<?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="E1:64"/><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;  <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#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#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#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#K22">`2</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:64"/><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="E3:64"/><b>then </b><i><font color="Green">E62</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#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#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#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#K22">`2</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:64"><i><font color="Green">E61</font></i></a>, <a class="ref" href="jordan7.html#T5">JORDAN7:5</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<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><b> such that </b><br/><a NAME="E5:64"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">c<sub>6</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>6</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 )
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>7</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="E7:64"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">c<sub>7</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>7</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#E3:64"><i><font color="Green">E62</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</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="E9:64"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>8</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>8</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#E3:64"><i><font color="Green">E62</font></i></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="E11:64"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">c<sub>9</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>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#E3:64"><i><font color="Green">E62</font></i></a></i>;<br/>
<a NAME="E12:64"/><i><font color="Green">E67</font></i>: 
(  <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>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E5:64"><i><font color="Green">E63</font></i></a>, <a class="ref" href="jgraph_5.html#T3" target="_self">Th3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:64_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 1
 ;<br/><a NAME="E2:64_1"/><b>then </b>
1 <a href="hidden.html#R1">=</a> 1 <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#E5:64"><i><font color="Green">E63</font></i></a>, <a class="ref" href="jgraph_3.html#T10">JGRAPH_3:10</a>, <a class="ref" href="square_1.html#T59">SQUARE_1:59</a></i>;<br/><a NAME="E3:64_1"/><b>then </b>
1 <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</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="square_1.html#K5">^2</a> 
 ;<br/><b>hence </b><a NAME="E4:64_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_5.html#E1:64"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/></div><b>end;</b></div>
<a NAME="E14:64"/><b>then </b>
<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> 1
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E12:64"><i><font color="Green">E67</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>10</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="E16:64"/><i><font color="Green">E68</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>10</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 <b>by </b><i><a class="ref" href="xreal_1.html#T7">XREAL_1:7</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</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/>
<a NAME="E18:64"/><i><font color="Green">E69</font></i>: 
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E12:64"><i><font color="Green">E67</font></i></a>, <a class="txt" href="jgraph_5.html#E16:64"><i><font color="Green">E68</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>12</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="E20:64"/><i><font color="Green">E70</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="jgraph_4.html#K5">-FanMorphN</a>  &amp; <font color="Maroon">c<sub>12</sub></font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  )
 <b>by </b><i><a class="ref" href="jgraph_4.html#T81">JGRAPH_4:81</a></i>;<br/>
<a NAME="E21:64"/><i><font color="Green">E71</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>12</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#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_4.html#T73">JGRAPH_4:73</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>12</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>14</sub></font> = <font color="Maroon">c<sub>12</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>15</sub></font> = <font color="Maroon">c<sub>12</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>16</sub></font> = <font color="Maroon">c<sub>12</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E22:64"/><i><font color="Green">E72</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>12</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#E7:64"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_4.html#T73">JGRAPH_4:73</a></i>;<br/>
<a NAME="E23:64"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>12</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#E1:64"><i><font color="Green">E61</font></i></a></i>;<br/>
<a NAME="E24:64"/><i><font color="Green">E74</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>12</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#E9:64"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_4.html#T73">JGRAPH_4:73</a></i>;<br/>
<a NAME="E25:64"/><b>then </b><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>12</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#E1:64"><i><font color="Green">E61</font></i></a></i>;<br/>
<a NAME="E26:64"/><i><font color="Green">E76</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>12</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#E11:64"><i><font color="Green">E66</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_4.html#T73">JGRAPH_4:73</a></i>;<br/>
<a NAME="E27:64"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>12</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#E1:64"><i><font color="Green">E61</font></i></a></i>;<br/>
