Global Instance valid_rnd_N : Valid_rnd Znearest.

Lemma round_N_really_small_pos :
forall x,
forall ex,
(Fcore_Raux.bpow beta (ex - 1) <= x < Fcore_Raux.bpow beta ex)%R ->
(ex < fexp ex)%Z ->
(round Znearest x = 0)%R.