proposition: Lemma enc_derivations_bound B n k x : M_opair k x ∈ M_enc_derivations B n -> k ∈ σ (numeral n).
proof: Proof. Proof using M_FST VIEQ. induction n; cbn. - intros H % sing_el. apply opair_inj in H as [-> _]. apply sigma_el. now right. - intros [H|H] % M_adj. + apply opair_inj in H as [-> _]. apply sigma_eq. + apply sigma_el. left. apply IHn, H. Qed.
imports: Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.FST Undecidability.FOL.Sets.FST Lia Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation)