elim y.
reflexivity.
intros; elim H0.
intros; elim H.
intro n; elim y.
intros; elim H.
simpl in |- *; intros; elim (le_antisym n n0 H H0); reflexivity.
intros; elim H.
intro n; elim y.
intros; elim H0.
intros; elim H0.
simpl in |- *; intros; elim (le_antisym n0 n H H0); reflexivity.
Qed.
Definition ltZ (x y : Z) := leZ (succZ x) y.
Definition lt_absZ (x y : Z) := ltZ (absZ x) (absZ y).

Lemma tech_lt_abs_OZ : forall x : Z, lt_absZ x (pos 0) -> x = OZ.
simple induction x.