<a NAME="E28:64"/><i><font color="Green">E78</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>12</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#E5:64"><i><font color="Green">E63</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_4.html#T73">JGRAPH_4:73</a></i>;<br/>
<a NAME="E29:64"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>12</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#E1:64"><i><font color="Green">E61</font></i></a></i>;<br/>
<a NAME="E30:64"/><i><font color="Green">E80</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="ref" href="jgraph_5.html#T50" target="_self">Th50</a></i>;<br/>
<a NAME="E31:64"/><i><font color="Green">E81</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="ref" href="jgraph_5.html#T50" target="_self">Th50</a></i>;<br/>
<a NAME="E32:64"/><i><font color="Green">E82</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="ref" href="jgraph_5.html#T50" target="_self">Th50</a></i>;<br/>
<a NAME="E33:64"/><b>then </b><i><font color="Green">E83</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>11</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E16:64"><i><font color="Green">E68</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E34:64"/><b>then </b><i><font color="Green">E84</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>11</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E31:64"><i><font color="Green">E81</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E35:64"/><i><font color="Green">E85</font></i>: 
<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="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> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E9:64"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E31:64"><i><font color="Green">E81</font></i></a>, <a class="txt" href="jgraph_5.html#E33:64"><i><font color="Green">E83</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E36:64"/><b>then </b><i><font color="Green">E86</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</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#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</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 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E9:64"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E18:64"><i><font color="Green">E69</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_5.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E37:64"/><i><font color="Green">E87</font></i>: 
<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="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> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E7:64"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E30:64"><i><font color="Green">E80</font></i></a>, <a class="txt" href="jgraph_5.html#E34:64"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E38:64"/><b>then </b><i><font color="Green">E88</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</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#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</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 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E7:64"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E18:64"><i><font color="Green">E69</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_5.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E39:64"/>
<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="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> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E5:64"><i><font color="Green">E63</font></i></a>, <a class="txt" href="jgraph_5.html#E16:64"><i><font color="Green">E68</font></i></a></i>;<br/>
<a NAME="E40:64"/><b>then </b><i><font color="Green">E89</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</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>12</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#NR4" target="_self">&gt;</a> 0 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E18:64"><i><font color="Green">E69</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_4.html#T83">JGRAPH_4:83</a></i>;<br/>
<a NAME="E41:64"/><i><font color="Green">E90</font></i>: 
( ( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</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>12</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#NR2" target="_self">&gt;=</a> 0 ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</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>12</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="hidden.html#R1">=</a> 0 ) ) &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</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>12</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#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E7:64"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E9:64"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E18:64"><i><font color="Green">E69</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="txt" href="jgraph_5.html#E35:64"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_5.html#E37:64"><i><font color="Green">E87</font></i></a>, <a class="ref" href="jgraph_5.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E42:64"/>
( <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="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#K21">`1</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E7:64"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E9:64"><i><font color="Green">E65</font></i></a>, <a class="ref" href="jgraph_5.html#T50" target="_self">Th50</a></i>;<br/>
<a NAME="E43:64"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</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> </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>12</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>12</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> </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>12</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E7:64"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jgraph_5.html#E9:64"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E18:64"><i><font color="Green">E69</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_5.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E44:64"/><b>then </b><i><font color="Green">E91</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>12</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>12</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E22:64"><i><font color="Green">E72</font></i></a>, <a class="txt" href="jgraph_5.html#E23:64"><i><font color="Green">E73</font></i></a>, <a class="txt" href="jgraph_5.html#E24:64"><i><font color="Green">E74</font></i></a>, <a class="txt" href="jgraph_5.html#E25:64"><i><font color="Green">E75</font></i></a>, <a class="txt" href="jgraph_5.html#E36:64"><i><font color="Green">E86</font></i></a>, <a class="txt" href="jgraph_5.html#E38:64"><i><font color="Green">E88</font></i></a>, <a class="ref" href="jgraph_5.html#T56" target="_self">Th56</a></i>;<br/>
