(*s Operation [Ddplus] on $D_{\infty}$ *)

Definition Ddplus (dd : option D) (d' : D) :=
  match dd with
  | Some d => Some (Dplus d d')
  | _ => dd
  end.

Lemma Ddle_plus_mono : forall (dd dd' : option D) (d d' : D), Ddle dd dd' = true -> Dle d d' = true -> Ddle (Ddplus dd d) (Ddplus dd' d') = true.