\).  Therefore \( \tau M^* \tau^{-1} = \tau(M)^* \).
</p>
<h2 id="proof">Proof</h2>
<p>
  The ideas presented in the previous sections will now be extended to
  formulate a general proof.  For clarity, the lemma is stated once
  again below before proceeding with the proof.
</p>
<p>
  <strong>Lemma 12.1.</strong>
  <em>
    Suppose that \( L/K \) is a field extension, \( M \) is an
    intermediate field, and \( \tau \) is a \( K \)-automorphism of \(
    L \).  Then \( \tau M^* \tau^{-1} = \tau(M)^{*} \).
