Hint Resolve Compact_is_in_Carrier.

(* Specifications: *)
Theorem Compatible_is_reflexive : forall x : U, Compatible U D x x.
Hint Resolve Compatible_is_reflexive.
Theorem Couple_is_symmetric :
forall x y : U, Couple U x y = Couple U y x :>Ensemble U.
Theorem Compatible_is_symmetric :
forall x y : U, Compatible U D x y -> Compatible U D y x.