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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></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> 2</span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><a NAME="E1:63"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 </span>}</span>  &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 ;<br/>

<a NAME="E2:63"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="topreal2.html#NR1" target="_self">is_simple_closed_curve</a> 
 
<b>by </b><i><a class="ref" href="jgraph_3.html#T36">JGRAPH_3:36</a></i>;<br/>
<a NAME="E3:63"/><b>then </b><i><font color="Green">E61</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 </span>}</span>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="ref" href="jordan7.html#T5">JORDAN7:5</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E5:63"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="ref" href="xreal_1.html#T7">XREAL_1:7</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>;<br/>
<a NAME="E7:63"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E5:63"><i><font color="Green">E62</font></i></a>, <a class="ref" href="jgraph_5.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E8:63"/><b>then </b><i><font color="Green">E63</font></i>: 
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E10:63"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>9</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E3:63"><i><font color="Green">E61</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E12:63"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>10</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E3:63"><i><font color="Green">E61</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E14:63"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>11</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E3:63"><i><font color="Green">E61</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E16:63"/><i><font color="Green">E67</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>12</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E3:63"><i><font color="Green">E61</font></i></a></i>;<br/>
<a NAME="E17:63"/>
 <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E10:63"><i><font color="Green">E64</font></i></a>, <a class="ref" href="jgraph_5.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E18:63"/><b>then </b><i><font color="Green">E68</font></i>: 
 <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E5:63"><i><font color="Green">E62</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E19:63"/>
<font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E5:63"><i><font color="Green">E62</font></i></a></i>;<br/>
<a NAME="E20:63"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E18:63"><i><font color="Green">E68</font></i></a>, <a class="ref" href="jgraph_2.html#T7">JGRAPH_2:7</a></i>;<br/>
<a NAME="E21:63"/><b>then </b><i><font color="Green">E69</font></i>: 
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E22:63"/><b>then </b><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>;<br/>
<a NAME="E23:63"/><b>then </b>
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E5:63"><i><font color="Green">E62</font></i></a>, <a class="ref" href="square_1.html#T74">SQUARE_1:74</a></i>;<br/>
<a NAME="E24:63"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<a NAME="E25:63"/><b>then </b><i><font color="Green">E71</font></i>: 
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> &amp;  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 
<b>by </b><i><a class="ref" href="jgraph_4.html#T5">JGRAPH_4:5</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E27:63"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="jgraph_4.html#K3">-FanMorphW</a>  &amp; <font color="Maroon">c<sub>13</sub></font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  )
 <b>by </b><i><a class="ref" href="jgraph_4.html#T48">JGRAPH_4:48</a></i>;<br/>
<a NAME="E28:63"/><i><font color="Green">E73</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> holds <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T40">JGRAPH_4:40</a></i>;<br/>
<a NAME="E29:63"/><i><font color="Green">E74</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E21:63"><i><font color="Green">E69</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E30:63"/><i><font color="Green">E75</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E12:63"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T40">JGRAPH_4:40</a></i>;<br/>
<a NAME="E31:63"/><b>then </b><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a></i>;<br/>
<a NAME="E32:63"/><i><font color="Green">E77</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E14:63"><i><font color="Green">E66</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T40">JGRAPH_4:40</a></i>;<br/>
<a NAME="E33:63"/><b>then </b><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a></i>;<br/>
<a NAME="E34:63"/><i><font color="Green">E79</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E16:63"><i><font color="Green">E67</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T40">JGRAPH_4:40</a></i>;<br/>
<a NAME="E35:63"/><b>then </b><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a></i>;<br/>
<a NAME="E36:63"/><i><font color="Green">E81</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E10:63"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T40">JGRAPH_4:40</a></i>;<br/>
<a NAME="E37:63"/><b>then </b><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a></i>;<br/>
<a NAME="E38:63"/><i><font color="Green">E83</font></i>: 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/>
<a NAME="E39:63"/><i><font color="Green">E84</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="ref" href="jgraph_5.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E40:63"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="ref" href="jgraph_5.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E41:63"/><i><font color="Green">E86</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a>  or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="ref" href="jgraph_5.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E42:63"/><b>then </b><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E40:63"><i><font color="Green">E85</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E43:63"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E39:63"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E44:63"/><b>then </b>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/>
