Definition ToInfinityP (r : R) (p : float) :=
  (r <= 0)%R /\ isMin b radix r p \/ (0 <= r)%R /\ isMax b radix r p.

(* Specifications: *)
Theorem ToInfinityTotal : TotalP ToInfinityP.
Theorem ToInfinityCompatible : CompatibleP ToInfinityP.
Theorem ToInfinityMinOrMax : MinOrMaxP ToInfinityP.
Theorem ToInfinityMonotone : MonotoneP radix ToInfinityP.
Theorem ToInfinityRoundedModeP : RoundedModeP ToInfinityP.
Theorem MinUniqueP : UniqueP (isMin b radix).
Theorem MaxUniqueP : UniqueP (isMax b radix).
Theorem ToZeroUniqueP : UniqueP ToZeroP.
Theorem ToInfinityUniqueP : UniqueP ToInfinityP.
Theorem MinOrMaxRep : forall P, MinOrMaxP P -> forall p q : float, P p q -> exists m : Z, q = Float m (Fexp p) :>R.
Theorem RoundedModeRep : forall P, RoundedModeP P -> forall p q : float, P p q -> exists m : Z, q = Float m (Fexp p) :>R.