Definition EvenClosest (r : R) (p : float) :=
  Closest r p /\
  (FNeven b radix precision p \/ (forall q : float, Closest r q -> q = p :>R)).

(* Specifications: *)
Theorem EvenClosestTotal : TotalP EvenClosest.
Theorem EvenClosestCompatible : CompatibleP b radix EvenClosest.
Theorem EvenClosestMinOrMax : MinOrMaxP b radix EvenClosest.
Theorem EvenClosestMonotone : MonotoneP radix EvenClosest.
Theorem EvenClosestRoundedModeP : RoundedModeP b radix EvenClosest.
Theorem EvenClosestUniqueP : UniqueP radix EvenClosest.
Theorem ClosestSymmetric : SymmetricP Closest.
Theorem EvenClosestSymmetric : SymmetricP EvenClosest.