Definition Fdigit (p : float) := digit radix (Fnum p).Definition Fshift (n : nat) (x : float) :=
  Float (Fnum x * Zpower_nat radix n) (Fexp x - n).

Theorem FshiftCorrectInv : forall x y : float, x = y :>R -> (Fexp x <= Fexp y)%Z -> Fshift (Zabs_nat (Fexp y - Fexp x)) y = x.