Show that the regular language is contained in another
It is just a simple subset proof:

Let $(u, v) \in (L_1 \otimes L_2)^+$. Thus, there is a decomposition of $(u, v)$ into $(u_1 \ldots u_k, v_1 \ldots v_k)$ with $u_i \in L_1$ and $v_i \in L_2$ and $k &gt; 0$. Hence, we have $u \in L_1^+, v \in L_2^+$. So overall we have $(u, v) \in L_1^+ \otimes L_2^+$.