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.