(** 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_abs_abs : forall P : R -> R -> Prop, ( forall rnd (Hr : Valid_rnd rnd) x, (0 <= x)%R -> P x (round rnd x) ) -> forall rnd {Hr : Valid_rnd rnd} x, P (Rabs x) (Rabs (round rnd x)).