| import OAI.ModelTheory.Choiceless.QueryMachine | |
| namespace OAI | |
| namespace CPTSeparation | |
| theorem main : | |
| (∀ (A B : Type) [Fintype A] [Fintype B] (S : Input A) (T : Input B), | |
| S.Iso T → (S.query ↔ T.query)) ∧ | |
| OrdinaryPolynomialTime ∧ | |
| ¬ FullCPT.EvaluationDefinable (fun {_} [_] I => I.query) := by | |
| refine ⟨?_, ?_, FullCPT.query_not_evaluationDefinable⟩ | |
| · intro A B _ _ S T e | |
| exact Input.query_invariant e | |
| · refine ⟨QueryMachine.answer, QueryMachine.polynomialAlgorithm, ?_, ?_⟩ | |
| · intro k | |
| change Finite QueryMachine.Letter | |
| infer_instance | |
| · intro A _ N e S | |
| let iso : S.Iso (S.ordered e) := | |
| { toEquiv := e | |
| rel_eq := by intro r x y; simp [Input.ordered] } | |
| exact (QueryMachine.answer_correct ⟨N,S.ordered e⟩).trans | |
| (Input.query_invariant iso).symm | |
| end CPTSeparation | |
| end OAI | |