proposition: Theorem Σrem_props_correct A : fo_form_fin_dec_SAT_in A X <-> fo_form_fin_dec_SAT_in (Σrem_props 0 A) X.
proof: Proof. split. + intros (M & H1 & H2 & phi & H3). apply Σrem_props_soundness with M phi; auto. + intros (M & H1 & H2 & phi & H3). apply Σrem_props_completeness 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)