split; try exact ClosestCompatible.
split; try exact ClosestMinOrMax.
try exact ClosestMonotone.
Qed.
Definition EvenClosest (r : R) (p : float) :=
Closest r p /\
(FNeven b radix precision p \/ (forall q : float, Closest r q -> q = p :>R)).

Theorem EvenClosestTotal : TotalP EvenClosest.
red in |- *; intros r.