<?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> be   <a href="struct_0.html#NM7">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<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>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <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>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a> ;<br/>





<b>assume </b><a NAME="E1:59"/><i><font color="Green">E67</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>3</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="xxreal_0.html#R1">&lt;=</a> 1 </span>}</span>  &amp; <font color="Maroon">c<sub>4</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 &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <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="Olive">b<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) </span>}</span>  &amp; <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 &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) </span>}</span>  &amp; <font color="Maroon">c<sub>6</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 &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <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="Olive">b<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) </span>}</span>  &amp; <font color="Maroon">c<sub>7</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 &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) </span>}</span>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>1</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="ref" href="jgraph_3.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_2.html#T19">FUNCT_2:19</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="ref" href="jgraph_3.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_2.html#T19">FUNCT_2:19</a></i>;<br/>
<b>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="E5:59"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a>  &amp; <font color="Maroon">c<sub>12</sub></font> is <a href="pre_topc.html#V5">continuous</a> )
 <b>by </b><i><a class="ref" href="jgraph_3.html#T52" target="_self">Th52</a></i>;<br/>
<a NAME="E6:59"/><i><font color="Green">E69</font></i>: 
 <a href="wellfnd1.html#K1">dom</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E7:59"/><i><font color="Green">E70</font></i>: 
 <a href="wellfnd1.html#K1">dom</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E8:59"/><i><font color="Green">E71</font></i>: 
 <a href="wellfnd1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E9:59"/><i><font color="Green">E72</font></i>: 
 <a href="wellfnd1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E10:59"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>10</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59"><i><font color="Green">E68</font></i></a>, <a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>
<a NAME="E11:59"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>10</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a>, <a class="txt" href="jgraph_3.html#E75"><i><font color="Green">Lemma63</font></i></a>, <a class="ref" href="funct_1.html#T46">FUNCT_1:46</a></i>;<br/>
<a NAME="E12:59"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>11</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59"><i><font color="Green">E68</font></i></a>, <a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>
<a NAME="E13:59"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>11</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a>, <a class="txt" href="jgraph_3.html#E75"><i><font color="Green">Lemma63</font></i></a>, <a class="ref" href="funct_1.html#T46">FUNCT_1:46</a></i>;<br/>
<a NAME="E14:59"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E6:59"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>13</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="E16:59"/><i><font color="Green">E78</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>13</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a></i>;<br/>
<a NAME="E17:59"/><i><font color="Green">E79</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; ( ( <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  ) or ( <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) ) )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E16:59"><i><font color="Green">E78</font></i></a>, <a class="ref" href="toprns_1.html#T24">TOPRNS_1:24</a></i>;<br/>
<a NAME="E18:59"/><b>then </b><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="ref" href="jgraph_3.html#T38" target="_self">Th38</a></i>;<br/>
<a NAME="E19:59"/><i><font color="Green">E81</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 1 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font>;<br/>
<a NAME="E1:59_1"/><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E6:59"><i><font color="Green">E69</font></i></a>, <a class="txt" href="jgraph_3.html#E16:59"><i><font color="Green">E78</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<a NAME="E2:59_1"/><i><font color="Green">E83</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E14:59"><i><font color="Green">E77</font></i></a>, <a class="txt" href="jgraph_3.html#E16:59"><i><font color="Green">E78</font></i></a>, <a class="txt" href="jgraph_3.html#E18:59"><i><font color="Green">E80</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E3:59_1"/>
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E4:59_1"/><b>then </b><i><font color="Green">E84</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/>
<div><i><font color="Green">E85</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_1_1"/><i><font color="Green">E86</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E2:59_1_1"/><b>then </b><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E2:59_1"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jgraph_3.html#E4:59_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><a NAME="E3:59_1_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E2:59_1"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jgraph_3.html#E4:59_1"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_1_1"><i><font color="Green">E86</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E4:59_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E17:59"><i><font color="Green">E79</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_1_1"><i><font color="Green">E87</font></i></a>, <a class="ref" href="euclid.html#T57">EUCLID:57</a>, <a class="ref" href="euclid.html#T58">EUCLID:58</a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:59_1"/>
( ( <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  ) or ( <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</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>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E16:59"><i><font color="Green">E78</font></i></a>, <a class="txt" href="jgraph_3.html#E4:59_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<a NAME="E7:59_1"/><b>then </b>
( ( <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E2:59_1"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jgraph_3.html#E4:59_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<a NAME="E8:59_1"/><b>then </b><i><font color="Green">E86</font></i>: 
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E2:59_1"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jgraph_3.html#E4:59_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<a NAME="E9:59_1"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="jgraph_3.html#T54" target="_self">Th54</a>, <a class="ref" href="funct_1.html#T54">FUNCT_1:54</a></i>;<br/>
<a NAME="E10:59_1"/><i><font color="Green">E88</font></i>: 
<a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E5:59_1"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E8:59_1"><i><font color="Green">E86</font></i></a>, <a class="ref" href="jgraph_3.html#D1" target="_self">Def1</a>, <a class="ref" href="jgraph_2.html#T11">JGRAPH_2:11</a></i>;<br/>
<a NAME="E11:59_1"/><i><font color="Green">E89</font></i>: 
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`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>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E12:59_1"/><i><font color="Green">E90</font></i>: 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E13:59_1"/><b>then </b><i><font color="Green">E91</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/>
<a NAME="E14:59_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E5:59_1"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E8:59_1"><i><font color="Green">E86</font></i></a></i>;<br/>
<a NAME="E15:59_1"/><b>then </b><i><font color="Green">E92</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>13</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E9:59_1"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E10:59_1"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_1"><i><font color="Green">E89</font></i></a>, <a class="ref" href="jgraph_1.html#T46">JGRAPH_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="txt" href="jgraph_3.html#E12:59_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E12:59_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
;<br/>
<a NAME="E17:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E16:59"><i><font color="Green">E78</font></i></a></i>;<br/>
<a NAME="E18:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E12:59_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E19:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/>
<a NAME="E20:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E15:59_1"><i><font color="Green">E92</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E21:59_1"/><b>then </b><i><font color="Green">E93</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E22:59_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E5:59_1"><i><font color="Green">E85</font></i></a>, <a class="ref" href="complex1.html#T2">COMPLEX1:2</a></i>;<br/>
<a NAME="E23:59_1"/><b>then </b><i><font color="Green">E94</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E21:59_1"><i><font color="Green">E93</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<div><i><font color="Green">E95</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_1_3"/><i><font color="Green">E96</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 1
