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

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