helm/www/matita/docs/manual-0.5.9/tac_elim.html

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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>elim</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_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_destruct.html" title="destruct" /><link rel="next" href="tac_elimType.html" title="elimType" /></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">elim</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_destruct.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_elimType.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_elim"></a>elim</h2></div></div></div><p><strong class="userinput"><code>elim t pattern using th hyps</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>elim</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span> [<span class="bold"><strong>using</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>] <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.intros-spec">intros-spec</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>t</strong></span> must inhabit an inductive type and
   4              <span class="command"><strong>th</strong></span> must be an elimination principle for that
   5              inductive type. If <span class="command"><strong>th</strong></span> is omitted the appropriate
   6              standard elimination principle is chosen.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It proceeds by cases on the values of <span class="command"><strong>t</strong></span>,
   7              according to the elimination principle <span class="command"><strong>th</strong></span>.
   8              The induction predicate is restricted by
   9              <span class="command"><strong>pattern</strong></span>. In particular, if some hypothesis
  10              is listed in <span class="command"><strong>pattern</strong></span>, the hypothesis is
  11              generalized and cleared before eliminating <span class="command"><strong>t</strong></span>
  12             </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens one new sequent for each case. The names of
  13              the new hypotheses are picked by <span class="command"><strong>hyps</strong></span>, if
  14              provided. If hyps specifies also a number of hypotheses that
  15              is less than the number of new hypotheses for a new sequent,
  16              then the exceeding hypothesis will be kept as implications in
  17              the conclusion of the sequent.</p></dd></dl></div><p>
  18     </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_destruct.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_elimType.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">destruct </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> elimType</td></tr></table></div></body></html>