proposition: Theorem PCP_ZFeq' B : (exists V (M : interp V), standard M /\ forall rho, rho ⊫ ZFeq') -> entailment_ZFeq' (solvable B) -> PCPb B.
proof: Proof. intros (M & H1 & H2 & H3) H. rewrite PCPb_iff_dPCPb. specialize (H M H1 (fun _ => @i_func _ _ _ _ eset Vector.nil) H3). apply PCP_ZF2 in H as [s Hs]; trivial. now exists s. Qed.
imports: Undecidability.FOL.ZF Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Sets(ZF) Undecidability.FOL.Sets.ZF Undecidability.FOL.Reductions.PCPb_to_ZF Lia Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation) Morphisms