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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>default</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_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_coercion.html" title="coercion" /><link rel="next" href="command_hint.html" title="hint" /></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">default</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_coercion.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_hint.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_default"></a>default</h2></div></div></div><p><strong class="userinput"><code>default "s" u<sub>1</sub> … u<sub>n</sub></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>default</strong></span>
   4             <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri">uri</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri">uri</a></em></span>]…
   5            </p></dd><dt><span class="term">Action:</span></dt><dd><p>It registers a cluster of related definitions and
   6             theorems to be used by tactics and the rendering engine.
   7             Some functionalities of Matita are not available when some
   8             clusters have not been registered. Overloading a cluster
   9             registration is possible: the last registration will be the
  10             default one, but the previous ones are still in effect.</p><p>
  11             <span class="command"><strong>s</strong></span> is an identifier of the cluster and
  12             <span class="command"><strong>u<sub>1</sub> … u<sub>n</sub></strong></span>
  13             are the URIs of the definitions and theorems of the cluster.
  14             The number <span class="command"><strong>n</strong></span> of required URIs depends on the
  15             cluster. The following clusters are supported.
  16            </p><div class="table"><a id="idp73808912"></a><p class="title"><strong>Table 9.1. clusters</strong></p><div class="table-contents"><table summary="clusters" style="border-collapse: collapse;border-top: 0.5pt solid ; border-bottom: 0.5pt solid ; border-left: 0.5pt solid ; border-right: 0.5pt solid ; "><colgroup><col /><col /><col /><col /><col /><col /></colgroup><thead><tr><th style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">name</th><th style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">expected object for 1st URI</th><th style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">expected object for 2nd URI</th><th style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">expected object for 3rd URI</th><th style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">expected object for 4th URI</th><th style="border-bottom: 0.5pt solid ; ">expected object for 5th URI</th><th style="border-bottom: 0.5pt solid ; ">expected object for 6th URI</th><th style="border-bottom: 0.5pt solid ; ">expected object for 7th URI</th><th style="border-bottom: 0.5pt solid ; ">expected object for 8th URI</th><th style="border-bottom: 0.5pt solid ; ">expected object for 9th URI</th><th style="border-bottom: 0.5pt solid ; ">expected object for 10th URI</th><th style="border-bottom: 0.5pt solid ; ">expected object for 11th URI</th></tr></thead><tbody><tr><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">equality</td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">an inductive type (say, of type <span class="command"><strong>eq</strong></span>) of type ∀A:Type.A <span class="bold"><strong>→</strong></span> <span class="bold"><strong>Prop</strong></span> with one family parameter and one constructor of type ∀x:A.eq A x</td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">a theorem of type <span class="bold"><strong>∀</strong></span>A.<span class="bold"><strong>∀</strong></span>x,y:A.eq A x y <span class="bold"><strong>→</strong></span> eq A y x</td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">a theorem of type <span class="bold"><strong>∀</strong></span>A.<span class="bold"><strong>∀</strong></span>x,y,z:A.eq A x y <span class="bold"><strong>→</strong></span> eq A y z <span class="bold"><strong>→</strong></span> eq A x z</td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; "><span class="bold"><strong>∀</strong></span>A.<span class="bold"><strong>∀</strong></span>a.<span class="bold"><strong>∀</strong></span> P:A <span class="bold"><strong>→</strong></span> <span class="bold"><strong>Prop</strong></span>.P x <span class="bold"><strong>→</strong></span> <span class="bold"><strong>∀</strong></span>y.eq A x y <span class="bold"><strong>→</strong></span> P y</td><td style="border-bottom: 0.5pt solid ; "><span class="bold"><strong>∀</strong></span>A.