elim (mult_eq_zero a b H); auto with arith.
intro h.
absurd (a = 0); auto with arith.
Qed.
Hint Immediate mult_eq_zero_bis.

Lemma lt_nm_mult : forall n m : nat, 0 < n -> 0 < m -> 0 < n * m.
intros n m H1 H2.