proposition: Lemma enc_derivations_eq T B n x : ZFeq' <<= T -> T ⊢ opair (tnumeral n) x ∈ enc_derivations B n -> T ⊢ x ≡ enc_stack (derivations B n).
proof: Proof. intros HT H. destruct n; cbn in *. - eapply opair_inj2; trivial. eapply ZF_sing_iff; eauto. - apply ZF_bunion_inv in H; trivial. apply (DE H). + apply Exp. eapply IE. apply (ZF_numeral_wf (S n)). auto. eapply ZF_derivations_bound. auto. auto. + eapply opair_inj2. auto. apply ZF_sing_iff. auto. auto. Qed.
imports: Undecidability.FOL.ZF Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Sets.ZF Undecidability.FOL.Reductions.PCPb_to_ZF Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation)