Local Hint Resolve lt_0_2pp : a.

(* Specifications: *)
Lemma lt_x_xmax : x < 2 ^ (p + w).
unfold x. apply Zle_lt_trans with ((2 ^ p - 1) * 2 ^ w + (2 ^ w - 1)). apply Zplus_le_compat.
Lemma le_0_wm1 : 0 <= w - 1.
clear. cut (0 < w). omega. exact lt_0_w. Qed.
Lemma le_0_wm1 : 0 <= w - 1.
cut (0 < w). omega. exact lt_0_w. Qed.