elim H; auto with arith.
intros.
simpl in |- *.
elim plus_n_O.
elim H1; auto with arith.
Qed.
Hint Resolve exp_2_incr.

Lemma exp_2_n_plus_m : forall n m : nat, exp_2 (n + m) = exp_2 n * exp_2 m.
simple induction n.