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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 have</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_existselim.html" title="let such that" /><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 have</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_existselim.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_andelim"></a>we have</h2></div></div></div><p><strong class="userinput"><code>justification we have A (H1) and B (H2)</code></strong>
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   4       </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>we have</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
   5                     <span class="bold"><strong>( </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> ) and </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
   6                       <span class="bold"><strong> ( </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
   7               None.
   8           </p></dd><dt><span class="term">Action:</span></dt><dd><p>
   9                   It applies the left multiplicative introduction rule for the conjunction on the formula <span class="command"><strong>A ∧ B</strong></span> (in Natural Deduction this corresponds to the elimination rule for the conjunction).
  10           </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>A new sequent with <span class="command"><strong>A ∧ B</strong></span> as the conclusion is opened and then immediately closed using the given justification. A new sequent with the conclusion of the sequent on which this tactic was applied is opened, and two new hypotheses <span class="command"><strong>H1 : A</strong></span> and <span class="command"><strong>H2 : B</strong></span> are added to the context.</p></dd></dl></div><p>
  11     </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_existselim.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">let such that </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>