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derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive

  <ul>
    <li>Higher-Order Logic</li>

    <li style="list-style: none">
      <ul>
        <li><a href="HOL/index.html">HOL (Higher-Order Logic)</a>
        is a version of classical higher-order logic resembling
        that of the <a href="http://www.cl.cam.ac.uk/Research/HVG/HOL/">HOL System</a>.
        </li>
      </ul>
      <ul>
        <li>HOL with explicit <a href="HOL-Proofs/index.html">proof terms</a>.
        </li>
      </ul>
    </li>
  </ul>

  <ul>
    <li>First-Order Logic</li>

    <li style="list-style: none">
      <ul>
        <li><a href="FOL/index.html">FOL (Many-sorted First-Order Logic)</a>
        provides basic classical and intuitionistic first-order logic. It is
        polymorphic.
        </li>

        <li><a href="ZF/index.html">ZF (Set Theory)</a>
        offers a formulation of Zermelo-Fraenkel set theory on top of FOL.
        </li>

        <li><a href="CCL/index.html">CCL (Classical Computational Logic)</a></li>

        <li><a href="LCF/index.html">LCF (Logic of Computable Functions)</a></li>

        <li><a href="FOLP/index.html">FOLP (FOL with Proof Terms)</a></li>
      </ul>
    </li>
  </ul>

  <ul>
    <li>Miscellaneous</li>

    <li style="list-style: none">
      <ul>
        <li><a href="Sequents/index.html">Sequents (first-order, modal and linear logics)</a></li>

        <li><a href="CTT/index.html">CTT (Constructive Type Theory)</a>
        is an extensional version of Martin-L&ouml;f's Type Theory.</li>

        <li><a href="Cube/index.html">Cube (The Lambda Cube)</a></li>
      </ul>
    </li>
  </ul>