<?xml version="1.0"?>
<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">R</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/>



<b>thus </b><a NAME="E1:39"/>
(  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">R</font> &amp; <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Maroon">R</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_1"/><i><font color="Green">E17</font></i>: 
(  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">R</font> &amp; <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<font color="Maroon">R</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="relat_1.html#K5">*</a> <font color="Maroon">R</font>
<b>by </b><i><a class="ref" href="relat_1.html#T94">RELAT_1:94</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sysrel.html#T13" target="_self">Th13</a>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sysrel.html#T13" target="_self">Th13</a>, <a class="ref" href="relat_1.html#T51">RELAT_1:51</a></i>
<br/>.= 
 <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E3:39_1"/>
<font color="Maroon">R</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:39"/>
(  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">R</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_2"/><i><font color="Green">E18</font></i>: 
(  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">R</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">R</font> = 
<font color="Maroon">R</font> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T123">RELAT_1:123</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="sysrel.html#T13" target="_self">Th13</a>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
<a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sysrel.html#T13" target="_self">Th13</a>, </i>
<br/>.= 
 <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E3:39_2"/>
<font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font>
 ;<br/>


</div><b>end;</b></div>


</div>
