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   2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we proceed by cases on</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets V1.78.1" /><link rel="home" href="index.html" title="Matita V0.5.9 User Manual (rev. 0.5.9 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_andelim.html" title="we have" /><link rel="next" href="tac_weproceedbyinduction.html" title="we proceed by induction on" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we proceed by cases on</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_andelim.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_weproceedbyinduction.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_weproceedbycases"></a>we proceed by cases on</h2></div></div></div><p><strong class="userinput"><code>we proceed by cases on t to prove th</code></strong></p><p>
   3         </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>we proceed by cases on</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>to prove</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p><span class="command"><strong>t</strong></span> must inhabitant of an inductive type and
   4           <span class="command"><strong>th</strong></span> must be the conclusion to be proved by
   5           cases.</p></dd><dt><span class="term">Action:</span></dt><dd><p> It proceeds by cases on <span class="command"><strong>t</strong></span> </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens one new sequent for each constructor of the
   6                 type of <span class="command"><strong>t</strong></span>.</p></dd></dl></div><p>
   7        </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_andelim.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_weproceedbyinduction.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we have </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we proceed by induction on</td></tr></table></div></body></html>