proposition: Fact bt_pow_spec t x : x ∈ bt_pow t <-> x ⊆ t.
proof: Proof. revert x; induction t as [ | s t Ht ] using bt_rect'; intros x; simpl. + rewrite btm_inv, btm_inv_0, bti_inv_0, bte_inv_0; tauto. + rewrite bti_inv, bt_cup_spec, bt_mcomp_spec, Ht. split; intros [ | (y & H) ]; auto; right; exists y; revert H; rewrite Ht; auto. Qed.
imports: List Arith Lia Max Wellfounded Setoid Eqdep_dec Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list utils_decidable finite seteq) Undecidability.Shared.Libs.DLW.Vec(pos) Undecidability.Shared.Libs.DLW.Wf(wf_finite wf_chains) Undecidability.FOL.TRAKHTENBROT(notations fol_ops)