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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<a NAME="E1:25"/><i><font color="Green">E17</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K1">REAL</a> 2
 
<b>by </b><i><a class="ref" href="euclid.html#T25">EUCLID:25</a></i>;<br/>
<span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="euclid.html#K12">.|</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="rvsum_1.html#K11">sqr</a> <span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></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"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p3">(<span class="default">0 <a href="square_1.html#K5">^2</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="topreal6.html#T16" target="_self">Th16</a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">0 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T107">RVSUM_1:107</a></i>
<br/>.= 
 <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="complex1.html#T158">COMPLEX1:158</a></i>
;<br/>
<b>hence </b><a NAME="E3:25"/>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="euclid.html#K23">]|</a></span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="topreal6.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="ref" href="jgraph_1.html#D5">JGRAPH_1:def 5</a></i>;<br/>

<span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,0</span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="euclid.html#K12">.|</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="rvsum_1.html#K11">sqr</a> <span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,0</span><a href="finseq_4.html#K2">*&gt;</a></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"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span>,<span class="p3">(<span class="default">0 <a href="square_1.html#K5">^2</a> </span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="topreal6.html#T16" target="_self">Th16</a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T107">RVSUM_1:107</a></i>
<br/>.= 
 <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="complex1.html#T158">COMPLEX1:158</a></i>
;<br/>
<b>hence </b><a NAME="E5:25"/>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,0</span><a href="euclid.html#K23">]|</a></span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="topreal6.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="ref" href="jgraph_1.html#D5">JGRAPH_1:def 5</a></i>;<br/>


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