proposition: Lemma HF_numeral_wf T n : HFeq <<= T -> T ⊢ ¬ (tnumeral n ∈ tnumeral n).
proof: Proof. intros HT. induction n; cbn. - now apply HF_eset'. - apply bunion_use; trivial. + eapply IE. apply (Weak IHn). auto. eapply IE. eapply IE. apply HF_numeral_trans; auto. auto. apply HF_sig_el. auto. + eapply IE. apply (Weak IHn). auto. eapply HF_eq_elem. auto. apply HF_refl'. auto. auto. apply HF_sig_el. auto. Qed.
imports: Undecidability.FOL.ZF Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Sets.ZF Undecidability.FOL.Reductions.PCPb_to_HF Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation)