(** IEEE-754 roundings: up, down and to zero *)

Global Instance valid_rnd_DN : Valid_rnd Zfloor.Global Instance valid_rnd_UP : Valid_rnd Zceil.Global Instance valid_rnd_ZR : Valid_rnd Ztrunc.Global Instance valid_rnd_AW : Valid_rnd Zaway.

Theorem round_large_pos_ge_pow : forall x e, (0 < round rnd x)%R -> (bpow e <= x)%R -> (bpow e <= round rnd x)%R.