Definition Fdiff (x y : float) :=
  (Fnum x * Zpower_nat radix (Zabs_nat (Fexp x - Zmin (Fexp x) (Fexp y))) -
   Fnum y * Zpower_nat radix (Zabs_nat (Fexp y - Zmin (Fexp x) (Fexp y))))%Z.

Theorem Fdiff_correct : forall x y : float, (Fdiff x y * powerRZ radix (Zmin (Fexp x) (Fexp y)))%R = (x - y)%R.