elim H.
rewrite minus_SS_n; auto with arith.
intros.
elim minus_Sn_m.
simpl in |- *.
auto with arith.
apply le_trans with (S (S n)); auto with arith.
Qed.
Hint Resolve lt_neq_O_pred.

(* Specifications: *)
Lemma minus_Sn_n : forall n : nat, S n - n = 1.
simple induction n; auto with arith.