auto with sets.
Qed.
#[local]
Hint Resolve Strict_Rel_Transitive Strict_Rel_is_Strict_Included : core.

(* Specifications: *)
Lemma Strict_inclusion_is_transitive_with_inclusion :
forall x y z:Ensemble U,
Strict_Included U x y -> Included U y z -> Strict_Included U x z.