intros H'; inversion H'.
intros q'; case p.
intros H' H'0; simpl in |- *; apply le_lt_trans with (m := r);
auto with arith.
intros p' H' H'0; apply le_lt_trans with (m := S q' * r); auto with arith.
Qed.
Hint Resolve lt_comp_mult: arith.

Theorem mult_eq_inv : forall n m p : nat, 0 < n -> n * m = n * p -> m = p.
intros n m p H' H'0.