<?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">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="E2:32"/>
 <a href="euclid.html#K6">-</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K19">-</a> <font color="Maroon">w</font>
 
<b>by </b><i><a class="ref" href="euclid.html#D12">EUCLID:def 12</a></i>;<br/>
<b>then </b><span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K19">-</a> <font color="Maroon">w</font></span>)</span></span><a href="toprns_1.html#K5" target="_self">.|</a></span> = 
<span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K6">-</a> <font color="Maroon">s</font></span>)</span></span><a href="euclid.html#K12">.|</a></span>
<b>by </b><i/>
<br/>.= 
<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>
<b>by </b><i><a class="ref" href="euclid.html#T13">EUCLID:13</a></i>
<br/>.= 
<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>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E4:32"/>
<span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K19">-</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="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>
 ;<br/>


</div>
