proposition: Lemma list2hfs_spec L x : hfs_mem x (list2hfs L) <-> x el L.
proof: Proof. induction L; cbn. - apply hfs_empty_spec. - split. + intros [<-|H] % hfs_cons_spec; auto. right. now apply IHL. + intros [<-|H]; apply hfs_cons_spec; auto. right. now apply IHL. 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)