intros U R x y H'; elim H'; auto.
intros x0 y0 z H'0 H'1 H'2; right; exists y0; auto.
Qed.

(* Specifications: *)
Theorem Rstar_equiv_Rstar1 :
forall (U : Type) (R : Relation U), same_relation U (Rstar U R) (Rstar1 U R).