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

(* Specifications: *)
Theorem ToZeroTotal : TotalP ToZeroP.
Theorem ToZeroCompatible : CompatibleP ToZeroP.
Theorem ToZeroMinOrMax : MinOrMaxP ToZeroP.
Theorem ToZeroMonotone : MonotoneP radix ToZeroP.
Theorem ToZeroRoundedModeP : RoundedModeP ToZeroP.