intros x y z H' H'0; try assumption.
elim Strict_Rel_is_Strict_Included.
unfold contains.
intros H'1 H'2; try assumption.
apply H'1.
apply Strict_Rel_Transitive_with_Rel_left with (y := y); auto with sets.
Qed.

(* Specifications: *)
Lemma Strict_inclusion_is_transitive :
Transitive (Ensemble U) (Strict_Included U).