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

(* Specifications: *)
Theorem ToZeroSymmetric : SymmetricP ToZeroP.
Theorem ToInfinitySymmetric : SymmetricP ToInfinityP.
Theorem ScalableRoundedModeP : forall P (f s t : float), RoundedModeP P -> Fbounded b f -> P (radix * f)%R s -> P (s / radix)%R t -> f = t :>R.
Theorem RoundLessThanIsMax : forall P, RoundedModeP P -> forall (p m : float) (x : R), P x p -> isMax b radix x m -> (p <= m)%R.