proposition: Theorem Σn1_Σ_correct A : fo_form_fin_dec_SAT A <-> fo_form_fin_dec_SAT (Σn1_Σ A).
proof: Proof. split. + intros (X & M & H1 & H2 & phi & H3). apply convert_soundness with X M phi; auto. + intros (X & M & H1 & H2 & phi & H3). apply convert_completeness with X 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 Sig2_SigSSn1)