proposition: Lemma BPCP_prv' (s : peirce) : dPCPb R -> [] ⊢ F.
proof: Proof. intros [u H]. apply drv_prv with (s:=s) in H. unfold F. repeat eapply impl_prv. simpl_list. eapply II. assert (ctx_S ⊢ (∀ Pr $0 $0 → Q)). apply Ctx. now unfold ctx_S. eapply AllE with (t := enc u) in H0. cbn in H0. now eapply (IE H0). 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)