(*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.