intros m n; case (Z_eq_dec n 0); intros Z1.
rewrite Z1; unfold Zquotient in |- *; case n; case m; simpl in |- *; auto.
case (ZquotientProp m n); auto; intros r1 (H'2, (H'3, H'4)); auto with zarith.
apply sym_equal;
apply ZquotientUnique with (q := (- Zquotient m n)%Z) (r := (- r1)%Z);
auto.
pattern m at 1 in |- *; rewrite H'2; ring.
rewrite <- Zopp_mult_distr_l; repeat rewrite Zabs_Zopp; auto.
rewrite Zabs_Zopp; auto.
Qed.

Theorem ZquotientMonotone :
forall n m q : Z,
(Zabs n <= Zabs m)%Z -> (Zabs (Zquotient n q) <= Zabs (Zquotient m q))%Z.