Definition R_p4 (x y : Z) :=
  0 <= x /\ 1 < y /\ exists d : Z, y = d * d * x /\ 1 < d.

Lemma prop4 : forall p q : Z, 0 <= p -> 0 <= q -> rel_prime p q -> is_sqr (p * q) -> is_sqr p /\ is_sqr q.