjoint B H → WinsIn win n M B | |
| abbrev Cell := ℤ × ℤ | |
| def snaky : Finset Cell := {(0, 0), (1, 0), (2, 0), (3, 0), (3, 1), (4, 1)} | |
| def orient (r : Fin 8) (p : Cell) : Cell := | |
| match r.val with | |
| | 0 => (p.1, p.2) | |
| | 1 => (p.2, p.1) | |
| | 2 => (p.1, -p.2) | |
| | 3 => (-p.2, p.1) | |
| | 4 => (-p.1, p.2) | |
| | 5 => (p.2, -p.1) | |
| | 6 => (-p.1, -p.2) | |
| | _ => (-p.2, -p.1) | |
| def placement (r : Fin 8) (t p : Cell) : Cell := orient r p + t | |
| def HasSnaky (M : Finset Cell) : Prop := | |
| ∃ (r : Fin 8) (t : Cell), snaky.image (placement r t) ⊆ M | |
| end SnakyConditional | |
| end OAI | |