intros a b X H' H'0; red.
intros x H'1; elim H'1; auto with sets.
Qed.
#[local]
Hint Resolve Union_minimal : core.

(* Specifications: *)
Theorem Intersection_maximal :
forall a b X:Ensemble U,
Included U X a -> Included U X b -> Included U X (Intersection U a b).