intros x y H' H'0; red in |- *; auto 20.
intros x0 H'1; elim H'1; auto 20.
Qed.
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.