proposition: Theorem Σfull_mon_red'_no_syms : fol_syms Σfull_mon_red' = nil.
proof: Proof. cut (incl (fol_syms Σfull_mon_red') nil). + generalize (fol_syms Σfull_mon_red'). intros [ | x l ] H; auto. destruct (H x); simpl; auto. + simpl. rewrite Σfull_mon_rec_syms, fol_syms_mquant. rewrite fol_syms_bigop, app_nil_r; simpl. intros x; rewrite in_flat_map. intros (u & H & Hu); revert H. rewrite in_map_iff. intros (c & <- & Hc). revert Hu. destruct c as (([|s w]&?),r); simpl; auto. Qed.
imports: List Arith Bool Lia Eqdep_dec 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 fo_logic fo_sat Sig_no_syms)