| import Mathlib | |
| import OAI.Computability.VertexCover.Machines.NatDiv | |
| namespace OAI | |
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| namespace VertexCover.Machine | |
| def finCode {n : ℕ} (i : Fin n) : List Bool := natBits i.val | |
| theorem finCode_injective (n : ℕ) : Function.Injective (finCode (n := n)) := by | |
| intro a b h | |
| apply Fin.ext | |
| have := congrArg List.length h | |
| simpa [finCode] using this | |
| noncomputable def Poly.finMod (n : ℕ) (hn : 0 < n) : | |
| Poly natBits (finCode (n := n)) (fun i => (⟨i%n,Nat.mod_lt i hn⟩ : Fin n)) := | |
| (((Poly.identity natBits).pair (Poly.const natBits natBits n)).comp Poly.natMod).encodeCongr | |
| id (fun _ => rfl) (fun _ => rfl) | |
| noncomputable def Poly.finVal (n : ℕ) : Poly (finCode (n := n)) natBits Fin.val := | |
| (Poly.identity natBits).encodeCongr Fin.val (fun _ => rfl) (fun _ => rfl) | |
| end VertexCover.Machine | |
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| end OAI | |