Definition Closest (r : R) (p : float) :=
  Fbounded b p /\
  (forall f : float, Fbounded b f -> (Rabs (p - r) <= Rabs (f - r))%R).

Theorem ClosestMaxEq : forall (r : R) (min max p : float), isMin b radix r min -> isMax b radix r max -> (min + max < 2%nat * r)%R -> Closest r p -> p = max :>R.