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 FshiftCorrectSym : forall x y : float, x = y :>R -> exists n : nat, (exists m : nat, Fshift n x = Fshift m y).