<a NAME="E45:63"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E38:63"><i><font color="Green">E83</font></i></a>, <a class="ref" href="square_1.html#T77">SQUARE_1:77</a></i>;<br/>
<a NAME="E46:63"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 
;<br/>
<a NAME="E47:63"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 
;<br/>
<a NAME="E48:63"/><b>then </b>
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/>
<a NAME="E49:63"/><b>then </b><i><font color="Green">E88</font></i>: 
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E8:63"><i><font color="Green">E63</font></i></a>, <a class="txt" href="jgraph_5.html#E22:63"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E50:63"/><i><font color="Green">E89</font></i>: 
1 <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </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"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E12:63"><i><font color="Green">E65</font></i></a>, <a class="ref" href="jgraph_3.html#T10">JGRAPH_3:10</a></i>;<br/>
<a NAME="E51:63"/><i><font color="Green">E90</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E12:63"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E29:63"><i><font color="Green">E74</font></i></a>, <a class="txt" href="jgraph_5.html#E49:63"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_5.html#E50:63"><i><font color="Green">E89</font></i></a>, <a class="ref" href="jgraph_2.html#T6">JGRAPH_2:6</a></i>;<br/>
<a NAME="E52:63"/><b>then </b><i><font color="Green">E91</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E25:63"><i><font color="Green">E71</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T50">JGRAPH_4:50</a></i>;<br/>
<a NAME="E53:63"/>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E42:63"><i><font color="Green">E87</font></i></a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/>
<a NAME="E54:63"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E38:63"><i><font color="Green">E83</font></i></a>, <a class="ref" href="square_1.html#T77">SQUARE_1:77</a></i>;<br/>
<a NAME="E55:63"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 
;<br/>
<a NAME="E56:63"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 
;<br/>
<a NAME="E57:63"/><b>then </b>
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/>
<a NAME="E58:63"/><b>then </b><i><font color="Green">E92</font></i>: 
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E8:63"><i><font color="Green">E63</font></i></a>, <a class="txt" href="jgraph_5.html#E22:63"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E59:63"/><i><font color="Green">E93</font></i>: 
1 <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a> </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"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E14:63"><i><font color="Green">E66</font></i></a>, <a class="ref" href="jgraph_3.html#T10">JGRAPH_3:10</a></i>;<br/>
<a NAME="E60:63"/><i><font color="Green">E94</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E14:63"><i><font color="Green">E66</font></i></a>, <a class="txt" href="jgraph_5.html#E29:63"><i><font color="Green">E74</font></i></a>, <a class="txt" href="jgraph_5.html#E58:63"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_5.html#E59:63"><i><font color="Green">E93</font></i></a>, <a class="ref" href="jgraph_2.html#T6">JGRAPH_2:6</a></i>;<br/>
<a NAME="E61:63"/><b>then </b><i><font color="Green">E95</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E25:63"><i><font color="Green">E71</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T50">JGRAPH_4:50</a></i>;<br/>
<a NAME="E62:63"/>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E41:63"><i><font color="Green">E86</font></i></a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/>
<a NAME="E63:63"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E38:63"><i><font color="Green">E83</font></i></a>, <a class="ref" href="square_1.html#T77">SQUARE_1:77</a></i>;<br/>
<a NAME="E64:63"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 
;<br/>
<a NAME="E65:63"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 
;<br/>
<a NAME="E66:63"/><b>then </b>
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/>
<a NAME="E67:63"/><b>then </b><i><font color="Green">E96</font></i>: 
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E8:63"><i><font color="Green">E63</font></i></a>, <a class="txt" href="jgraph_5.html#E22:63"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E68:63"/><i><font color="Green">E97</font></i>: 
1 <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </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"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E16:63"><i><font color="Green">E67</font></i></a>, <a class="ref" href="jgraph_3.html#T10">JGRAPH_3:10</a></i>;<br/>
<a NAME="E69:63"/><i><font color="Green">E98</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E16:63"><i><font color="Green">E67</font></i></a>, <a class="txt" href="jgraph_5.html#E29:63"><i><font color="Green">E74</font></i></a>, <a class="txt" href="jgraph_5.html#E67:63"><i><font color="Green">E96</font></i></a>, <a class="txt" href="jgraph_5.html#E68:63"><i><font color="Green">E97</font></i></a>, <a class="ref" href="jgraph_2.html#T6">JGRAPH_2:6</a></i>;<br/>
<a NAME="E70:63"/><b>then </b><i><font color="Green">E99</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E25:63"><i><font color="Green">E71</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T50">JGRAPH_4:50</a></i>;<br/>
<a NAME="E71:63"/><i><font color="Green">E100</font></i>: 
