{-1} \phi_1 \tau \) and
  \( \tau^{-1} \phi_3 \tau \) fix the elements of \( M \), they are
  both \( M \)-automorphisms of \( L \).  Therefore \( \tau^{-1}
  \tau(M)^* \tau \subseteq M^* \) which implies \( \tau M^* \tau^{-1}
  \supseteq \tau(M)^* \).
</p>
<h3 id="lhs-equals-rhs">LHS = RHS</h3>
<p>
  The previous two sections complete the illustration of the lemma
  with the chosen example.  We have shown that \( \tau M^* \tau^{-1}
  \subseteq \tau(M)^{*} \) and \( \tau M^* \tau^{-1} \supseteq
  \tau(M)^* 