proposition: Lemma cnd_XM: (forall (phi : form falsity_on), cprv nil phi -> valid phi) -> forall P, ~~ P -> P.
proof: Proof. intros H P. specialize (H ((¬¬Q) → Q)). refine (H _ unit (iUnit P) (fun _ => tt)). eapply II. eapply DN. eauto. 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.FOL.Reductions.PCPb_to_FOL Undecidability.PCP.Reductions.PCPb_iff_dPCPb List Undecidability(Shared.ListAutomation)