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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   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>



<b>thus </b><a NAME="E1:11"/>
<font color="Maroon">r</font> <a href="integra2.html#K1" target="_self">*</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Olive">x</font></span>)</span> where <font color="Olive">x</font> is   <a href="real_1.html#NM1">Real</a> : <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">y</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><br/>

<b>assume </b><a NAME="E1:11_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">r</font> <a href="integra2.html#K1" target="_self">*</a> <font color="Maroon">X</font>
 ;<br/>

<b>then consider </b><font color="Maroon">z</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:11_1"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">z</font> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E4:11_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Olive">x</font></span>)</span> where <font color="Olive">x</font> is   <a href="real_1.html#NM1">Real</a> : <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> </span>}</span> 
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">y</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><br/>

<b>assume </b><a NAME="E2:11"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Olive">x</font></span>)</span> where <font color="Olive">x</font> is   <a href="real_1.html#NM1">Real</a> : <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">z</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:11"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">z</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 ;<br/>
<b>thus </b><a NAME="E5:11"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">r</font> <a href="integra2.html#K1" target="_self">*</a> <font color="Maroon">X</font>
 <b>by </b><i>, </i>;<br/>


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