intros; apply (H OZ); intros.
unfold lt_absZ in H0; unfold absZ at 2 in H0; elim (lt_OZ m); assumption.
Qed.
(**********************************)
Inductive and_set_set_set (S1 S2 : Set) : Set :=
and_set_set_set_i : S2 -> S1 -> and_set_set_set S1 S2.
(*****************)
Definition and_recZ (p : nat) (P : Z -> Set) :=
forall n : nat, n <= p -> and_set_set_set (P (pos n)) (P (neg n)).

(**********)
Lemma Zrec2 :
forall P : Z -> Set,
(forall n : Z, (forall m : Z, lt_absZ m n -> P m) -> P n) -> and_recZ 0 P.