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

Theorem RoundedModeRep : forall P, RoundedModeP P -> forall p q : float, P p q -> exists m : Z, q = Float m (Fexp p) :>R.