Relationship between Kleene Star of a subset of regular language and the regular language If $L(R_1) \subseteq L(R_2) \subseteq L(R_3)$ then $L(R_1)^* \subseteq L(R_2)^* \subseteq L(R_3)^*$. Does this also imply that $L(R_1)^* \subseteq L(R_3)$?
Of course not: Consider R1='a', R2='a|b', R3='a|b|c', for instance.