intros r; apply MaxEx with (precision := precision); auto with arith.
split; try exact MaxCompatible.
split; try apply MonotoneMax; red in |- *; auto.
Qed.
Definition ToZeroP (r : R) (p : float) :=
(0 <= r)%R /\ isMin b radix r p \/ (r <= 0)%R /\ isMax b radix r p.

Theorem ToZeroTotal : TotalP ToZeroP.
red in |- *; intros r; case (Rle_or_lt r 0); intros H1.