apply Zlog_sup_seq. apply Mset_l. apply Zle_lt_trans with (w - 1).
rewrite <- Zlog_sup_pow with (i := w - 1). apply Zlog_sup_seq. apply Mset_r. cut (0 < w). omega.
exact lt_0_w. omega. Qed.

Lemma pex : forall M : Mset, in_Z_ w (Zlog_sup M).
intros. apply p1ex_2le; omega. Qed.