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

Lemma Rcross_prod : forall a b c d : R, (b <> 0 -> d <> 0 -> a / b = c / d -> a * d = b * c)%R.