intros.
apply (leZ_antisymmetric x OZ).
rewrite H.
exact (le_opp_OZ_l y H1).
exact H0.
Qed.
Let opp_inv : forall x y : Z, x = oppZ y -> y = oppZ x.
intros x y; elim y; simpl in |- *.
intro H'; rewrite H'; auto with arith.
intros n H'; rewrite H'; auto with arith.
intros n H'; rewrite H'; auto with arith.
Qed.

Lemma le_opp_OZ2 :
forall x y : Z, x = oppZ y -> leZ OZ x -> leZ OZ y -> x = y.