proposition: Lemma numeral_numeral n x : x ∈ numeral n -> exists k, x = numeral k.
proof: Proof. Proof using M_FST VIEQ. intros H. induction n; cbn in *. - now apply M_eset in H. - apply sigma_el in H as [H|H]. + apply IHn, H. + exists n. apply H. Qed.
imports: Undecidability.FOL(Syntax.Facts Semantics.Tarski.FullFacts FST) Undecidability.FOL(Sets.FST) Undecidability.FOL.TRAKHTENBROT(hfs) Undecidability.Shared.Libs.DLW.Utils(finite) Undecidability(Shared.ListAutomation) Coq(Lia)