proposition: Fact hfs_card_empty n : ∅ ∈ hfs_card (S n).
proof: Proof. apply hfs_pos_card. exists pos0. apply hfs_mem_ext. intros x; rewrite hfs_empty_spec; split; simpl; try tauto. unfold hfs_pos; rewrite btm_repr_cls. unfold pos2bt; rewrite pos2nat_fst; simpl. btm simpl. Qed.
imports: List Arith Lia Max Wellfounded Setoid Eqdep_dec Bool Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list finite) Undecidability.Shared.Libs.DLW.Vec(pos vec) Undecidability.Shared.Libs.DLW.Wf(wf_finite wf_chains) Undecidability.FOL.TRAKHTENBROT(notations fol_ops membership btree)