(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
Inductive Z : Set :=
| OZ : Z
| pos : nat -> Z
| neg : nat -> Z.
Definition IZ := pos 0.
Definition is_posn (x y : Z) :=
match x, y with
| pos n, pos m => n = m
| _, _ => False
end.
unfold not in |- *; intros.
cut (is_posn (pos n) (pos m)).
simpl in |- *; exact H.
rewrite H0; simpl in |- *; reflexivity.
Qed.

Lemma eq_OZ_dec : forall x : Z, {x = OZ} + {x <> OZ}.