auto with arith.
intros n H_rec H.
right.
elim (plus_eq_zero (n * b) b); auto with arith.
simpl in H; elim plus_comm.
auto with arith.
Qed.
Hint Resolve mult_eq_zero.

Lemma lt_mult_S_S : forall n m : nat, 0 < S n * S m.
simple induction n; simpl in |- *; auto with arith.