 ;<br/><a NAME="E2:59_1_3"/><b>then </b><i><font color="Green">E97</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E9:59_1"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E10:59_1"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_1"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E13:59_1"><i><font color="Green">E91</font></i></a>, <a class="ref" href="real_2.html#T127">REAL_2:127</a></i>;<br/><a NAME="E3:59_1_3"/>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</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"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E16:59"><i><font color="Green">E78</font></i></a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><a NAME="E4:59_1_3"/><b>then </b>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E9:59_1"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E10:59_1"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_1"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E13:59_1"><i><font color="Green">E91</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_1_3"><i><font color="Green">E96</font></i></a>, <a class="ref" href="real_2.html#T127">REAL_2:127</a></i>;<br/><a NAME="E5:59_1_3"/><b>then </b>
 <a href="real_1.html#K1">-</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>13</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="real_1.html#K1">-</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><b>hence </b><a NAME="E6:59_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E16:59"><i><font color="Green">E78</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_1_3"><i><font color="Green">E97</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E25:59_1"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E6:59"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>16</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="E27:59_1"/><i><font color="Green">E97</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <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>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a></i>;<br/>
<a NAME="E28:59_1"/><i><font color="Green">E98</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; ( ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  ) or ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) ) )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E27:59_1"><i><font color="Green">E97</font></i></a>, <a class="ref" href="toprns_1.html#T24">TOPRNS_1:24</a></i>;<br/>
<a NAME="E29:59_1"/><b>then </b><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="ref" href="jgraph_3.html#T38" target="_self">Th38</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>;<br/>
<a NAME="E30:59_1"/><i><font color="Green">E100</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E25:59_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="jgraph_3.html#E27:59_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="jgraph_3.html#E29:59_1"><i><font color="Green">E99</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E31:59_1"/>
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E32:59_1"/><b>then </b><i><font color="Green">E101</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/>
<div><i><font color="Green">E102</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_1_4"/><i><font color="Green">E103</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E2:59_1_4"/><b>then </b><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E30:59_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jgraph_3.html#E32:59_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><a NAME="E3:59_1_4"/>
<font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E30:59_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jgraph_3.html#E32:59_1"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_1_4"><i><font color="Green">E103</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E4:59_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E28:59_1"><i><font color="Green">E98</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_1_4"><i><font color="Green">E104</font></i></a>, <a class="ref" href="euclid.html#T57">EUCLID:57</a>, <a class="ref" href="euclid.html#T58">EUCLID:58</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E103</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_5"><b>now </b></a><div class="add"><a NAME="E1:59_1_5"/>
( ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E27:59_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="jgraph_3.html#E32:59_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><b>hence </b><a NAME="E2:59_1_5"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E30:59_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jgraph_3.html#E32:59_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/></div><b>end;</b></div>
<a NAME="E35:59_1"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E25:59_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="jgraph_3.html#E27:59_1"><i><font color="Green">E97</font></i></a>, <a class="ref" href="jgraph_3.html#T54" target="_self">Th54</a>, <a class="ref" href="funct_1.html#T54">FUNCT_1:54</a></i>;<br/>
<a NAME="E36:59_1"/><i><font color="Green">E105</font></i>: 
<a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E30:59_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jgraph_3.html#E33:59_1"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jgraph_3.html#E34:59_1"><i><font color="Green">E103</font></i></a>, <a class="ref" href="jgraph_3.html#D1" target="_self">Def1</a>, <a class="ref" href="jgraph_2.html#T11">JGRAPH_2:11</a></i>;<br/>
<a NAME="E37:59_1"/><i><font color="Green">E106</font></i>: 
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`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>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E38:59_1"/><i><font color="Green">E107</font></i>: 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E39:59_1"/><b>then </b><i><font color="Green">E108</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/>
<a NAME="E40:59_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E30:59_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jgraph_3.html#E33:59_1"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jgraph_3.html#E34:59_1"><i><font color="Green">E103</font></i></a></i>;<br/>
<a NAME="E41:59_1"/><b>then </b><i><font color="Green">E109</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E35:59_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jgraph_3.html#E36:59_1"><i><font color="Green">E105</font></i></a>, <a class="txt" href="jgraph_3.html#E37:59_1"><i><font color="Green">E106</font></i></a>, <a class="ref" href="jgraph_1.html#T46">JGRAPH_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="txt" href="jgraph_3.html#E38:59_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E38:59_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
;<br/>
<a NAME="E43:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E27:59_1"><i><font color="Green">E97</font></i></a></i>;<br/>
<a NAME="E44:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E38:59_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E45:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <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="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/>
<a NAME="E46:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E41:59_1"><i><font color="Green">E109</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E47:59_1"/><b>then </b><i><font color="Green">E110</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E48:59_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E33:59_1"><i><font color="Green">E102</font></i></a>, <a class="ref" href="complex1.html#T2">COMPLEX1:2</a></i>;<br/>
<a NAME="E49:59_1"/><b>then </b><i><font color="Green">E111</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E47:59_1"><i><font color="Green">E110</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<div><i><font color="Green">E112</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_7"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_1_7"/><i><font color="Green">E113</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 ;<br/><a NAME="E2:59_1_7"/><b>then </b><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <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_3.html#E35:59_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jgraph_3.html#E36:59_1"><i><font color="Green">E105</font></i></a>, <a class="txt" href="jgraph_3.html#E37:59_1"><i><font color="Green">E106</font></i></a>, <a class="txt" href="jgraph_3.html#E39:59_1"><i><font color="Green">E108</font></i></a>, <a class="ref" href="real_2.html#T128">REAL_2:128</a></i>;<br/><a NAME="E3:59_1_7"/>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</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>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E27:59_1"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><a NAME="E4:59_1_7"/><b>then </b>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E35:59_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jgraph_3.html#E36:59_1"><i><font color="Green">E105</font></i></a>, <a class="txt" href="jgraph_3.html#E37:59_1"><i><font color="Green">E106</font></i></a>, <a class="txt" href="jgraph_3.html#E39:59_1"><i><font color="Green">E108</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_1_7"><i><font color="Green">E113</font></i></a>, <a class="ref" href="real_2.html#T128">REAL_2:128</a></i>;<br/><a NAME="E5:59_1_7"/><b>then </b>
 <a href="real_1.html#K1">-</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>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="real_1.html#K1">-</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><b>hence </b><a NAME="E6:59_1_7"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E27:59_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_1_7"><i><font color="Green">E114</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E51:59_1"/><i><font color="Green">E113</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E7:59"><i><font color="Green">E70</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>18</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="E53:59_1"/><i><font color="Green">E114</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>18</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a></i>;<br/>
<a NAME="E54:59_1"/><i><font color="Green">E115</font></i>: 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</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"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E53:59_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/>
<a NAME="E55:59_1"/><b>then </b><i><font color="Green">E116</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; ( ( <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a>  ) or ( <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> ) ) )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E53:59_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="toprns_1.html#T24">TOPRNS_1:24</a></i>;<br/>
<a NAME="E56:59_1"/><b>then </b><i><font color="Green">E117</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="ref" href="jgraph_3.html#T40" target="_self">Th40</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font>;<br/>
<a NAME="E57:59_1"/><i><font color="Green">E118</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E51:59_1"><i><font color="Green">E113</font></i></a>, <a class="txt" href="jgraph_3.html#E53:59_1"><i><font color="Green">E114</font></i></a>, <a class="txt" href="jgraph_3.html#E56:59_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E58:59_1"/>
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E59:59_1"/><b>then </b><i><font color="Green">E119</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/>
<div><i><font color="Green">E120</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_8"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_1_8"/><i><font color="Green">E121</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</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>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E2:59_1_8"/><b>then </b><i><font color="Green">E122</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E57:59_1"><i><font color="Green">E118</font></i></a>, <a class="txt" href="jgraph_3.html#E59:59_1"><i><font color="Green">E119</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><a NAME="E3:59_1_8"/>
<font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E57:59_1"><i><font color="Green">E118</font></i></a>, <a class="txt" href="jgraph_3.html#E59:59_1"><i><font color="Green">E119</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_1_8"><i><font color="Green">E121</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E4:59_1_8"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E55:59_1"><i><font color="Green">E116</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_1_8"><i><font color="Green">E122</font></i></a>, <a class="ref" href="euclid.html#T57">EUCLID:57</a>, <a class="ref" href="euclid.html#T58">EUCLID:58</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E121</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_9"><b>now </b></a><div class="add"><a NAME="E1:59_1_9"/>
( ( <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a>  ) or ( <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</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>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E53:59_1"><i><font color="Green">E114</font></i></a>, <a class="txt" href="jgraph_3.html#E54:59_1"><i><font color="Green">E115</font></i></a>, <a class="txt" href="jgraph_3.html#E59:59_1"><i><font color="Green">E119</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E2:59_1_9"/><b>then </b>
( ( <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E57:59_1"><i><font color="Green">E118</font></i></a>, <a class="txt" href="jgraph_3.html#E59:59_1"><i><font color="Green">E119</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><b>hence </b><a NAME="E3:59_1_9"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E57:59_1"><i><font color="Green">E118</font></i></a>, <a class="txt" href="jgraph_3.html#E59:59_1"><i><font color="Green">E119</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/></div><b>end;</b></div>
<a NAME="E62:59_1"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E51:59_1"><i><font color="Green">E113</font></i></a>, <a class="txt" href="jgraph_3.html#E53:59_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="jgraph_3.html#T54" target="_self">Th54</a>, <a class="ref" href="funct_1.html#T54">FUNCT_1:54</a></i>;<br/>
<a NAME="E63:59_1"/><i><font color="Green">E123</font></i>: 
<a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E57:59_1"><i><font color="Green">E118</font></i></a>, <a class="txt" href="jgraph_3.html#E60:59_1"><i><font color="Green">E120</font></i></a>, <a class="txt" href="jgraph_3.html#E61:59_1"><i><font color="Green">E121</font></i></a>, <a class="ref" href="jgraph_3.html#T14" target="_self">Th14</a>, <a class="ref" href="jgraph_2.html#T11">JGRAPH_2:11</a></i>;<br/>
<a NAME="E64:59_1"/><i><font color="Green">E124</font></i>: 
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`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>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E65:59_1"/><i><font color="Green">E125</font></i>: 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E66:59_1"/><b>then </b><i><font color="Green">E126</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/>
<a NAME="E67:59_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E57:59_1"><i><font color="Green">E118</font></i></a>, <a class="txt" href="jgraph_3.html#E60:59_1"><i><font color="Green">E120</font></i></a>, <a class="txt" href="jgraph_3.html#E61:59_1"><i><font color="Green">E121</font></i></a></i>;<br/>
<a NAME="E68:59_1"/><b>then </b><i><font color="Green">E127</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>18</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E62:59_1"><i><font color="Green">E122</font></i></a>, <a class="txt" href="jgraph_3.html#E63:59_1"><i><font color="Green">E123</font></i></a>, <a class="txt" href="jgraph_3.html#E64:59_1"><i><font color="Green">E124</font></i></a>, <a class="ref" href="jgraph_1.html#T46">JGRAPH_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="txt" href="jgraph_3.html#E65:59_1"><i><font color="Green">E125</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E65:59_1"><i><font color="Green">E125</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
;<br/>
<a NAME="E70:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E53:59_1"><i><font color="Green">E114</font></i></a></i>;<br/>
<a NAME="E71:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E65:59_1"><i><font color="Green">E125</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E72:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/>
<a NAME="E73:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E68:59_1"><i><font color="Green">E127</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E74:59_1"/><b>then </b><i><font color="Green">E128</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E75:59_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E60:59_1"><i><font color="Green">E120</font></i></a>, <a class="ref" href="complex1.html#T2">COMPLEX1:2</a></i>;<br/>
<a NAME="E76:59_1"/><b>then </b><i><font color="Green">E129</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E74:59_1"><i><font color="Green">E128</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<div><i><font color="Green">E130</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_11"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_1_11"/><i><font color="Green">E131</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 1
 ;<br/><a NAME="E2:59_1_11"/><b>then </b><i><font color="Green">E132</font></i>: 
<font color="Maroon">c<sub>18</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_3.html#E62:59_1"><i><font color="Green">E122</font></i></a>, <a class="txt" href="jgraph_3.html#E63:59_1"><i><font color="Green">E123</font></i></a>, <a class="txt" href="jgraph_3.html#E64:59_1"><i><font color="Green">E124</font></i></a>, <a class="txt" href="jgraph_3.html#E66:59_1"><i><font color="Green">E126</font></i></a>, <a class="ref" href="real_2.html#T127">REAL_2:127</a></i>;<br/><a NAME="E3:59_1_11"/>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</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_3.html#E53:59_1"><i><font color="Green">E114</font></i></a>, <a class="txt" href="jgraph_3.html#E62:59_1"><i><font color="Green">E122</font></i></a>, <a class="txt" href="jgraph_3.html#E63:59_1"><i><font color="Green">E123</font></i></a>, <a class="txt" href="jgraph_3.html#E64:59_1"><i><font color="Green">E124</font></i></a>, <a class="txt" href="jgraph_3.html#E66:59_1"><i><font color="Green">E126</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_1_11"><i><font color="Green">E131</font></i></a>, <a class="ref" href="real_2.html#T127">REAL_2:127</a></i>;<br/><a NAME="E4:59_1_11"/><b>then </b>
 <a href="real_1.html#K1">-</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>18</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="real_1.html#K1">-</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><b>hence </b><a NAME="E5:59_1_11"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E53:59_1"><i><font color="Green">E114</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_1_11"><i><font color="Green">E132</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E78:59_1"/><i><font color="Green">E131</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E7:59"><i><font color="Green">E70</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>20</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="E80:59_1"/><i><font color="Green">E132</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>20</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>20</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a>  <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>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a></i>;<br/>
<a NAME="E81:59_1"/><i><font color="Green">E133</font></i>: 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</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>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E80:59_1"><i><font color="Green">E132</font></i></a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/>
<a NAME="E82:59_1"/><b>then </b><i><font color="Green">E134</font></i>: 
( <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; ( ( <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a>  ) or ( <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> ) ) )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E80:59_1"><i><font color="Green">E132</font></i></a>, <a class="ref" href="toprns_1.html#T24">TOPRNS_1:24</a></i>;<br/>
