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<b>let </b><font color="Maroon">r</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">s</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:46"/><i><font color="Green">E41</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2" target="_self">].</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_1.html#K2" target="_self">.[</a></span> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a><br/>

<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="rcomp_1.html#K2" target="_self">].</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_1.html#K2" target="_self">.[</a></span> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K2">}</a></span>;<br/>
<a NAME="E3:46"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2" target="_self">].</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_1.html#K2" target="_self">.[</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K2">}</a></span> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">r1</font> = <font color="Maroon">x</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E5:46"/>
<font color="Maroon">r1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">s1</font> where <font color="Olive">s1</font> is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">s1</font> &amp; <font color="Olive">s1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">s</font> ) </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">s1</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E7:46"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font> &amp; <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">s1</font> &amp; <font color="Maroon">s1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">s</font> )
 ;<br/>
<b>thus </b><a NAME="E8:46"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>


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