intros X bound H' H'0; elim H'0; auto with sets.
Qed.

Theorem Lub_is_unique :
Conditionally_complete U D ->
forall (C : Ensemble U) (bsup1 bsup2 : U),
Lub U D C bsup1 -> Lub U D C bsup2 -> bsup1 = bsup2.