intros m; case m; simpl in |- *; auto.
intros H'; inversion H'; auto.
intros n0 H' m; case m; simpl in |- *; auto.
intros H'0; inversion H'0; auto.
intros n1 H'0.
rewrite H'; auto with arith.
rewrite H'; auto with arith.
Qed.

Theorem exp_Pascal :
forall a b n : nat,
power (a + b) n =
sum_nm n 0 (fun k : nat => binomial n k * (power a (n - k) * power b k)).