Definition Fulp (p : float) :=
  powerRZ radix (Fexp (Fnormalize radix b precision p)).

Theorem InBinade : forall (P : R -> float -> Prop) (p q r : float) (e : Z), RoundedModeP b radix P -> Fbounded b p -> Fbounded b q -> P (p + q)%R r -> (- dExp b <= e)%Z -> (Float (Zpower_nat radix (pred precision)) e <= p)%R -> (p <= Float (pPred (vNum b)) e)%R -> (0%nat < q)%R -> (q < powerRZ radix e)%R -> r = p :>R \/ r = (p + powerRZ radix e)%R :>R.