<a NAME="E83:59_1"/><b>then </b><i><font color="Green">E135</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="ref" href="jgraph_3.html#T40" target="_self">Th40</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>;<br/>
<a NAME="E84:59_1"/><i><font color="Green">E136</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E78:59_1"><i><font color="Green">E131</font></i></a>, <a class="txt" href="jgraph_3.html#E80:59_1"><i><font color="Green">E132</font></i></a>, <a class="txt" href="jgraph_3.html#E83:59_1"><i><font color="Green">E135</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E85:59_1"/>
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E86:59_1"/><b>then </b><i><font color="Green">E137</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/>
<div><i><font color="Green">E138</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_12"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_1_12"/><i><font color="Green">E139</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</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>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E2:59_1_12"/><b>then </b><i><font color="Green">E140</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E84:59_1"><i><font color="Green">E136</font></i></a>, <a class="txt" href="jgraph_3.html#E86:59_1"><i><font color="Green">E137</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><a NAME="E3:59_1_12"/>
<font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E84:59_1"><i><font color="Green">E136</font></i></a>, <a class="txt" href="jgraph_3.html#E86:59_1"><i><font color="Green">E137</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_1_12"><i><font color="Green">E139</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E4:59_1_12"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E82:59_1"><i><font color="Green">E134</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_1_12"><i><font color="Green">E140</font></i></a>, <a class="ref" href="euclid.html#T57">EUCLID:57</a>, <a class="ref" href="euclid.html#T58">EUCLID:58</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E139</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_13"><b>now </b></a><div class="add"><a NAME="E1:59_1_13"/>
( ( <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E80:59_1"><i><font color="Green">E132</font></i></a>, <a class="txt" href="jgraph_3.html#E81:59_1"><i><font color="Green">E133</font></i></a>, <a class="txt" href="jgraph_3.html#E86:59_1"><i><font color="Green">E137</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><b>hence </b><a NAME="E2:59_1_13"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E84:59_1"><i><font color="Green">E136</font></i></a>, <a class="txt" href="jgraph_3.html#E86:59_1"><i><font color="Green">E137</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/></div><b>end;</b></div>
<a NAME="E89:59_1"/><i><font color="Green">E140</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E78:59_1"><i><font color="Green">E131</font></i></a>, <a class="txt" href="jgraph_3.html#E80:59_1"><i><font color="Green">E132</font></i></a>, <a class="ref" href="jgraph_3.html#T54" target="_self">Th54</a>, <a class="ref" href="funct_1.html#T54">FUNCT_1:54</a></i>;<br/>
<a NAME="E90:59_1"/><i><font color="Green">E141</font></i>: 
<a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E84:59_1"><i><font color="Green">E136</font></i></a>, <a class="txt" href="jgraph_3.html#E87:59_1"><i><font color="Green">E138</font></i></a>, <a class="txt" href="jgraph_3.html#E88:59_1"><i><font color="Green">E139</font></i></a>, <a class="ref" href="jgraph_3.html#T14" target="_self">Th14</a>, <a class="ref" href="jgraph_2.html#T11">JGRAPH_2:11</a></i>;<br/>
<a NAME="E91:59_1"/><i><font color="Green">E142</font></i>: 
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`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>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E92:59_1"/><i><font color="Green">E143</font></i>: 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E93:59_1"/><b>then </b><i><font color="Green">E144</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/>
<a NAME="E94:59_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E84:59_1"><i><font color="Green">E136</font></i></a>, <a class="txt" href="jgraph_3.html#E87:59_1"><i><font color="Green">E138</font></i></a>, <a class="txt" href="jgraph_3.html#E88:59_1"><i><font color="Green">E139</font></i></a></i>;<br/>
<a NAME="E95:59_1"/><b>then </b><i><font color="Green">E145</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>20</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E89:59_1"><i><font color="Green">E140</font></i></a>, <a class="txt" href="jgraph_3.html#E90:59_1"><i><font color="Green">E141</font></i></a>, <a class="txt" href="jgraph_3.html#E91:59_1"><i><font color="Green">E142</font></i></a>, <a class="ref" href="jgraph_1.html#T46">JGRAPH_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="txt" href="jgraph_3.html#E92:59_1"><i><font color="Green">E143</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E92:59_1"><i><font color="Green">E143</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
;<br/>
<a NAME="E97:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E80:59_1"><i><font color="Green">E132</font></i></a></i>;<br/>
<a NAME="E98:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E92:59_1"><i><font color="Green">E143</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E99:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <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="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/>
<a NAME="E100:59_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E95:59_1"><i><font color="Green">E145</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E101:59_1"/><b>then </b><i><font color="Green">E146</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E102:59_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E87:59_1"><i><font color="Green">E138</font></i></a>, <a class="ref" href="complex1.html#T2">COMPLEX1:2</a></i>;<br/>
<a NAME="E103:59_1"/><b>then </b><i><font color="Green">E147</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E101:59_1"><i><font color="Green">E146</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_15"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_1_15"/><i><font color="Green">E148</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 ;<br/><a NAME="E2:59_1_15"/><b>then </b><i><font color="Green">E149</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <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_3.html#E89:59_1"><i><font color="Green">E140</font></i></a>, <a class="txt" href="jgraph_3.html#E90:59_1"><i><font color="Green">E141</font></i></a>, <a class="txt" href="jgraph_3.html#E91:59_1"><i><font color="Green">E142</font></i></a>, <a class="txt" href="jgraph_3.html#E93:59_1"><i><font color="Green">E144</font></i></a>, <a class="ref" href="real_2.html#T128">REAL_2:128</a></i>;<br/><a NAME="E3:59_1_15"/>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E80:59_1"><i><font color="Green">E132</font></i></a>, <a class="txt" href="jgraph_3.html#E89:59_1"><i><font color="Green">E140</font></i></a>, <a class="txt" href="jgraph_3.html#E90:59_1"><i><font color="Green">E141</font></i></a>, <a class="txt" href="jgraph_3.html#E91:59_1"><i><font color="Green">E142</font></i></a>, <a class="txt" href="jgraph_3.html#E93:59_1"><i><font color="Green">E144</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_1_15"><i><font color="Green">E148</font></i></a>, <a class="ref" href="real_2.html#T128">REAL_2:128</a></i>;<br/><a NAME="E4:59_1_15"/><b>then </b>
 <a href="real_1.html#K1">-</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>20</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="real_1.html#K1">-</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><b>hence </b><a NAME="E5:59_1_15"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E80:59_1"><i><font color="Green">E132</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_1_15"><i><font color="Green">E149</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E105:59_1"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E23:59_1"><i><font color="Green">E94</font></i></a>, <a class="txt" href="jgraph_3.html#E24:59_1"><i><font color="Green">E95</font></i></a>, <a class="txt" href="jgraph_3.html#E49:59_1"><i><font color="Green">E111</font></i></a>, <a class="txt" href="jgraph_3.html#E50:59_1"><i><font color="Green">E112</font></i></a>, <a class="txt" href="jgraph_3.html#E76:59_1"><i><font color="Green">E129</font></i></a>, <a class="txt" href="jgraph_3.html#E77:59_1"><i><font color="Green">E130</font></i></a>, <a class="txt" href="jgraph_3.html#E103:59_1"><i><font color="Green">E147</font></i></a>, <a class="txt" href="jgraph_3.html#E79"><i><font color="Green">Lemma66</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E20:59"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>  holds <br/>(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a> ;<br/>

<a NAME="E1:59_2"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E6:59"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<a NAME="E2:59_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E8:59"><i><font color="Green">E71</font></i></a>, <a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<a NAME="E3:59_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>15</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="E5:59_2"/><i><font color="Green">E83</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a></i>;<br/>
<div><i><font color="Green">E84</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:59_2_1_1"/>
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K16">0.REAL</a> 2 or ( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; ( ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  ) or ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) ) ) or ( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1_1_1"><b>case </b></a><a NAME="E1:59_2_1_1_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K16">0.REAL</a> 2
 ;<br/><div class="add"><a NAME="E2:59_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K16">0.REAL</a> 2
