intros z Hz i Hi Hl Hh. apply Zlog_sup_unique with (z := z). assumption. apply Zlog_sup_correct1.
assumption. assumption. elim (Zlog_sup_correct2 z). tauto. assumption. elim (Zlog_sup_correct2 z).
tauto. assumption. assumption. assumption. Qed.

Lemma Zlog_sup_seq : forall p q : Z, p <= q -> Zlog_sup p <= Zlog_sup q.
intros p q H. elim (Zle_or_lt p 0). intro Hp. replace (Zlog_sup p) with 0. elim (Zle_or_lt q 0).