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<b>assume </b><a NAME="E1:5"/>
 <a href="arytm_2.html#K2">REAL+</a>  <a href="subset_1.html#R2">meets</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="arytm_3.html#K13">{}</a> </span><a href="tarski.html#K1">}</a></span>,<a href="arytm_2.html#K2">REAL+</a> </span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<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="E3:5"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="arytm_2.html#K2">REAL+</a> 
 <b>and </b><br/><a NAME="E4:5"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="arytm_3.html#K13">{}</a> </span><a href="tarski.html#K1">}</a></span>,<a href="arytm_2.html#K2">REAL+</a> </span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:5"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="arytm_3.html#K13">{}</a> </span><a href="tarski.html#K1">}</a></span>
 <b>and </b><br/><a NAME="E7:5"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="arytm_2.html#K2">REAL+</a>  &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T103">ZFMISC_1:103</a></i>;<br/>
<a NAME="E8:5"/>
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a>  <a href="arytm_3.html#K13">{}</a> 
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E9:5"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="arytm_2.html#T3">ARYTM_2:3</a></i>;<br/>


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