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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">n</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:16_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <span class="p2">(<span class="default"><a href="euclid.html#K10" target="_self">abs</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K10" target="_self">abs</a> <font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span> <a href="square_1.html#K3">^2</a> 
<b>by </b><i><a class="ref" href="rvsum_1.html#T79">RVSUM_1:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> 
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span> <a href="square_1.html#K3">^2</a> 
<b>by </b><i><a class="ref" href="complex1.html#T161">COMPLEX1:161</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="euclid.html#K11" target="_self">sqr</a> <font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="rvsum_1.html#T78">RVSUM_1:78</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:16"/>
 <a href="rvsum_1.html#K12">sqr</a> <span class="p1">(<span class="default"><a href="euclid.html#K10" target="_self">abs</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K11" target="_self">sqr</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T139">FINSEQ_2:139</a></i>;<br/>


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