| import Mathlib | |
| import OAI.Combinatorics.IndependentSets.Model | |
| namespace OAI | |
| namespace LargeIndependentSets | |
| structure GraphReduction (δ : ℚ) where | |
| reduce : List Bool → Graph | |
| computation : Turing.TM2ComputableInPolyTime (id : List Bool → List Bool) graphBits reduce | |
| finiteAlphabets : ∀ k : computation.tm.K, Finite (computation.tm.Γ k) | |
| outputBound : Polynomial ℕ | |
| outputSize : ∀ b, (graphBits (reduce b)).length ≤ outputBound.eval b.length | |
| completeness : ∀ φ : Formula, φ.Satisfiable → (reduce (formulaBits φ)).ThreeColorable | |
| soundness : ∀ φ : Formula, ¬φ.Satisfiable → | |
| ((reduce (formulaBits φ)).independenceNumber : ℚ) < | |
| δ * (reduce (formulaBits φ)).vertices | |
| def MainStatement : Prop := | |
| ∀ δ : ℚ, 0 < δ → δ < 1 / 3 → Nonempty (GraphReduction δ) | |
| end LargeIndependentSets | |
| end OAI | |