ies that \( \gamma' \) is an
  \( \tau(M) \)-automorphism of \( L \) which allows us to conclude
  that \( \gamma'(x') = x' \) for \( x' \in \tau(M) \).  Since every
  \( \tau^{-1} \gamma' \tau \in \tau^{-1} \tau(M)^* \tau \) fixes all
  elements \( x \in M \), each \( \tau^{-1} \gamma' \tau \) must be an
  \( M \)-automorphism of \( L \).  Thus \( \tau^{-1} \tau(M)^* \tau
  \subseteq M^* \).  This implies \( \tau M^* \tau^{-1} \supseteq
  \tau(M)^* \).
</p>
<p>
  We have shown that \( \tau M^* \tau^{-1} \s