Hint Resolve Finite_plus_one_is_finite.

(* Specifications: *)
Theorem Singleton_is_finite : forall x : U, Finite U (Singleton U x).
Hint Resolve Singleton_is_finite.
Theorem Union_of_finite_is_finite :
forall X Y : Ensemble U,
Finite U X -> Finite U Y -> Finite U (Union U X Y).