proposition: Fact fol_def_equiv R T : (forall φ, R φ <-> T φ) -> fol_definable R -> fol_definable T.
proof: Proof. intros H (A & H1 & H2 & H3); exists A; msplit 2; auto; intro; rewrite <- H; auto. Qed.
imports: List Arith Lia Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list finite) Undecidability.Shared.Libs.DLW.Vec(pos vec) Undecidability.FOL.TRAKHTENBROT(notations utils fol_ops fo_sig fo_terms fo_logic)