<span class="bold"><strong>∀</strong></span>a.<span class="bold"><strong>∀</strong></span> P:A <span class="bold"><strong>→</strong></span> <span class="bold"><strong>Prop</strong></span>.P x <span class="bold"><strong>→</strong></span> <span class="bold"><strong>∀</strong></span>y.eq A y x <span class="bold"><strong>→</strong></span> P y</td><td style="border-bottom: 0.5pt solid ; "><span class="bold"><strong>∀</strong></span>A.<span class="bold"><strong>∀</strong></span>a.<span class="bold"><strong>∀</strong></span> P:A <span class="bold"><strong>→</strong></span> <span class="bold"><strong>Set</strong></span>.P x <span class="bold"><strong>→</strong></span> <span class="bold"><strong>∀</strong></span>y.eq A x y <span class="bold"><strong>→</strong></span> P y</td><td style="border-bottom: 0.5pt solid ; "><span class="bold"><strong>∀</strong></span>A.<span class="bold"><strong>∀</strong></span>a.<span class="bold"><strong>∀</strong></span> P:A <span class="bold"><strong>→</strong></span> <span class="bold"><strong>Set</strong></span>.P x <span class="bold"><strong>→</strong></span> <span class="bold"><strong>∀</strong></span>y.eq A y x <span class="bold"><strong>→</strong></span> P y</td><td style="border-bottom: 0.5pt solid ; "><span class="bold"><strong>∀</strong></span>A.<span class="bold"><strong>∀</strong></span>a.<span class="bold"><strong>∀</strong></span> P:A <span class="bold"><strong>→</strong></span> <span class="bold"><strong>Type</strong></span>.P x <span class="bold"><strong>→</strong></span> <span class="bold"><strong>∀</strong></span>y.eq A x y <span class="bold"><strong>→</strong></span> P y</td><td style="border-bottom: 0.5pt solid ; "><span class="bold"><strong>∀</strong></span>A.<span class="bold"><strong>∀</strong></span>a.<span class="bold"><strong>∀</strong></span> P:A <span class="bold"><strong>→</strong></span> <span class="bold"><strong>Type</strong></span>.P x <span class="bold"><strong>→</strong></span> <span class="bold"><strong>∀</strong></span>y.eq A y x <span class="bold"><strong>→</strong></span> P y</td><td style="border-bottom: 0.5pt solid ; "><span class="bold"><strong>∀</strong></span>A.<span class="bold"><strong>∀</strong></span>B.<span class="bold"><strong>∀</strong></span> f:A <span class="bold"><strong>→</strong></span> B.<span class="bold"><strong>∀</strong></span>x,y:A.eq A x y <span class="bold"><strong>→</strong></span> eq B (f x) (f y)</td><td style="border-bottom: 0.5pt solid ; "><span class="bold"><strong>∀</strong></span>A.<span class="bold"><strong>∀</strong></span>B.<span class="bold"><strong>∀</strong></span> f:A <span class="bold"><strong>→</strong></span> B.<span class="bold"><strong>∀</strong></span>x,y:A.eq A x y <span class="bold"><strong>→</strong></span> eq B (f y) (f x)</td></tr><tr><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">true</td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">an inductive type of type <span class="bold"><strong>Prop</strong></span> with only one constructor that has no arguments</td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; "> </td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; "> </td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; "> </td><td style="border-bottom: 0.5pt solid ; "> </td></tr><tr><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">false</td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; ">an inductive type of type <span class="bold"><strong>Prop</strong></span> without constructors</td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; "> </td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; "> </td><td style="border-right: 0.5pt solid ; border-bottom: 0.5pt solid ; "> </td><td style="border-bottom: 0.5pt solid ; "> </td></tr><tr><td style="border-right: 0.5pt solid ; ">absurd</td><td style="border-right: 0.5pt solid ; ">a theorem of type <span class="bold"><strong>∀</strong></span>A:Prop.<span class="bold"><strong>∀</strong></span>B:Prop.A <span class="bold"><strong>→</strong></span> Not A <span class="bold"><strong>→</strong></span> B</td><td style="border-right: 0.5pt solid ; "> </td><td style="border-right: 0.5pt solid ; "> </td><td style="border-right: 0.5pt solid ; "> </td><td style=""> </td></tr></tbody></table></div></div><br class="table-break" /></dd></dl></div><p>
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