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<b>let </b><font color="Maroon">A</font> be   <a href="roughs_1.html#NM2">Tolerance_Space</a>;<br/>

<b>assume </b><a NAME="E1:41"/>
 <a href="roughs_1.html#K3" target="_self">LAp</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:41"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="roughs_1.html#K3" target="_self">LAp</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E4:41"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">y</font> where <font color="Olive">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font> :  <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Olive">y</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">A</font> </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font><b> such that </b><br/><a NAME="E6:41"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp;  <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Maroon">y</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">A</font> )
 ;<br/>
<a NAME="E7:41"/>
 <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="roughs_1.html#T1" target="_self">Th1</a>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<b>hence </b><a NAME="E8:41"/>
contradiction
 <b>by </b><i><a class="ref" href="eqrel_1.html#T28">EQREL_1:28</a></i>;<br/>


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