proposition: Fact hfs_pow_spec s x : x ∈ hfs_pow s <-> x ⊆ s.
proof: Proof. unfold hfs_pow. rewrite btm_repr_cls, bt_pow_spec. split. + intros H z Hz. rewrite <- (bt_cls_hfs_repr z). apply btm_cls_repr, H; auto. + intros H z. specialize (H (cls z)). do 2 rewrite btm_cls_repr in H; auto. 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)