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meta name="generator" content="DocBook XSL Stylesheets V1.68.1" /><link rel="start" href="index.html" title="Matita V0.1.0 Manual (rev. 0)" /><link rel="up" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="prev" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="next" href="proofs.html" title="Proofs" /></head><body><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Definitions and declarations</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_terms.html">Prev</a> </td><th width="60%" align="center">Chapter 4. Syntax</th><td width="20%" align="right"> <a accesskey="n" href="proofs.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="axiom_definition_declaration"></a>Definitions and declarations</h2></div></div></div><div class="sect2" lang="en" xml:lang="en"><div class="titlepage"><div><div><h3 class="title"><a id="axiom"></a><span class="bold"><strong>axiom</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></h3></div></div></div><p><strong class="userinput"><code>axiom H: P</code></strong></p><p><span><strong class="command">H</strong></span> is declared as an axiom that states <span><strong class="command">P</strong></span></p></div><div class="sect2" lang="en" xml:lang="en"><div class="titlepage"><div><div><h3 class="title"><a id="definition"></a><span class="bold"><strong>definition</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>definition f: T ≝ t</code></strong></p><p><span><strong class="command">f</strong></span> is defined as <span><strong class="command">t</strong></span>;
+<html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Definitions and declarations</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 User Manual (rev. 1α)" /><link rel="up" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="prev" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="next" href="proofs.html" title="Proofs" /></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">Definitions and declarations</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_terms.html">Prev</a> </td><th width="60%" align="center">Chapter 4. Syntax</th><td width="20%" align="right"> <a accesskey="n" href="proofs.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="axiom_definition_declaration"></a>Definitions and declarations</h2></div></div></div><div class="sect2" lang="en" xml:lang="en"><div class="titlepage"><div><div><h3 class="title"><a id="axiom"></a><span class="bold"><strong>axiom</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></h3></div></div></div><p><strong class="userinput"><code>axiom H: P</code></strong></p><p><span><strong class="command">H</strong></span> is declared as an axiom that states <span><strong class="command">P</strong></span></p></div><div class="sect2" lang="en" xml:lang="en"><div class="titlepage"><div><div><h3 class="title"><a id="definition"></a><span class="bold"><strong>definition</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>definition f: T ≝ t</code></strong></p><p><span><strong class="command">f</strong></span> is defined as <span><strong class="command">t</strong></span>;
<span><strong class="command">T</strong></span> is its type. An error is raised if the type of
<span><strong class="command">t</strong></span> is not convertible to <span><strong class="command">T</strong></span>.</p><p><span><strong class="command">T</strong></span> is inferred from <span><strong class="command">t</strong></span> if
omitted.</p><p><span><strong class="command">t</strong></span> can be omitted only if <span><strong class="command">T</strong></span> is
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