proposition: Theorem Σfull_mon_red'_correct : fo_form_fin_dec_SAT_in A K <-> fo_form_fin_dec_SAT_in Σfull_mon_red' K.
proof: Proof. Proof using HwA. rewrite Σfull_mon_red_correct. split. + apply Σfull_mon_red'_sound. + intros (M & H1 & H2 & phi & H3). apply Σfull_mon_red'_complete with M phi; 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)