End monotone.

(* Specifications: *)
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)).