apply Zlog_sup_seq. omega. intro H. right. symmetry. trivial. assumption. Qed.

Lemma lt_2pm1_M : 2 ^ (p - 1) < M \/ M = 1.
elim (Zle_lt_or_eq 1 M). intro H. rewrite p_M. generalize le_1_M. case M. intro. absurd (2 <= 0); omega.