intros n m p H' H'0.
case H'; intros z1 Hz1.
case H'0; intros z2 Hz2.
exists (z1 - z2)%Z; rewrite Hz1; rewrite Hz2; ring.
Qed.

Theorem ZDivides_mult :
forall n m p q : Z, Zdivides n p -> Zdivides m q -> Zdivides (n * m) (p * q).