(*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.