proposition: Corollary fol_sem_lift φ t A : ⟪A⦃fol_lift t⦄⟫ φ <-> ⟪A⟫ (⟦t⟧ φ)·φ.
proof: Proof. rewrite fol_sem_subst. apply fol_sem_ext; intros [ | n ] _; simpl; rew fot; auto. Qed.
imports: List Arith Lia Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list utils_nat finite) Undecidability.Shared.Libs.DLW.Vec(pos vec) Undecidability.FOL.TRAKHTENBROT(notations utils fol_ops fo_sig fo_terms) Undecidability.Shared.ListAutomation