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<b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>



<b>consider </b><font color="Maroon">x</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E2:10"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E4:10"/>
 ex <font color="Olive">z</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Olive">z</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:10"/>
not <font color="Maroon">r</font> <a href="integra2.html#K1" target="_self">*</a> <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i/>;<br/>


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