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2"><i><font color="Green">E83</font></i></a>, <a class="ref" href="jgraph_3.html#T38" target="_self">Th38</a></i>;<br/><b>hence </b><a NAME="E3:59_2_1_1_1"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="ref" href="jgraph_2.html#T11">JGRAPH_2:11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1_1_2"><b>case </b></a><a NAME="E1:59_2_1_1_2"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; ( ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  ) or ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) ) )
 ;<br/><div class="add"><a NAME="E2:59_2_1_1_2"/><b>then </b><i><font color="Green">E86</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="ref" href="jgraph_3.html#T38" target="_self">Th38</a></i>;<br/><b>set </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font>;<br/><a NAME="E3:59_2_1_1_2"/><i><font color="Green">E87</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_2_1_1_2"><i><font color="Green">E86</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/><a NAME="E4:59_2_1_1_2"/>
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E5:59_2_1_1_2"/><b>then </b><i><font color="Green">E88</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/><div><i><font color="Green">E89</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_2_1_1_2_1"/><i><font color="Green">E90</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E2:59_2_1_1_2_1"/><b>then </b><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_1_1_2"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2_1_1_2"><i><font color="Green">E88</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><a NAME="E3:59_2_1_1_2_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_1_1_2"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2_1_1_2"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_2_1_1_2_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E4:59_2_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2_1_1_2"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_2_1_1_2_1"><i><font color="Green">E91</font></i></a>, <a class="ref" href="euclid.html#T57">EUCLID:57</a>, <a class="ref" href="euclid.html#T58">EUCLID:58</a></i>;<br/></div><b>end;</b></div><a NAME="E7:59_2_1_1_2"/>
( ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  ) or ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</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>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2_1_1_2"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2_1_1_2"><i><font color="Green">E88</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E8:59_2_1_1_2"/><b>then </b>
( ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_1_1_2"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2_1_1_2"><i><font color="Green">E88</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E9:59_2_1_1_2"/><b>then </b><i><font color="Green">E90</font></i>: 
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_1_1_2"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2_1_1_2"><i><font color="Green">E88</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E10:59_2_1_1_2"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2"><i><font color="Green">E83</font></i></a>, <a class="ref" href="jgraph_3.html#T54" target="_self">Th54</a>, <a class="ref" href="funct_1.html#T54">FUNCT_1:54</a></i>;<br/><a NAME="E11:59_2_1_1_2"/><i><font color="Green">E92</font></i>: 
<a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E6:59_2_1_1_2"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E9:59_2_1_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="jgraph_3.html#D1" target="_self">Def1</a>, <a class="ref" href="jgraph_2.html#T11">JGRAPH_2:11</a></i>;<br/><a NAME="E12:59_2_1_1_2"/><i><font color="Green">E93</font></i>: 
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`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>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/><a NAME="E13:59_2_1_1_2"/><i><font color="Green">E94</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/><a NAME="E14:59_2_1_1_2"/><i><font color="Green">E95</font></i>: 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E15:59_2_1_1_2"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="ref" href="toprns_1.html#T26">TOPRNS_1:26</a></i>;<br/><a NAME="E16:59_2_1_1_2"/><b>then </b>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E5:59_2"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jgraph_3.html#E6"><i><font color="Green">Lemma6</font></i></a></i>;<br/><a NAME="E17:59_2_1_1_2"/><b>then </b><i><font color="Green">E96</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="jgraph_3.html#E5:59_2"><i><font color="Green">E83</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E18:59_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E6:59_2_1_1_2"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E9:59_2_1_1_2"><i><font color="Green">E90</font></i></a></i>;<br/><a NAME="E19:59_2_1_1_2"/><b>then </b><i><font color="Green">E97</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E10:59_2_1_1_2"><i><font color="Green">E91</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_2_1_1_2"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_3.html#E12:59_2_1_1_2"><i><font color="Green">E93</font></i></a>, <a class="ref" href="jgraph_1.html#T46">JGRAPH_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="txt" href="jgraph_3.html#E14:59_2_1_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E14:59_2_1_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
;<br/><a NAME="E21:59_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E14:59_2_1_1_2"><i><font color="Green">E95</font></i></a>, <a class="txt" href="jgraph_3.html#E17:59_2_1_1_2"><i><font color="Green">E96</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E22:59_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E14:59_2_1_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E23:59_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/><a NAME="E24:59_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><a NAME="E25:59_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="txt" href="jgraph_3.html#E13:59_2_1_1_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E26:59_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 <b>by </b><i><a class="txt" href="jgraph_3.html#E19:59_2_1_1_2"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E27:59_2_1_1_2"/><b>then </b><i><font color="Green">E98</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E78"><i><font color="Green">Lemma65</font></i></a></i>;<br/><a NAME="E28:59_2_1_1_2"/><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E6:59_2_1_1_2"><i><font color="Green">E89</font></i></a>, <a class="ref" href="complex1.html#T2">COMPLEX1:2</a></i>;<br/><a NAME="E29:59_2_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/><a NAME="E30:59_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="real_1.html#K3">+</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E13:59_2_1_1_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E31:59_2_1_1_2"/><b>then </b><i><font color="Green">E100</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E27:59_2_1_1_2"><i><font color="Green">E98</font></i></a>, <a class="txt" href="jgraph_3.html#E28:59_2_1_1_2"><i><font color="Green">E99</font></i></a>, <a class="ref" href="real_2.html#T122">REAL_2:122</a></i>;<br/><a NAME="E32:59_2_1_1_2"/><b>then </b><i><font color="Green">E101</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E15"><i><font color="Green">Lemma7</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_1_1_2_3"><b>now </b></a><div class="add"><a NAME="E1:59_2_1_1_2_3"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E9:59_2_1_1_2"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E32:59_2_1_1_2"><i><font color="Green">E101</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><a NAME="E2:59_2_1_1_2_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><a NAME="E3:59_2_1_1_2_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E32:59_2_1_1_2"><i><font color="Green">E101</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E4:59_2_1_1_2_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E32:59_2_1_1_2"><i><font color="Green">E101</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><b>hence </b><a NAME="E5:59_2_1_1_2_3"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 ) )
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E34:59_2_1_1_2"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E31:59_2_1_1_2"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jgraph_3.html#E15"><i><font color="Green">Lemma7</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1_1_3"><b>case </b></a><a NAME="E1:59_2_1_1_3"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 ;<br/><div class="add"><a NAME="E2:59_2_1_1_3"/><b>then </b><i><font color="Green">E86</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="ref" href="jgraph_3.html#T38" target="_self">Th38</a></i>;<br/><a NAME="E3:59_2_1_1_3"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; ( ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  ) or ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> ) ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2_1_1_3"><i><font color="Green">E85</font></i></a>, <a class="ref" href="jgraph_2.html#T23">JGRAPH_2:23</a></i>;<br/><b>set </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font>;<br/><a NAME="E4:59_2_1_1_3"/><i><font color="Green">E88</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_2_1_1_3"><i><font color="Green">E86</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/><a NAME="E5:59_2_1_1_3"/>
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E6:59_2_1_1_3"/><b>then </b><i><font color="Green">E89</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/><div><i><font color="Green">E90</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_1_1_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_2_1_1_3_1"/><i><font color="Green">E91</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</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>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E2:59_2_1_1_3_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_1_1_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_1_1_3"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E3:59_2_1_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2_1_1_3"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E4:59_2_1_1_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_1_1_3"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_2_1_1_3_1"><i><font color="Green">E91</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E91</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_1_1_3_2"><b>now </b></a><div class="add"><a NAME="E1:59_2_1_1_3_2"/>
( ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  ) or ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</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>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_1_1_3"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_1_1_3"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E2:59_2_1_1_3_2"/><b>then </b>
( ( <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_1_1_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_1_1_3"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><b>hence </b><a NAME="E3:59_2_1_1_3_2"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_1_1_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_1_1_3"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/></div><b>end;</b></div><a NAME="E9:59_2_1_1_3"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2"><i><font color="Green">E83</font></i></a>, <a class="ref" href="jgraph_3.html#T54" target="_self">Th54</a>, <a class="ref" href="funct_1.html#T54">FUNCT_1:54</a></i>;<br/><a NAME="E10:59_2_1_1_3"/><i><font color="Green">E93</font></i>: 
<a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_1_1_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E7:59_2_1_1_3"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E8:59_2_1_1_3"><i><font color="Green">E91</font></i></a>, <a class="ref" href="jgraph_3.html#T14" target="_self">Th14</a>, <a class="ref" href="jgraph_2.html#T11">JGRAPH_2:11</a></i>;<br/><a NAME="E11:59_2_1_1_3"/><i><font color="Green">E94</font></i>: 
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`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>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/><a NAME="E12:59_2_1_1_3"/><i><font color="Green">E95</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/><a NAME="E13:59_2_1_1_3"/><i><font color="Green">E96</font></i>: 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E14:59_2_1_1_3"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="ref" href="toprns_1.html#T26">TOPRNS_1:26</a></i>;<br/><a NAME="E15:59_2_1_1_3"/><b>then </b>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E5:59_2"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jgraph_3.html#E6"><i><font color="Green">Lemma6</font></i></a></i>;<br/><a NAME="E16:59_2_1_1_3"/><b>then </b><i><font color="Green">E97</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="jgraph_3.html#E5:59_2"><i><font color="Green">E83</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E17:59_2_1_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_1_1_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E7:59_2_1_1_3"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E8:59_2_1_1_3"><i><font color="Green">E91</font></i></a></i>;<br/><a NAME="E18:59_2_1_1_3"/><b>then </b><i><font color="Green">E98</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E9:59_2_1_1_3"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_3.html#E10:59_2_1_1_3"><i><font color="Green">E93</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_2_1_1_3"><i><font color="Green">E94</font></i></a>, <a class="ref" href="jgraph_1.html#T46">JGRAPH_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="txt" href="jgraph_3.html#E13:59_2_1_1_3"><i><font color="Green">E96</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E13:59_2_1_1_3"><i><font color="Green">E96</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
;<br/><a NAME="E20:59_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E13:59_2_1_1_3"><i><font color="Green">E96</font></i></a>, <a class="txt" href="jgraph_3.html#E16:59_2_1_1_3"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E21:59_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E13:59_2_1_1_3"><i><font color="Green">E96</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E22:59_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/><a NAME="E23:59_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><a NAME="E24:59_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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_3.html#E12:59_2_1_1_3"><i><font color="Green">E95</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E25:59_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 <b>by </b><i><a class="txt" href="jgraph_3.html#E18:59_2_1_1_3"><i><font color="Green">E98</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E26:59_2_1_1_3"/><b>then </b><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E78"><i><font color="Green">Lemma65</font></i></a></i>;<br/><a NAME="E27:59_2_1_1_3"/><i><font color="Green">E100</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E7:59_2_1_1_3"><i><font color="Green">E90</font></i></a>, <a class="ref" href="complex1.html#T2">COMPLEX1:2</a></i>;<br/><a NAME="E28:59_2_1_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/><a NAME="E29:59_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="real_1.html#K3">+</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E12:59_2_1_1_3"><i><font color="Green">E95</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E30:59_2_1_1_3"/><b>then </b><i><font color="Green">E101</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E26:59_2_1_1_3"><i><font color="Green">E99</font></i></a>, <a class="txt" href="jgraph_3.html#E27:59_2_1_1_3"><i><font color="Green">E100</font></i></a>, <a class="ref" href="real_2.html#T122">REAL_2:122</a></i>;<br/><a NAME="E31:59_2_1_1_3"/><b>then </b><i><font color="Green">E102</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E15"><i><font color="Green">Lemma7</font></i></a></i>;<br/><a NAME="E32:59_2_1_1_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_1_1_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E8:59_2_1_1_3"><i><font color="Green">E91</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><a NAME="E33:59_2_1_1_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E31:59_2_1_1_3"><i><font color="Green">E102</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><a NAME="E34:59_2_1_1_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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> 1 ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E31:59_2_1_1_3"><i><font color="Green">E102</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E35:59_2_1_1_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 ) )
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><b>hence </b><a NAME="E36:59_2_1_1_3"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E30:59_2_1_1_3"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jgraph_3.html#E15"><i><font color="Green">Lemma7</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E7:59_2"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E7:59"><i><font color="Green">E70</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<a NAME="E8:59_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E9:59"><i><font color="Green">E72</font></i></a>, <a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<a NAME="E9:59_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>16</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="E11:59_2"/><i><font color="Green">E86</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font> &amp; <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:59_2_2_1"/>
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K16">0.REAL</a> 2 or ( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; ( ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  ) or ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) ) ) or ( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_2_1_1"><b>case </b></a><a NAME="E1:59_2_2_1_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K16">0.REAL</a> 2
 ;<br/><div class="add"><a NAME="E2:59_2_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K16">0.REAL</a> 2
 <b>by </b><i><a class="txt" href="jgraph_3.html#E7:59_2"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_2"><i><font color="Green">E86</font></i></a>, <a class="ref" href="jgraph_3.html#T38" target="_self">Th38</a></i>;<br/><b>hence </b><a NAME="E3:59_2_2_1_1"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="ref" href="jgraph_2.html#T11">JGRAPH_2:11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_2_1_2"><b>case </b></a><a NAME="E1:59_2_2_1_2"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; ( ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  ) or ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) ) )
 ;<br/><div class="add"><a NAME="E2:59_2_2_1_2"/><b>then </b><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="ref" href="jgraph_3.html#T38" target="_self">Th38</a></i>;<br/><b>set </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font>;<br/><a NAME="E3:59_2_2_1_2"/><i><font color="Green">E89</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E7:59_2"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_2"><i><font color="Green">E86</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_2_2_1_2"><i><font color="Green">E88</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/><a NAME="E4:59_2_2_1_2"/>
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E5:59_2_2_1_2"/><b>then </b><i><font color="Green">E90</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/><div><i><font color="Green">E91</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_2_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_2_2_1_2_1"/><i><font color="Green">E92</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E2:59_2_2_1_2_1"/><b>then </b><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_2_1_2"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2_2_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><a NAME="E3:59_2_2_1_2_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_2_1_2"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2_2_1_2"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_2_2_1_2_1"><i><font color="Green">E92</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E4:59_2_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2_2_1_2"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_2_2_1_2_1"><i><font color="Green">E93</font></i></a>, <a class="ref" href="euclid.html#T57">EUCLID:57</a>, <a class="ref" href="euclid.html#T58">EUCLID:58</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E92</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_2_1_2_2"><b>now </b></a><div class="add"><a NAME="E1:59_2_2_1_2_2"/>
( ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  ) or ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</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>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2_2_1_2"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2_2_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E2:59_2_2_1_2_2"/><b>then </b>
( ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_2_1_2"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2_2_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><b>hence </b><a NAME="E3:59_2_2_1_2_2"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_2_1_2"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E5:59_2_2_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/></div><b>end;</b></div><a NAME="E8:59_2_2_1_2"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E7:59_2"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_2"><i><font color="Green">E86</font></i></a>, <a class="ref" href="jgraph_3.html#T54" target="_self">Th54</a>, <a class="ref" href="funct_1.html#T54">FUNCT_1:54</a></i>;<br/><a NAME="E9:59_2_2_1_2"/><i><font color="Green">E94</font></i>: 
<a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_2_1_2"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_2_1_2"><i><font color="Green">E91</font></i></a>, <a class="txt" href="jgraph_3.html#E7:59_2_2_1_2"><i><font color="Green">E92</font></i></a>, <a class="ref" href="jgraph_3.html#D1" target="_self">Def1</a>, <a class="ref" href="jgraph_2.html#T11">JGRAPH_2:11</a></i>;<br/><a NAME="E10:59_2_2_1_2"/><i><font color="Green">E95</font></i>: 
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`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>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/><a NAME="E11:59_2_2_1_2"/><i><font color="Green">E96</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/><a NAME="E12:59_2_2_1_2"/><i><font color="Green">E97</font></i>: 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E13:59_2_2_1_2"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="ref" href="toprns_1.html#T26">TOPRNS_1:26</a></i>;<br/><a NAME="E14:59_2_2_1_2"/><b>then </b>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E11:59_2"><i><font color="Green">E86</font></i></a>, <a class="txt" href="jgraph_3.html#E6"><i><font color="Green">Lemma6</font></i></a></i>;<br/><a NAME="E15:59_2_2_1_2"/><b>then </b><i><font color="Green">E98</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="jgraph_3.html#E11:59_2"><i><font color="Green">E86</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E16:59_2_2_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_2_1_2"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_2_1_2"><i><font color="Green">E91</font></i></a>, <a class="txt" href="jgraph_3.html#E7:59_2_2_1_2"><i><font color="Green">E92</font></i></a></i>;<br/><a NAME="E17:59_2_2_1_2"/><b>then </b><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E8:59_2_2_1_2"><i><font color="Green">E93</font></i></a>, <a class="txt" href="jgraph_3.html#E9:59_2_2_1_2"><i><font color="Green">E94</font></i></a>, <a class="txt" href="jgraph_3.html#E10:59_2_2_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="jgraph_1.html#T46">JGRAPH_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="txt" href="jgraph_3.html#E12:59_2_2_1_2"><i><font color="Green">E97</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E12:59_2_2_1_2"><i><font color="Green">E97</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
;<br/><a NAME="E19:59_2_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E12:59_2_2_1_2"><i><font color="Green">E97</font></i></a>, <a class="txt" href="jgraph_3.html#E15:59_2_2_1_2"><i><font color="Green">E98</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E20:59_2_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E12:59_2_2_1_2"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E21:59_2_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/><a NAME="E22:59_2_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><a NAME="E23:59_2_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="txt" href="jgraph_3.html#E11:59_2_2_1_2"><i><font color="Green">E96</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E24:59_2_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 <b>by </b><i><a class="txt" href="jgraph_3.html#E17:59_2_2_1_2"><i><font color="Green">E99</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E25:59_2_2_1_2"/><b>then </b><i><font color="Green">E100</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E78"><i><font color="Green">Lemma65</font></i></a></i>;<br/><a NAME="E26:59_2_2_1_2"/><i><font color="Green">E101</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E6:59_2_2_1_2"><i><font color="Green">E91</font></i></a>, <a class="ref" href="complex1.html#T2">COMPLEX1:2</a></i>;<br/><a NAME="E27:59_2_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/><a NAME="E28:59_2_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="real_1.html#K3">+</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E11:59_2_2_1_2"><i><font color="Green">E96</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E29:59_2_2_1_2"/><b>then </b><i><font color="Green">E102</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E25:59_2_2_1_2"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jgraph_3.html#E26:59_2_2_1_2"><i><font color="Green">E101</font></i></a>, <a class="ref" href="real_2.html#T122">REAL_2:122</a></i>;<br/><a NAME="E30:59_2_2_1_2"/><b>then </b><i><font color="Green">E103</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E15"><i><font color="Green">Lemma7</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_2_1_2_4"><b>now </b></a><div class="add"><a NAME="E1:59_2_2_1_2_4"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_2_1_2"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E7:59_2_2_1_2"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_3.html#E30:59_2_2_1_2"><i><font color="Green">E103</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><a NAME="E2:59_2_2_1_2_4"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><a NAME="E3:59_2_2_1_2_4"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E30:59_2_2_1_2"><i><font color="Green">E103</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E4:59_2_2_1_2_4"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E30:59_2_2_1_2"><i><font color="Green">E103</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><b>hence </b><a NAME="E5:59_2_2_1_2_4"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 ) )
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E32:59_2_2_1_2"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E29:59_2_2_1_2"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jgraph_3.html#E15"><i><font color="Green">Lemma7</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_2_1_3"><b>case </b></a><a NAME="E1:59_2_2_1_3"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> ) )
 ;<br/><div class="add"><a NAME="E2:59_2_2_1_3"/><b>then </b><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="ref" href="jgraph_3.html#T38" target="_self">Th38</a></i>;<br/><a NAME="E3:59_2_2_1_3"/><i><font color="Green">E89</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K16">0.REAL</a> 2 &amp; ( ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  ) or ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> ) ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2_2_1_3"><i><font color="Green">E87</font></i></a>, <a class="ref" href="jgraph_2.html#T23">JGRAPH_2:23</a></i>;<br/><b>set </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font>;<br/><a NAME="E4:59_2_2_1_3"/><i><font color="Green">E90</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E7:59_2"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_2"><i><font color="Green">E86</font></i></a>, <a class="txt" href="jgraph_3.html#E2:59_2_2_1_3"><i><font color="Green">E88</font></i></a>, <a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/><a NAME="E5:59_2_2_1_3"/>
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E6:59_2_2_1_3"/><b>then </b><i><font color="Green">E91</font></i>: 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/><div><i><font color="Green">E92</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_2_1_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:59_2_2_1_3_1"/><i><font color="Green">E93</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</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>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E2:59_2_2_1_3_1"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_2_1_3"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_2_1_3"><i><font color="Green">E91</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E3:59_2_2_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="jgraph_3.html#E1:59_2_2_1_3"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E4:59_2_2_1_3"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_2_1_3"><i><font color="Green">E91</font></i></a>, <a class="txt" href="jgraph_3.html#E1:59_2_2_1_3_1"><i><font color="Green">E93</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E93</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_2_1_3_2"><b>now </b></a><div class="add"><a NAME="E1:59_2_2_1_3_2"/>
( ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  ) or ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</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>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E3:59_2_2_1_3"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_2_1_3"><i><font color="Green">E91</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E2:59_2_2_1_3_2"/><b>then </b>
