<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="csspace.html#NM1">ComplexUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>





<a NAME="E1:58"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>4</sub></font>) implies <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:58_1"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>4</sub></font>)
 ;<br/>

<a NAME="E2:58_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K5">0c</a> 
 
<b>by </b><i><a class="ref" href="csspace.html#D13" target="_self">Def13</a></i>;<br/>
<b>hence </b><a NAME="E3:58_1"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="csspace.html#E1:58_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="csspace.html#T32" target="_self">Th32</a>, <a class="ref" href="complex1.html#T130">COMPLEX1:130</a>, <a class="ref" href="square_1.html#T82">SQUARE_1:82</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:58"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>4</sub></font>) implies <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:58_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>4</sub></font>)
 ;<br/>

<a NAME="E2:58_2"/><b>then </b><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 
<b>by </b><i><a class="ref" href="csspace.html#D13" target="_self">Def13</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  <b>by </b><i><a class="ref" href="xcmplx_0.html#D2">XCMPLX_0:def 2</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="complex1.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<a NAME="E4:58_2"/><i><font color="Green">E56</font></i>: 
(  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp;  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="csspace.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E5:58_2"/><b>then </b>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<a NAME="E6:58_2"/><b>then </b><i><font color="Green">E57</font></i>: 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T29">COMPLEX1:29</a></i>;<br/>
<a NAME="E7:58_2"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="csspace.html#E4:58_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="complex1.html#T29">COMPLEX1:29</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="clvect_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="clvect_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="csspace.html#K12" target="_self">.|.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="clvect_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="clvect_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="csspace.html#E61"><i><font color="Green">Lemma51</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="csspace.html#E4:58_2"><i><font color="Green">E56</font></i></a>, <a class="txt" href="csspace.html#E6:58_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="complex1.html#T29">COMPLEX1:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="csspace.html#E7:58_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="csspace.html#D13" target="_self">Def13</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="csspace.html#E7:58_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="csspace.html#D13" target="_self">Def13</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>

;<br/>
<a NAME="E9:58_2"/><b>then </b><i><font color="Green">E59</font></i>: 
(  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp;  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="csspace.html#D13" target="_self">Def13</a></i>;<br/>
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T24">COMPLEX1:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">0 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>

;<br/>
<a NAME="E11:58_2"/><b>then </b><i><font color="Green">E60</font></i>: 
( (  <a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp;  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 ) or (  <a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 &amp;  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0 ) )
 
<b>by </b><i><a class="txt" href="csspace.html#E9:58_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="square_1.html#T25">SQUARE_1:25</a></i>;<br/>
<a NAME="E12:58_2"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="csspace.html#E2:58_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="complex1.html#T131">COMPLEX1:131</a></i>;<br/>
<a NAME="E13:58_2"/><b>then </b><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="csspace.html#E4:58_2"><i><font color="Green">E56</font></i></a>, <a class="txt" href="csspace.html#E6:58_2"><i><font color="Green">E57</font></i></a>, <a class="txt" href="csspace.html#E11:58_2"><i><font color="Green">E60</font></i></a>, <a class="ref" href="complex1.html#T29">COMPLEX1:29</a>, <a class="ref" href="complex1.html#T19">COMPLEX1:19</a></i>;<br/>
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> = 
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T34">COMPLEX1:34</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="csspace.html#D13" target="_self">Def13</a></i>
;<br/>
<a NAME="E15:58_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="csspace.html#E13:58_2"><i><font color="Green">E61</font></i></a></i>;<br/>
<a NAME="E16:58_2"/><b>then </b><i><font color="Green">E62</font></i>: 
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/>
<a NAME="E17:58_2"/><i><font color="Green">E63</font></i>: 
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T126">COMPLEX1:126</a></i>;<br/>
<a NAME="E18:58_2"/>
( <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/>
<a NAME="E19:58_2"/><b>then </b><i><font color="Green">E64</font></i>: 
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 0
 
<b>by </b><i><a class="txt" href="csspace.html#E17:58_2"><i><font color="Green">E63</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E20:58_2"/><b>then </b>
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<a NAME="E21:58_2"/><b>then </b><i><font color="Green">E65</font></i>: 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="csspace.html#E16:58_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="csspace.html#E19:58_2"><i><font color="Green">E64</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<a NAME="E22:58_2"/>
(  <a href="complex1.html#K4">Im</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="txt" href="csspace.html#E4:58_2"><i><font color="Green">E56</font></i></a>, <a class="txt" href="csspace.html#E6:58_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="csspace.html#D13" target="_self">Def13</a>, <a class="ref" href="complex1.html#T29">COMPLEX1:29</a></i>;<br/>
<a NAME="E23:58_2"/><b>then </b><i><font color="Green">E66</font></i>: 
 <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K4">*</a> 0</span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> 0</span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T24">COMPLEX1:24</a></i>;<br/>
<a NAME="E24:58_2"/><b>then </b><i><font color="Green">E67</font></i>: 
(  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="complex1.html#T126">COMPLEX1:126</a></i>;<br/>
<a NAME="E25:58_2"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="csspace.html#E23:58_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="complex1.html#T136">COMPLEX1:136</a></i>;<br/>
<a NAME="E26:58_2"/><b>then </b>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
 
<b>by </b><i><a class="txt" href="csspace.html#E21:58_2"><i><font color="Green">E65</font></i></a>, <a class="txt" href="csspace.html#E24:58_2"><i><font color="Green">E67</font></i></a>, <a class="ref" href="complex1.html#T136">COMPLEX1:136</a></i>;<br/>
<a NAME="E27:58_2"/><b>then </b>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span>)</span></span><a href="complex1.html#K17">.|</a></span>
 
<b>by </b><i><a class="txt" href="csspace.html#E7:58_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="complex1.html#T151">COMPLEX1:151</a></i>;<br/>
<a NAME="E28:58_2"/><b>then </b>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="complex1.html#K15">*'</a> </span>)</span></span><a href="complex1.html#K17">.|</a></span>
 
<b>by </b><i><a class="ref" href="complex1.html#T151">COMPLEX1:151</a></i>;<br/>
<a NAME="E29:58_2"/><b>then </b>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span>
 
<b>by </b><i><a class="ref" href="complex1.html#T139">COMPLEX1:139</a></i>;<br/>
<a NAME="E30:58_2"/><b>then </b><i><font color="Green">E68</font></i>: 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="square_1.html#K5">^2</a> 
 
;<br/>
<a NAME="E31:58_2"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/>
<a NAME="E32:58_2"/><b>then </b><i><font color="Green">E69</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="csspace.html#E30:58_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="square_1.html#T94">SQUARE_1:94</a></i>;<br/>
<a NAME="E33:58_2"/><i><font color="Green">E70</font></i>: 
( <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="ref" href="complex1.html#T132">COMPLEX1:132</a></i>;<br/>
<a NAME="E34:58_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="csspace.html#E32:58_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="square_1.html#T97">SQUARE_1:97</a></i>;<br/>
<b>hence </b><a NAME="E35:58_2"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="csspace.html#E33:58_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="square_1.html#T89">SQUARE_1:89</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:58"/>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2"><a href="complex1.html#K17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="csspace.html#K12" target="_self">.|.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="csspace.html#E1:58"><i><font color="Green">E54</font></i></a></i>;<br/>


</div>
