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   3 <html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Proofs</title><link rel="stylesheet" href="docbook.css" type="text/css" /><meta name="generator" content="DocBook XSL Stylesheets V1.68.1" /><link rel="start" href="index.html" title="Matita V0.1.0&#10; User Manual (rev. 1α)" /><link rel="up" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="prev" href="axiom_definition_declaration.html" title="Definitions and declarations" /><link rel="next" href="sec_usernotation.html" title="Chapter 5. Extending the syntax" /></head><body><a xmlns="" href="../../"><div class="matita_logo"><img src="../../images/matita-tiny.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">Proofs</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="axiom_definition_declaration.html">Prev</a> </td><th width="60%" align="center">Chapter 4. Syntax</th><td width="20%" align="right"> <a accesskey="n" href="sec_usernotation.html">Next</a></td></tr></table><hr /></div><div class="sect1" lang="en" xml:lang="en"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="proofs"></a>Proofs</h2></div></div></div><div class="sect2" lang="en" xml:lang="en"><div class="titlepage"><div><div><h3 class="title"><a id="theorem"></a><span class="bold"><strong>theorem</strong></span> <span class="emphasis"><em><a href="sec_terms.html#id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a href="sec_terms.html#term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a href="sec_terms.html#term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>theorem f: P ≝ p</code></strong></p><p>Proves a new theorem <span><strong class="command">f</strong></span> whose thesis is
   4      <span><strong class="command">P</strong></span>.</p><p>If <span><strong class="command">p</strong></span> is provided, it must be a proof term for
   5      <span><strong class="command">P</strong></span>. Otherwise an interactive proof is started.</p><p><span><strong class="command">P</strong></span> can be omitted only if the proof is not
   6      interactive.</p><p>Proving a theorem already proved in the library is an error.
   7      To provide an alternative name and proof for the same theorem, use
   8      <span><strong class="command">variant f: P ≝ p</strong></span>.</p><p>A warning is raised if the name of the theorem cannot be obtained
   9       by mangling the name of the constants in its thesis.</p><p>Notice that the command is equivalent to <span><strong class="command">definition f: T ≝ t</strong></span>.</p></div><div class="sect2" lang="en" xml:lang="en"><div class="titlepage"><div><div><h3 class="title"><a id="variant"></a><span class="bold"><strong>variant</strong></span> <span class="emphasis"><em><a href="sec_terms.html#id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a href="sec_terms.html#term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a href="sec_terms.html#term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>variant f: T ≝ t</code></strong></p><p>Same as <span><strong class="command">theorem f: T ≝ t</strong></span>, but it does not
  10      complain if the theorem has already been proved. To be used to give
  11      an alternative name or proof to a theorem.</p></div><div class="sect2" lang="en" xml:lang="en"><div class="titlepage"><div><div><h3 class="title"><a id="lemma"></a><span class="bold"><strong>lemma</strong></span> <span class="emphasis"><em><a href="sec_terms.html#id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a href="sec_terms.html#term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a href="sec_terms.html#term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>lemma f: T ≝ t</code></strong></p><p>Same as <span><strong class="command">theorem f: T ≝ t</strong></span></p></div><div class="sect2" lang="en" xml:lang="en"><div class="titlepage"><div><div><h3 class="title"><a id="fact"></a><span class="bold"><strong>fact</strong></span> <span class="emphasis"><em><a href="sec_terms.html#id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a href="sec_terms.html#term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a href="sec_terms.html#term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>fact f: T ≝ t</code></strong></p><p>Same as <span><strong class="command">theorem f: T ≝ t</strong></span></p></div><div class="sect2" lang="en" xml:lang="en"><div class="titlepage"><div><div><h3 class="title"><a id="remark"></a><span class="bold"><strong>remark</strong></span> <span class="emphasis"><em><a href="sec_terms.html#id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a href="sec_terms.html#term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a href="sec_terms.html#term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>remark f: T ≝ t</code></strong></p><p>Same as <span><strong class="command">theorem f: T ≝ t</strong></span></p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="axiom_definition_declaration.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_terms.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_usernotation.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Definitions and declarations </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 5. Extending the syntax</td></tr></table></div></body></html>