proposition: Lemma star_equiv: forall (L1 L2:language), Equiv L1 L2 -> Equiv (Star L1) (Star L2).
proof: Proof. split; intros. + apply star_to_pow in H0. destruct H0 as (n, Hi). apply pow_to_star with (n:=n). eauto using pow_equiv_in. + apply star_to_pow in H0. destruct H0 as (n, Hi). apply pow_to_star with (n:=n). apply equiv_sym in H. eauto using pow_equiv_in. Qed.
imports: Coq.Lists.List