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<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">w1</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>let </b><font color="Maroon">w2</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">s1</font> = <font color="Maroon">w1</font>, <font color="Maroon">s2</font> = <font color="Maroon">w2</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="E2:38"/>
<font color="Maroon">s1</font> <a href="euclid.html#K7">+</a> <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w1</font> <a href="euclid.html#K17">+</a> <font color="Maroon">w2</font>
 
<b>by </b><i><a class="ref" href="euclid.html#D10">EUCLID:def 10</a></i>;<br/>
<a NAME="E3:38"/><b>then </b><i><font color="Green">E44</font></i>: 
<span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">w1</font> <a href="euclid.html#K17">+</a> <font color="Maroon">w2</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">s1</font> <a href="euclid.html#K7">+</a> <font color="Maroon">s2</font></span>)</span></span><a href="euclid.html#K12">.|</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:38"/><i><font color="Green">E45</font></i>: 
<span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">s1</font></span><a href="euclid.html#K12">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">s2</font></span><a href="euclid.html#K12">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K7">+</a> <font color="Maroon">s2</font></span>)</span></span><a href="euclid.html#K12">.|</a></span>
 
<b>by </b><i><a class="ref" href="euclid.html#T17">EUCLID:17</a></i>;<br/>
<a NAME="E5:38"/>
<span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">s1</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">w1</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:38"/>
<span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w1</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="real_1.html#K5">-</a> <span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w2</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</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">w1</font> <a href="euclid.html#K17">+</a> <font color="Maroon">w2</font></span>)</span></span><a href="toprns_1.html#K5" target="_self">.|</a></span>
 <b>by </b><i>, , </i>;<br/>


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