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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>thus </b><span class="p1"><a href="euclid.html#K12" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K6" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="euclid.html#K12" target="_self">.|</a></span> = 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><a href="euclid.html#K11" target="_self">sqr</a> <span class="p3">(<span class="default"><a href="euclid.html#K6" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <span class="p3">(<span class="default"><a href="euclid.html#K10" target="_self">abs</a> <span class="p4">(<span class="default"><a href="euclid.html#K6" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclid.html#E13"><i><font color="Green">Lemma8</font></i></a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <span class="p3">(<span class="default"><a href="euclid.html#K10" target="_self">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T8" target="_self">Th8</a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><a href="euclid.html#K11" target="_self">sqr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclid.html#E13"><i><font color="Green">Lemma8</font></i></a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K12" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="euclid.html#K12" target="_self">.|</a></span>

;<br/>


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