try exact ToZeroTotal.
try exact ToZeroCompatible.
try exact ToZeroMinOrMax.
try exact ToZeroMonotone.
Qed.
Definition ToInfinityP (r : R) (p : float) :=
(r <= 0)%R /\ isMin b radix r p \/ (0 <= r)%R /\ isMax b radix r p.

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