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

<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">T</font> be   <a href="eqrel_1.html#NM1" title="EQREL_1:NM.1">Tolerance</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><a NAME="E1:29"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is   <a href="toler_1.html#NM2" title="TOLER_1:NM.2">TolClass</a> of <font color="Maroon" title="c2">T</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c3">00</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="toler_1.html#NM2" title="TOLER_1:NM.2">TolClass</a> of <font color="Maroon" title="c2">T</font> ;<br/>
<b>assume </b><a NAME="E3:29"/>
<font color="Maroon" title="c2">T</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:29"/><i><font color="Green" title="E15">A1</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T56" title="RELAT_1:th.56">RELAT_1:56</a></i>;<br/>
<a NAME="E6:29"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="toler_1.html#E5:29"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E7:29"/><b>then </b>
 ex <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">00</font> &amp; not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Olive" title="b1">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">T</font> )
 
<b>by </b><i><a class="ref" href="toler_1.html#D4" target="_self" title="TOLER_1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E8:29"/>
contradiction
 ;<br/>


</div>