( ( <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_2_1_3"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_2_1_3"><i><font color="Green">E91</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><b>hence </b><a NAME="E3:59_2_2_1_3_2"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_2_1_3"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E6:59_2_2_1_3"><i><font color="Green">E91</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/></div><b>end;</b></div><a NAME="E9:59_2_2_1_3"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E7:59_2"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_2"><i><font color="Green">E86</font></i></a>, <a class="ref" href="jgraph_3.html#T54" target="_self">Th54</a>, <a class="ref" href="funct_1.html#T54">FUNCT_1:54</a></i>;<br/><a NAME="E10:59_2_2_1_3"/><i><font color="Green">E95</font></i>: 
<a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_2_1_3"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E7:59_2_2_1_3"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_3.html#E8:59_2_2_1_3"><i><font color="Green">E93</font></i></a>, <a class="ref" href="jgraph_3.html#T14" target="_self">Th14</a>, <a class="ref" href="jgraph_2.html#T11">JGRAPH_2:11</a></i>;<br/><a NAME="E11:59_2_2_1_3"/><i><font color="Green">E96</font></i>: 
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`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>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/><a NAME="E12:59_2_2_1_3"/><i><font color="Green">E97</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/><a NAME="E13:59_2_2_1_3"/><i><font color="Green">E98</font></i>: 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </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_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E14:59_2_2_1_3"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="ref" href="toprns_1.html#T26">TOPRNS_1:26</a></i>;<br/><a NAME="E15:59_2_2_1_3"/><b>then </b>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E11:59_2"><i><font color="Green">E86</font></i></a>, <a class="txt" href="jgraph_3.html#E6"><i><font color="Green">Lemma6</font></i></a></i>;<br/><a NAME="E16:59_2_2_1_3"/><b>then </b><i><font color="Green">E99</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="jgraph_3.html#E11:59_2"><i><font color="Green">E86</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E17:59_2_2_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_2_1_3"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E7:59_2_2_1_3"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jgraph_3.html#E8:59_2_2_1_3"><i><font color="Green">E93</font></i></a></i>;<br/><a NAME="E18:59_2_2_1_3"/><b>then </b><i><font color="Green">E100</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E9:59_2_2_1_3"><i><font color="Green">E94</font></i></a>, <a class="txt" href="jgraph_3.html#E10:59_2_2_1_3"><i><font color="Green">E95</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59_2_2_1_3"><i><font color="Green">E96</font></i></a>, <a class="ref" href="jgraph_1.html#T46">JGRAPH_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</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#K3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <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>
<b>by </b><i><a class="txt" href="jgraph_3.html#E13:59_2_2_1_3"><i><font color="Green">E98</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_3.html#E13:59_2_2_1_3"><i><font color="Green">E98</font></i></a>, <a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
;<br/><a NAME="E20:59_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E13:59_2_2_1_3"><i><font color="Green">E98</font></i></a>, <a class="txt" href="jgraph_3.html#E16:59_2_2_1_3"><i><font color="Green">E99</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E21:59_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_3.html#E13:59_2_2_1_3"><i><font color="Green">E98</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E22:59_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/><a NAME="E23:59_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><a NAME="E24:59_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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_3.html#E12:59_2_2_1_3"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E25:59_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> 
 <b>by </b><i><a class="txt" href="jgraph_3.html#E18:59_2_2_1_3"><i><font color="Green">E100</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E26:59_2_2_1_3"/><b>then </b><i><font color="Green">E101</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E78"><i><font color="Green">Lemma65</font></i></a></i>;<br/><a NAME="E27:59_2_2_1_3"/><i><font color="Green">E102</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E7:59_2_2_1_3"><i><font color="Green">E92</font></i></a>, <a class="ref" href="complex1.html#T2">COMPLEX1:2</a></i>;<br/><a NAME="E28:59_2_2_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/><a NAME="E29:59_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="real_1.html#K3">+</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E12:59_2_2_1_3"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E30:59_2_2_1_3"/><b>then </b><i><font color="Green">E103</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="jgraph_3.html#E26:59_2_2_1_3"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jgraph_3.html#E27:59_2_2_1_3"><i><font color="Green">E102</font></i></a>, <a class="ref" href="real_2.html#T122">REAL_2:122</a></i>;<br/><a NAME="E31:59_2_2_1_3"/><b>then </b><i><font color="Green">E104</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E15"><i><font color="Green">Lemma7</font></i></a></i>;<br/><a NAME="E32:59_2_2_1_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E4:59_2_2_1_3"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jgraph_3.html#E8:59_2_2_1_3"><i><font color="Green">E93</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><a NAME="E33:59_2_2_1_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E31:59_2_2_1_3"><i><font color="Green">E104</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><a NAME="E34:59_2_2_1_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <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> 1 ) )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E31:59_2_2_1_3"><i><font color="Green">E104</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E35:59_2_2_1_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 ) )
 <b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/><b>hence </b><a NAME="E36:59_2_2_1_3"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E30:59_2_2_1_3"><i><font color="Green">E103</font></i></a>, <a class="txt" href="jgraph_3.html#E15"><i><font color="Green">Lemma7</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E13:59_2"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E6:59_2"><i><font color="Green">E84</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E21:59"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>10</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E1:59"><i><font color="Green">E67</font></i></a>, <a class="txt" href="jgraph_3.html#E10:59"><i><font color="Green">E73</font></i></a>, <a class="txt" href="jgraph_3.html#E11:59"><i><font color="Green">E74</font></i></a>, <a class="txt" href="jgraph_3.html#E12:59"><i><font color="Green">E75</font></i></a>, <a class="txt" href="jgraph_3.html#E13:59"><i><font color="Green">E76</font></i></a>, <a class="txt" href="jgraph_3.html#E19:59"><i><font color="Green">E81</font></i></a>, <a class="ref" href="jgraph_1.html#T65">JGRAPH_1:65</a></i>;<br/>
<a NAME="E22:59"/><b>then </b><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>14</sub></font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>;<br/>
<a NAME="E24:59"/><i><font color="Green">E83</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E22:59"><i><font color="Green">E82</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>15</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E26:59"/><i><font color="Green">E84</font></i>: 
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="wellfnd1.html#K1">dom</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>16</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E28:59"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="wellfnd1.html#K1">dom</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> )
 <b>by </b><i><a class="txt" href="jgraph_3.html#E24:59"><i><font color="Green">E83</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E29:59"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E26:59"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<a NAME="E30:59"/><i><font color="Green">E87</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="jgraph_3.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E31:59"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="wellfnd1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E26:59"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/>
<a NAME="E32:59"/><b>then </b><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E33:59"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="wellfnd1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E28:59"><i><font color="Green">E85</font></i></a>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/>
<a NAME="E34:59"/><b>then </b><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E35:59"/>
<font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jgraph_3.html#K1" target="_self">Sq_Circ</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E28:59"><i><font color="Green">E85</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<a NAME="E36:59"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E26:59"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jgraph_3.html#E28:59"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jgraph_3.html#E29:59"><i><font color="Green">E86</font></i></a>, <a class="txt" href="jgraph_3.html#E30:59"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jgraph_3.html#E32:59"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E34:59"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jgraph_3.html#E75"><i><font color="Green">Lemma63</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<a NAME="E37:59"/><b>then </b>
<span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="jgraph_3.html#E32:59"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jgraph_3.html#E34:59"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E38:59"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>


</div>
