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

<b>thus </b><a NAME="E1:80_1_1"/>
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> implies for <font color="Olive">r</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds <br/> ( <font color="Olive">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff <font color="Olive">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> ) )
 ;<br/>

<b>assume </b><a NAME="E2:80_1_1"/>
for <font color="Olive">r</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds <br/> ( <font color="Olive">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff <font color="Olive">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 ;<br/>

<a NAME="E3:80_1_1"/><b>then </b>
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:80_1_1"/>
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


</div>
