proposition: Theorem BPCP_prv R : PCPb R <-> nil ⊢M (F R).
proof: Proof. rewrite PCPb_iff_dPCPb. split. - apply BPCP_prv'. - intros H % soundness'. eapply PCPb_iff_dPCPb. now apply (@BPCP_valid falsity_off R). Qed.
imports: Undecidability.PCP(PCP Util.PCP_facts) Undecidability.FOL(Deduction.FragmentNDFacts Semantics.Tarski.FragmentFacts Semantics.Tarski.FragmentSoundness Syntax.Core Syntax.Facts) Undecidability.FOL(FOL) Undecidability.Synthetic(Definitions DecidabilityFacts EnumerabilityFacts ReducibilityFacts MoreReducibilityFacts) Undecidability.PCP.Reductions.PCPb_iff_dPCPb Undecidability(Shared.ListAutomation)