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<b>set </b><font color="Maroon">R</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">r</font>,<font color="Olive">s</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">r</font> is   <a href="real_1.html#NM1">Real</a>, <font color="Olive">s</font> is   <a href="real_1.html#NM1">Real</a> : <font color="Olive">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">s</font> </span>}</span> ;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="relset_1.html#D1">RELSET_1:def 1</a><br/>

<b>assume </b><a NAME="E1:8_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">r</font>,<font color="Olive">s</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">r</font> is   <a href="real_1.html#NM1">Real</a>, <font color="Olive">s</font> is   <a href="real_1.html#NM1">Real</a> : <font color="Olive">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">s</font> </span>}</span> 
 ;<br/>

<a NAME="E2:8_1_1"/><b>then </b>
 ex <font color="Olive">r</font>, <font color="Olive">s</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <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="Olive">r</font>,<font color="Olive">s</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Olive">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">s</font> )
 
;<br/>
<b>hence </b><a NAME="E3:8_1_1"/>
<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"><a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> </span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>


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