1 <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a> </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"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E10:63"><i><font color="Green">E64</font></i></a>, <a class="ref" href="jgraph_3.html#T10">JGRAPH_3:10</a></i>;<br/>
<a NAME="E72:63"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E8:63"><i><font color="Green">E63</font></i></a>, <a class="txt" href="jgraph_5.html#E10:63"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E22:63"><i><font color="Green">E70</font></i></a>, <a class="txt" href="jgraph_5.html#E29:63"><i><font color="Green">E74</font></i></a>, <a class="txt" href="jgraph_5.html#E71:63"><i><font color="Green">E100</font></i></a>, <a class="ref" href="jgraph_2.html#T6">JGRAPH_2:6</a></i>;<br/>
<a NAME="E73:63"/><b>then </b><i><font color="Green">E101</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E25:63"><i><font color="Green">E71</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="txt" href="jgraph_5.html#E51:63"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_5.html#E60:63"><i><font color="Green">E94</font></i></a>, <a class="txt" href="jgraph_5.html#E69:63"><i><font color="Green">E98</font></i></a>, <a class="ref" href="jgraph_4.html#T50">JGRAPH_4:50</a></i>;<br/>
<a NAME="E74:63"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="toprns_1.html#K5">.|</a></span> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E12:63"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E14:63"><i><font color="Green">E66</font></i></a>, <a class="ref" href="jgraph_5.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E75:63"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E25:63"><i><font color="Green">E71</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T53">JGRAPH_4:53</a></i>;<br/>
<a NAME="E76:63"/><b>then </b><i><font color="Green">E102</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E30:63"><i><font color="Green">E75</font></i></a>, <a class="txt" href="jgraph_5.html#E31:63"><i><font color="Green">E76</font></i></a>, <a class="txt" href="jgraph_5.html#E32:63"><i><font color="Green">E77</font></i></a>, <a class="txt" href="jgraph_5.html#E33:63"><i><font color="Green">E78</font></i></a>, <a class="txt" href="jgraph_5.html#E52:63"><i><font color="Green">E91</font></i></a>, <a class="txt" href="jgraph_5.html#E61:63"><i><font color="Green">E95</font></i></a>, <a class="ref" href="jgraph_5.html#T54" target="_self">Th54</a></i>;<br/>
<a NAME="E77:63"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="toprns_1.html#K5">.|</a></span> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E14:63"><i><font color="Green">E66</font></i></a>, <a class="txt" href="jgraph_5.html#E16:63"><i><font color="Green">E67</font></i></a>, <a class="ref" href="jgraph_5.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E78:63"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E25:63"><i><font color="Green">E71</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T53">JGRAPH_4:53</a></i>;<br/>
<a NAME="E79:63"/><b>then </b><i><font color="Green">E103</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E32:63"><i><font color="Green">E77</font></i></a>, <a class="txt" href="jgraph_5.html#E33:63"><i><font color="Green">E78</font></i></a>, <a class="txt" href="jgraph_5.html#E34:63"><i><font color="Green">E79</font></i></a>, <a class="txt" href="jgraph_5.html#E35:63"><i><font color="Green">E80</font></i></a>, <a class="txt" href="jgraph_5.html#E61:63"><i><font color="Green">E95</font></i></a>, <a class="txt" href="jgraph_5.html#E70:63"><i><font color="Green">E99</font></i></a>, <a class="ref" href="jgraph_5.html#T54" target="_self">Th54</a></i>;<br/>
<a NAME="E80:63"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="toprns_1.html#K5">.|</a></span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E10:63"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E16:63"><i><font color="Green">E67</font></i></a>, <a class="ref" href="jgraph_5.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E81:63"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E25:63"><i><font color="Green">E71</font></i></a>, <a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="jgraph_4.html#T53">JGRAPH_4:53</a></i>;<br/>
<a NAME="E82:63"/><b>then </b>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="jgraph_5.html#E34:63"><i><font color="Green">E79</font></i></a>, <a class="txt" href="jgraph_5.html#E35:63"><i><font color="Green">E80</font></i></a>, <a class="txt" href="jgraph_5.html#E36:63"><i><font color="Green">E81</font></i></a>, <a class="txt" href="jgraph_5.html#E37:63"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jgraph_5.html#E73:63"><i><font color="Green">E101</font></i></a>, <a class="ref" href="jgraph_5.html#T54" target="_self">Th54</a></i>;<br/>
<b>hence </b><a NAME="E83:63"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  &amp; ( for <font color="Olive">b<sub>6</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> holds <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>6</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Olive">b<sub>6</sub></font></span><a href="toprns_1.html#K5">.|</a></span> ) &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Olive">b<sub>3</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Olive">b<sub>3</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Olive">b<sub>4</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Olive">b<sub>4</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Olive">b<sub>5</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Olive">b<sub>5</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp;  <a href="jordan6.html#R1">LE</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="jordan6.html#R1">LE</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="jgraph_5.html#E27:63"><i><font color="Green">E72</font></i></a>, <a class="txt" href="jgraph_5.html#E28:63"><i><font color="Green">E73</font></i></a>, <a class="txt" href="jgraph_5.html#E73:63"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jgraph_5.html#E76:63"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jgraph_5.html#E79:63"><i><font color="Green">E103</font></i></a></i>;<br/>


</div>