<a NAME="E45:64"/>
<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="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> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E11:64"><i><font color="Green">E66</font></i></a>, <a class="txt" href="jgraph_5.html#E16:64"><i><font color="Green">E68</font></i></a>, <a class="txt" href="jgraph_5.html#E32:64"><i><font color="Green">E82</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E46:64"/><b>then </b><i><font color="Green">E92</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</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#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</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 )
 
<b>by </b><i><a class="txt" href="jgraph_5.html#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E11:64"><i><font color="Green">E66</font></i></a>, <a class="txt" href="jgraph_5.html#E18:64"><i><font color="Green">E69</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_5.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E47:64"/>
( <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="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#K21">`1</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E9:64"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E11:64"><i><font color="Green">E66</font></i></a>, <a class="ref" href="jgraph_5.html#T50" target="_self">Th50</a></i>;<br/>
<a NAME="E48:64"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</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> </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>12</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>12</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> </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>12</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E9:64"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jgraph_5.html#E11:64"><i><font color="Green">E66</font></i></a>, <a class="txt" href="jgraph_5.html#E18:64"><i><font color="Green">E69</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_5.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E49:64"/><b>then </b><i><font color="Green">E93</font></i>: 
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>12</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>12</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E24:64"><i><font color="Green">E74</font></i></a>, <a class="txt" href="jgraph_5.html#E25:64"><i><font color="Green">E75</font></i></a>, <a class="txt" href="jgraph_5.html#E26:64"><i><font color="Green">E76</font></i></a>, <a class="txt" href="jgraph_5.html#E27:64"><i><font color="Green">E77</font></i></a>, <a class="txt" href="jgraph_5.html#E36:64"><i><font color="Green">E86</font></i></a>, <a class="txt" href="jgraph_5.html#E46:64"><i><font color="Green">E92</font></i></a>, <a class="ref" href="jgraph_5.html#T56" target="_self">Th56</a></i>;<br/>
<a NAME="E50:64"/>
( <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="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#K21">`1</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E5:64"><i><font color="Green">E63</font></i></a>, <a class="txt" href="jgraph_5.html#E11:64"><i><font color="Green">E66</font></i></a>, <a class="ref" href="jgraph_5.html#T50" target="_self">Th50</a></i>;<br/>
<a NAME="E51:64"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</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> </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>12</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>12</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> </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>12</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E5:64"><i><font color="Green">E63</font></i></a>, <a class="txt" href="jgraph_5.html#E11:64"><i><font color="Green">E66</font></i></a>, <a class="txt" href="jgraph_5.html#E18:64"><i><font color="Green">E69</font></i></a>, <a class="txt" href="jgraph_5.html#E20:64"><i><font color="Green">E70</font></i></a>, <a class="ref" href="jgraph_5.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E52:64"/><b>then </b>
 <a href="jordan6.html#R1">LE</a> <font color="Maroon">c<sub>12</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>12</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#E1:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jgraph_5.html#E26:64"><i><font color="Green">E76</font></i></a>, <a class="txt" href="jgraph_5.html#E27:64"><i><font color="Green">E77</font></i></a>, <a class="txt" href="jgraph_5.html#E28:64"><i><font color="Green">E78</font></i></a>, <a class="txt" href="jgraph_5.html#E29:64"><i><font color="Green">E79</font></i></a>, <a class="txt" href="jgraph_5.html#E40:64"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_5.html#E46:64"><i><font color="Green">E92</font></i></a>, <a class="ref" href="jgraph_5.html#T56" target="_self">Th56</a></i>;<br/>
<b>hence </b><a NAME="E53:64"/>
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#NR2" target="_self">&gt;=</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#NR2" target="_self">&gt;=</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#NR2" target="_self">&gt;=</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#NR2" target="_self">&gt;=</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#E20:64"><i><font color="Green">E70</font></i></a>, <a class="txt" href="jgraph_5.html#E21:64"><i><font color="Green">E71</font></i></a>, <a class="txt" href="jgraph_5.html#E40:64"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_5.html#E41:64"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_5.html#E44:64"><i><font color="Green">E91</font></i></a>, <a class="txt" href="jgraph_5.html#E46:64"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_5.html#E49:64"><i><font color="Green">E93</font></i></a></i>;<br/>


</div>
