<?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">P1</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/><b>let </b><font color="Maroon">P2</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/>





<b>assume </b><a NAME="E1:124"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">P1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P2</font>
 ;<br/>

<a NAME="E2:124"/>
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">Y</font> <a href="relat_1.html#K8" target="_self">|</a> <font color="Maroon">P1</font> 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">Y</font> <a href="relat_1.html#K8" target="_self">|</a> <font color="Maroon">P2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="124_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="E1:124_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">Y</font> <a href="relat_1.html#K8" target="_self">|</a> <font color="Maroon">P1</font>
 ;<br/>

<a NAME="E2:124_1"/><b>then </b>
( <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">P1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T21" target="_self">Th21</a></i>;<br/>
<b>hence </b><a NAME="E3:124_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">Y</font> <a href="relat_1.html#K8" target="_self">|</a> <font color="Maroon">P2</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T44" target="_self">Th44</a>, <a class="ref" href="relat_1.html#T21" target="_self">Th21</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:124"/>
<font color="Maroon">Y</font> <a href="relat_1.html#K8" target="_self">|</a> <font color="Maroon">P1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> <a href="relat_1.html#K8" target="_self">|</a> <font color="Maroon">P2</font>
 <b>by </b><i/>;<br/>


</div>
