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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:2"/><i><font color="Green" title="E2">A1</font></i>: 
 <a href="toler_1.html#NK1" title="TOLER_1:NK.1">Total</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<b>assume </b><a NAME="E2:2"/>
not <font color="Maroon" title="c1">X</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:2"/><i><font color="Green" title="E3">A2</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font> )
 <b>by </b><i><a class="ref" href="realset1.html#T14" title="REALSET1:th.14">REALSET1:14</a></i>;<br/>
<a NAME="E5:2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">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>  <a href="toler_1.html#NK1" title="TOLER_1:NK.1">Total</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="roughs_1.html#E4:2"><i><font color="Green" title="E3">A2</font></i></a>, <a class="ref" href="toler_1.html#T15" title="TOLER_1:th.15">TOLER_1:15</a></i>;<br/>
<b>hence </b><a NAME="E6:2"/>
contradiction
 <b>by </b><i><a class="txt" href="roughs_1.html#E1:2"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="roughs_1.html#E4:2"><i><font color="Green" title="E3">A2</font></i></a>, <a class="ref" href="relat_1.html#D10" title="RELAT_1:def.10">RELAT_1:def 10</a></i>;<br/>


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