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

Lemma sqr_inv : forall a b : Z, b <> 0 -> (1 + IZR a * / IZR b * (IZR a * / IZR b) <> 0)%R.