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

Lemma Zsgn_16 : forall x y : Z, Z.sgn (x * y) = 1%Z -> {(0 < x)%Z /\ (0 < y)%Z} + {(x < 0)%Z /\ (y < 0)%Z}.