proposition: Lemma enc_derivations_el B n k x : M_opair k x ∈ M_enc_derivations B n -> exists l, k = numeral l /\ x = M_enc_stack (derivations B l).
proof: Proof. Proof using M_FST VIEQ. induction n; cbn. - intros H % sing_el. exists 0. apply (opair_inj H). - intros [H|H] % M_adj. + exists (S n). apply (opair_inj H). + 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)