elim D.
intros C R n o.
elim n.
intros x H'; exists x.
apply Upper_Bound_definition; auto.
intros y H'0; elim H'0; auto.
Qed.
Hint Resolve Empty_set_has_Upper_Bound.

Theorem Empty_set_has_lub :
Cpo U D -> exists bsup : U, Lub U D (Empty_set U) bsup.