unfold contains in |- *.
intros U R S H' x y H'0; elim H'0; auto.
generalize Rstar_transitive; intro T; red in T.
intros x0 y0 z H'1 H'2 H'3; apply T with y0; auto.
Qed.

(* Specifications: *)
Theorem star_monotone :
forall (U : Type) (R S : Relation U),
contains U S R -> contains U (Rstar U S) (Rstar U R).