intros i j Hi Hij. elim (Zle_lt_or_eq i j). intro. apply Zlt_le_weak. apply Zlt_pow_lt.
assumption. assumption. intro H. rewrite H. omega. assumption. Qed.

(* Specifications: *)
Lemma lt_pow_lt :
forall i j : Z, 0 <= i -> 0 <= j -> 2 ^ i < 2 ^ j -> i < j.