 I have reversed the LHS and
  RHS to maintain consistency with the equations that appear in the
  discussion below.
</p>
<p>
  To build intuition for this lemma, I'll first present an
  illustration, followed by a proof.  The discussion below assumes
  familiarity with field extensions and field automorphisms, as
  several notations and results from these areas will be used
  implicitly without detailed justification.  This post is meant to
  serve as a set of notes on the lemma, not a comprehensive tutori