generalize Rstar_contains_R; intro T; red in T.
intros U R; unfold same_relation, contains in |- *.
split; intros x y H'; elim H'; auto.
generalize Rstar_transitive; intro T1; red in T1.
intros x0 y0 z H'0 H'1 H'2 H'3; apply T1 with y0; auto.
intros x0 y0 z H'0 H'1 H'2; apply Rstar1_n with y0; auto.
Qed.

Theorem Rsym_imp_Rstarsym :
forall (U : Type) (R : Relation U), Symmetric U R -> Symmetric U (Rstar U R).