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

<b>consider </b><font color="Maroon">M</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:6_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 <b>and </b><br/><a NAME="E3:6_1_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Olive">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">X</font> holds <br/><font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 <b>and </b><br/><a NAME="E4:6_1_1"/>
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> holds <br/> ex <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; ( for <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">X</font> holds <br/><font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Olive">Z</font> ) )
 <b>and </b><br/><a NAME="E5:6_1_1"/>
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   holds <br/>(  not <font color="Olive">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">M</font> or <font color="Olive">X</font>,<font color="Maroon">M</font> <a href="tarski.html#R2">are_equipotent</a>  or <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> )
 <b>by </b><i><a class="ref" href="tarski.html#T9">TARSKI:9</a></i>;<br/>
<b>consider </b><font color="Maroon">IT</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:6_1_1"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> iff ( <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">Y</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon">IT</font>
;<br/>

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

<b>thus </b><a NAME="E8:6_1_1"/>
( <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> implies <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E9:6_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E10:6_1_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E11:6_1_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 <b>by </b><i>, </i>;<br/>


</div>
