proposition: Theorem BPCP_FIN_DEC_EQ_SAT : BPCP_problem ⪯ᵢ @fo_form_fin_dec_eq_SAT Σbpcp Σbpcp_eq eq_refl.
proof: Proof. apply ireduces_dependent; intros lc. exists (Σbpcp_encode lc); split. + intros (l & Hl); revert Hl; apply Sig_bpcp_encode_sound. + apply Sig_bpcp_encode_complete. Qed.
imports: List Arith Bool Lia Eqdep_dec Undecidability.Synthetic.Definitions Undecidability.Synthetic.ReducibilityFacts Undecidability.Synthetic.InformativeDefinitions Undecidability.Synthetic.InformativeReducibilityFacts Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list utils_nat finite) Undecidability.Shared.Libs.DLW.Vec(pos vec) Undecidability.Shared.Libs.DLW.Wf(wf_finite) Undecidability.FOL.TRAKHTENBROT(notations utils decidable bpcp fo_sig fo_terms fo_logic fo_sat red_utils Sig_discrete BPCP_SigBPCP Sig_rem_syms Sig_uniform Sig_one_rel Sig_rem_cst Sign_Sig2 Sig2_Sign Sign_Sig Sig_Sig_fin Sig2_SigSSn1 Sign1_Sig )