elim minus_Sn_m.
apply eq_S.
elim minus_Sn_m.
apply eq_S.
elim minus_n_n; auto with arith.
auto with arith.
auto with arith.
Qed.
Hint Resolve minus_SS_n.

Lemma minus_S : forall n m : nat, n - m = S n - S m.
intros; simpl in |- *; auto with arith.