<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">N</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">w</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">N</font></span>)</span>;<br/>





<b>reconsider </b><font color="Maroon">s</font> = <font color="Maroon">w</font> as    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">N</font> <b>by </b><i><a class="ref" href="euclid.html#T25">EUCLID:25</a></i>;<br/>
<a NAME="E2:15"/>
<font color="Maroon">r</font> <a href="euclid.html#K18">*</a> <font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="euclid.html#K9">*</a> <font color="Maroon">s</font>
 
<b>by </b><i><a class="ref" href="euclid.html#D11">EUCLID:def 11</a></i>;<br/>
<a NAME="E3:15"/><b>then </b>
( <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">s</font></span><a href="euclid.html#K12">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> &amp; <span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="euclid.html#K18">*</a> <font color="Maroon">w</font></span>)</span></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="euclid.html#K9">*</a> <font color="Maroon">s</font></span>)</span></span><a href="euclid.html#K12">.|</a></span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:15"/>
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="euclid.html#K18">*</a> <font color="Maroon">w</font></span>)</span></span><a href="toprns_1.html#K5" target="_self">.|</a></span>
 <b>by </b><i><a class="ref" href="euclid.html#T14">EUCLID:14</a></i>;<br/>


</div>
