intros n m H' H'0; case H'0; intros q E; rewrite E.
rewrite Zabs_Zmult.
pattern (Zabs m) at 1 in |- *; replace (Zabs m) with (Zabs m * 1)%Z;
[ idtac | ring ].
apply Zle_Zmult_comp_l; auto with zarith.
generalize E H'; case q; simpl in |- *; auto;
try (intros H1 H2; case H2; rewrite H1; ring; fail);
intros p; case p; unfold Zle in |- *; simpl in |- *;
intros; red in |- *; discriminate.
Qed.

Theorem Zquotient_mult_comp :
forall m n p : Z, p <> 0%Z -> Zquotient (m * p) (n * p) = Zquotient m n.