intros.
rewrite exp_2_n_plus_n.
rewrite S_pred_n; auto with arith.
Qed.
Hint Resolve exp_2_plus_pn_pn.

(* Specifications: *)
Lemma exp_2_le_pn_n : forall n : nat, exp_2 (pred n) <= exp_2 n.
simple induction n; auto with arith.