Hint Resolve Couple_included_in_carrier.

(* Specifications: *)
Theorem Lub_is_in_Carrier :
forall (bsup : U) (X : Ensemble U),
Included U X (Carrier_of U D) ->
Lub U D X bsup -> In U (Carrier_of U D) bsup.
Theorem Singleton_has_lub :
forall x : U, In U (Carrier_of U D) x -> Lub U D (Singleton U x) x.