intro.
simpl in |- *.
elim plus_n_O; reflexivity.
intros.
simpl in |- *.
elim plus_n_O.
apply sym_equal.
elim plus_n_O.
rewrite H.
elim mult_plus_distr_r; reflexivity.
Qed.
Hint Resolve exp_2_n_plus_m.
(************************************************************************)
(********************************** Base n ******************************)
(************************************************************************)

Lemma exp_n_incr : forall n m p : nat, n <= m -> exp_n n p <= exp_n m p.
simple induction p; auto with arith.