split.
apply Rnd_NE_pt_total.
apply Rnd_NE_pt_monotone.
Qed.

(* Specifications: *)
Lemma round_NE_pt_pos :
forall x,
(0 < x)%R ->
Rnd_NE_pt x (round beta fexp ZnearestE x).
Lemma round_NE_pt_pos :
forall x,
(0 < x)%R ->
Rnd_NE_pt x (round beta fexp ZnearestE x).