Section more_lemmas.
Variable U : Type.
Variable B : Ensemble U.
Variable D : PO U.
intros X bound H' H'0; elim H'0; auto with sets.
Qed.
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.