intros p H. absurd (0 < Zneg p). simplify_eq. assumption. Qed.

(* Specifications: *)
Lemma Zlog_sup_correct2 : forall z : Z, 0 < z -> 2 ^ (Zlog_sup z - 1) < z <= 2 ^ Zlog_sup z.
intros z H. elim (Zle_or_lt z 1). intro Hz. cut (z = 1). intro H0. rewrite H0. simpl. omega. omega.