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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>compose</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_clearbody.html" title="clearbody" /><link rel="next" href="tac_change.html" title="change" /></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">compose</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_clearbody.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_change.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_compose"></a>compose</h2></div></div></div><p><strong class="userinput"><code>compose n t1 with t2 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>compose</strong></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> [<span class="bold"><strong>with</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></p></dd><dt><span class="term">Action:</span></dt><dd><p>Composes t1 with t2 in every possible way
   4               <span class="command"><strong>n</strong></span> times introducing generated terms
   5               as if <span class="command"><strong>intros hyps</strong></span> was issued.</p><p>If <span class="command"><strong>t1:∀x:A.B[x]</strong></span> and
   6             <span class="command"><strong>t2:∀x,y:A.B[x]→B[y]→C[x,y]</strong></span> it generates:
   7              </p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p><span class="command"><strong>λx,y:A.t2 x y (t1 x) : ∀x,y:A.B[y]→C[x,y]</strong></span></p></li><li class="listitem"><p><span class="command"><strong>λx,y:A.λH:B[x].t2 x y H (t1 y) : ∀x,y:A.B[x]→C[x,y]
   8                   </strong></span></p></li></ul></div><p>
   9           </p><p>If <span class="command"><strong>t2</strong></span> is omitted it composes
  10             <span class="command"><strong>t1</strong></span>
  11               with every hypothesis that can be introduced.
  12               <span class="command"><strong>n</strong></span> iterates the process.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>The same, but with more hypothesis eventually introduced
  13             by the <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.intros-spec">intros-spec</a></em></span>.</p></dd></dl></div><p>
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