intros x y z H' H'0 H'1 H'2 H'3.
apply Upper_Bound_definition; auto with sets.
intros y0 H'4; elim H'4; auto with sets.
Qed.
Hint Resolve Upper_Bound_Couple_intro.

Theorem Upper_Bound_Couple_inv :
forall x y z : U,
Upper_Bound U D (Couple U x y) z ->
Rel_of U D x z /\ Rel_of U D y z /\ In U (Carrier_of U D) z.