| import Mathlib | |
| namespace OAI | |
| open Set Matroid | |
| namespace InfiniteMatroidCounterexample | |
| abbrev D := (m : ℕ) × ((Fin m → Bool) → Bool) | |
| abbrev E0 := D × Bool | |
| abbrev E := ℤ × D | |
| def contractOnto {α : Type*} (M : Matroid α) (C : Set α) : Matroid α := | |
| (M.dual ↾ C).dual | |
| def HasPackingCovering {α : Type*} (M₀ M₁ : Matroid α) : Prop := | |
| ∃ P C S₀ S₁ I₀ I₁ : Set α, | |
| Disjoint P C ∧ P ∪ C = M₀.E ∧ M₁.E = M₀.E ∧ | |
| S₀ ⊆ P ∧ S₁ ⊆ P ∧ Disjoint S₀ S₁ ∧ | |
| (M₀ ↾ P).Spanning S₀ ∧ (M₁ ↾ P).Spanning S₁ ∧ | |
| I₀ ⊆ C ∧ I₁ ⊆ C ∧ | |
| (contractOnto M₀ C).Indep I₀ ∧ | |
| (contractOnto M₁ C).Indep I₁ ∧ I₀ ∪ I₁ = C | |
| end InfiniteMatroidCounterexample | |
| end OAI | |