Local Hint Resolve le_0_w lt02w le02w : a.
Local Hint Resolve le_0_p : a.

(* Specifications: *)
Lemma le_M_2pp : M <= 2 ^ p.
clear x_i_in_Z_ x_i.
Lemma le_M_2pp : M <= 2 ^ p.
rewrite p_M. generalize le_1_M. case M. intro. absurd (2 <= 0); omega. intros q H.