Definition Fnormalize (p : float) :=
  match Z_zerop (Fnum p) with
  | left _ => Float 0 (- dExp b)
  | right _ =>
      Fshift radix
        (min (precision - Fdigit radix p) (Zabs_nat (dExp b + Fexp p))) p
  end.

Theorem boundedNorMinGivesExp : forall (x : Z) (p : float), Fbounded b p -> (- dExp b <= x)%Z -> (Float nNormMin x <= p)%R -> (p <= Float (pPred (vNum b)) x)%R -> Fexp (Fnormalize p) = x.