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

<b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">R</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/>



<b>assume </b><a NAME="E1:77"/><i><font color="Green">E31</font></i>: 
 <a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">R</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E2:77"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">R</font> <a href="relat_1.html#K5" target="_self">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" target="_self">id</a> <font color="Maroon">Y</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">R</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:77"/>
<font color="Maroon">R</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">R</font> <a href="relat_1.html#K5" target="_self">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" target="_self">id</a> <font color="Maroon">Y</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_1.html#D3" target="_self">RELAT_1:def 3</a><br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:77_1"/><i><font color="Green">E37</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">R</font>
 ;<br/>

<a NAME="E2:77_1"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">R</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:77_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K6" target="_self">id</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="txt" href="relat_1.html#E1:77"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:77_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">R</font> <a href="relat_1.html#K5" target="_self">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" target="_self">id</a> <font color="Maroon">Y</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:77"/>
<font color="Maroon">R</font> <a href="relat_1.html#K5" target="_self">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" target="_self">id</a> <font color="Maroon">Y</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


</div>
