proposition: Fact fol_def_ext R : fol_definable R -> forall φ ψ, (forall n, φ n = ψ n) -> R φ <-> R ψ.
proof: Proof. intros (A & _ & _ & HA) phi psi H. rewrite <- HA, <- HA; apply fol_sem_ext. intros; 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)