proposition: Lemma FST_numeral_wf T n : FSTeq <<= T -> T ⊢ ¬ (tnumeral n ∈ tnumeral n).
proof: Proof. intros HT. induction n; cbn. - now apply FST_eset'. - apply II. assert1 H. apply FST_adj in H; auto. apply (DE H). + eapply IE. apply (Weak IHn); auto. eapply FST_eq_elem; auto. + eapply IE. apply (Weak IHn); auto. eapply IE. eapply IE. eapply FST_numeral_trans; auto. auto. apply FST_adj; auto. apply DI1. apply FST_refl'. auto. Qed.
imports: Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Deduction.FullNDFacts Undecidability.FOL.Sets.FST Undecidability.FOL.FST Undecidability.FOL.Reductions.PCPb_to_FST Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation)