intros.
rewrite (plus_n_O q).
rewrite H0.
elim plus_mult.
apply plus_lt_compat_l.
apply (no_zero_div n 2 H q H0).
Qed.
Hint Resolve lt_quotient2_n.

Lemma less_div : forall n a b : nat, 0 < n -> n = a * b -> b <= n.
intros.