elim lt_0_p; intro H; omega. Qed.
Local Hint Resolve le_M_2pp le_1_p lt_0_p le_0_pm1 : a.

(* Specifications: *)
Lemma lt_2pm1_M : 2 ^ (p - 1) < M \/ M = 1.
clear x_i_in_Z_ x_i.