<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>assume </b><a NAME="E1:28"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font>
 ;<br/>

<a NAME="E2:28"/><b>then </b>
<font color="Maroon">g</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T105">RELAT_1:105</a></i>;<br/>
<a NAME="E3:28"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>;<br/>
<a NAME="E4:28"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">g</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:28_1"/><i><font color="Green">E22</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span>
 ;<br/>

<a NAME="E2:28_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#D11">RELAT_1:def 11</a></i>;<br/>
<a NAME="E3:28_1"/><b>then </b><i><font color="Green">E27</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>;<br/>
<a NAME="E4:28_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> )
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#D11">RELAT_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E5:28_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">g</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D1">FUNCT_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:28"/><b>then </b>
<font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#D3">RELAT_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:28"/>
<font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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