Definition SymmetricP (P : R -> float -> Prop) :=
  forall (r : R) (p : float), P r p -> P (- r)%R (Fopp p).

Theorem RoundLessThanIsMax : forall P, RoundedModeP P -> forall (p m : float) (x : R), P x p -> isMax b radix x m -> (p <= m)%R.