(*s The order [Dle] extended to $D_{\infty}$ *)
Definition Ddle (dd dd' : option D) :=
  match dd, dd' with
  | _, None => true
  | None, _ => false
  | Some d, Some d' => Dle d d'
  end.

Lemma Ddle_trans : forall dd dd' dd'' : option D, Ddle dd dd' = true -> Ddle dd' dd'' = true -> Ddle dd dd'' = true.