(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
Section more_lemmas.
Variable U : Type.
Variable B : Ensemble U.
Variable D : PO U.

Theorem Upper_Bound_is_in_Carrier :
forall (X : Ensemble U) (bound : U),
Included U X (Carrier_of U D) ->
Upper_Bound U D X bound -> In U (Carrier_of U D) bound.