simpl. intros. cut (2 ^ (w - 1) < 2 ^ w). omega. exact lt_2wm1_2w. apply Zlog_sup_pow. exact le_0_w. Qed.

(* Specifications: *)
Lemma xhex : forall (M : Mset) (x : Z_ (2 ^ (Zlog_sup M + w))),
in_Z_ (2 ^ w) (x / 2 ^ w).