Definition pred_nat : forall (x : Z) (Hx : (0 < x)%Z), nat.

Lemma Zind_wf_double : forall (P : Z -> Z -> Prop) (p0 q0 : Z), (forall n m : Z, (forall p q : Z, (q0 <= q)%Z -> (p0 <= p < n)%Z -> P p q) -> (forall p : Z, (q0 <= p < m)%Z -> P n p) -> P n m) -> forall p q : Z, (q0 <= q)%Z -> (p0 <= p)%Z -> P p q.