<?xml version="1.0"?>
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<b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be  <a href="xxreal_0.html#V2">positive</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:101"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal9.html#K1">Ball</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="topreal9.html#K2">cl_Ball</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> = <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> = <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>16</sub></font> =  <a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/>
<a NAME="E2:101"/><i><font color="Green">E76</font></i>: 
<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="toprealb.html#D6">TOPREALB:def 6</a></i>;<br/>
<a NAME="E3:101"/><i><font color="Green">E77</font></i>: 
 <a href="topreal9.html#K1">Ball</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="subset_1.html#R1">misses</a>  <a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="topreal9.html#T19">TOPREAL9:19</a></i>;<br/>
<a NAME="E4:101"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E5:101"/><i><font color="Green">E79</font></i>: 
 <a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a>  <a href="topreal9.html#K2">cl_Ball</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="topreal9.html#T17">TOPREAL9:17</a></i>;<br/>
<a NAME="E6:101"/><i><font color="Green">E80</font></i>: 
 <a href="topreal9.html#K1">Ball</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a>  <a href="topreal9.html#K2">cl_Ball</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="topreal9.html#T16">TOPREAL9:16</a></i>;<br/>
<a NAME="E7:101"/><i><font color="Green">E81</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2">Tdisk</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="topreal9.html#K2">cl_Ball</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="brouwer.html#T3">BROUWER:3</a></i>;<br/>
<a NAME="E8:101"/><i><font color="Green">E82</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E9:101"/><i><font color="Green">E83</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>17</sub></font> = <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>18</sub></font> =  <a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>19</sub></font> =  <a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>20</sub></font> =  <a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> =  <a href="jordan.html#K5" target="_self">diffX1_X2_1</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></font> =  <a href="jordan.html#K6" target="_self">diffX1_X2_2</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>23</sub></font> =  <a href="jordan.html#K7" target="_self">Proj2_1</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>24</sub></font> =  <a href="jordan.html#K8" target="_self">Proj2_2</a> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a>  as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>26</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="borsuk_1.html#K1">--&gt;</a> <font color="Maroon">c<sub>25</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>27</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="borsuk_1.html#K1">--&gt;</a> <font color="Maroon">c<sub>25</sub></font> as  <a href="pscomp_1.html#V9">continuous</a> <a href="pscomp_1.html#NM1">RealMap</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <b>by </b><i><a class="txt" href="jordan.html#E23"><i><font color="Green">Lemma18</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>29</sub></font> = <a href="jordan.html#K7" target="_self">Proj2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>30</sub></font> = <a href="jordan.html#K8" target="_self">Proj2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>31</sub></font> = <a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>32</sub></font> = <a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>33</sub></font> = <span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>34</sub></font> = <span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>35</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>36</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>37</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span>;<br/>
<a NAME="E12:101"/><i><font color="Green">E84</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E13:101"/><i><font color="Green">E85</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E14:101"/><i><font color="Green">E86</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E15:101"/><i><font color="Green">E87</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E16:101"/><i><font color="Green">E88</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span><br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>38</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>39</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>;<br/>



<a NAME="E1:101_1"/><i><font color="Green">E89</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>thus </b><a NAME="E2:101_1"/>
<span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E1:101_1"><i><font color="Green">E89</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E17:101"/><i><font color="Green">E89</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span><br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>38</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>39</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>;<br/>



<a NAME="E1:101_2"/><i><font color="Green">E90</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>thus </b><a NAME="E2:101_2"/>
<span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E1:101_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E18:101"/><i><font color="Green">E90</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span><br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="jordan.html#K7" target="_self">Proj2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K7" target="_self">Proj2_1</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>38</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>39</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>;<br/>



<a NAME="E1:101_3"/><i><font color="Green">E91</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>thus </b><a NAME="E2:101_3"/>
<span class="p1">(<span class="default"><a href="jordan.html#K7" target="_self">Proj2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K7" target="_self">Proj2_1</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E1:101_3"><i><font color="Green">E91</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E19:101"/><i><font color="Green">E91</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span><br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="jordan.html#K8" target="_self">Proj2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K8" target="_self">Proj2_2</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>38</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>39</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>;<br/>



<a NAME="E1:101_4"/><i><font color="Green">E92</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>thus </b><a NAME="E2:101_4"/>
<span class="p1">(<span class="default"><a href="jordan.html#K8" target="_self">Proj2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K8" target="_self">Proj2_2</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E1:101_4"><i><font color="Green">E92</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E20:101"/><i><font color="Green">E92</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span><br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>38</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>39</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>;<br/>



<a NAME="E1:101_5"/><i><font color="Green">E93</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>thus </b><a NAME="E2:101_5"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E1:101_5"><i><font color="Green">E93</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E21:101"/><i><font color="Green">E93</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span><br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>38</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>39</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>;<br/>



<a NAME="E1:101_6"/><i><font color="Green">E94</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>thus </b><a NAME="E2:101_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E1:101_6"><i><font color="Green">E94</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E22:101"/><i><font color="Green">E94</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span><br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>38</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>39</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>;<br/>



<a NAME="E1:101_7"/><i><font color="Green">E95</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>thus </b><a NAME="E2:101_7"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>39</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E1:101_7"><i><font color="Green">E95</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>38</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>assume </b><a NAME="E1:101_8"/>
<font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>39</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:101_8"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>39</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:101_8"/><i><font color="Green">E96</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>39</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>38</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>40</sub></font>, <font color="Maroon">c<sub>41</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:101_8"/><i><font color="Green">E97</font></i>: 
( <font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">c<sub>41</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>39</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>41</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="txt" href="jordan.html#E3:101_8"><i><font color="Green">E95</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E7:101_8"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E6:101_8"><i><font color="Green">E97</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>42</sub></font> = <font color="Maroon">c<sub>40</sub></font>, <font color="Maroon">c<sub>43</sub></font> = <font color="Maroon">c<sub>41</sub></font> as   <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>by </b><i><a class="txt" href="jordan.html#E6:101_8"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E9:101_8"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>43</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E3:101"><i><font color="Green">E77</font></i></a>, <a class="txt" href="jordan.html#E6:101_8"><i><font color="Green">E97</font></i></a>, <a class="txt" href="jordan.html#E7:101_8"><i><font color="Green">E98</font></i></a>, <a class="txt" href="jordan.html#E1:101"><i><font color="Green">E75</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><a NAME="E10:101_8"/>
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K1" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E22"><i><font color="Green">Lemma17</font></i></a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/><a NAME="E11:101_8"/><b>then </b><i><font color="Green">E100</font></i>: 
( <font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K1" target="_self">`1</a>  &amp; <font color="Maroon">c<sub>43</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a>  )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E12:101_8"/><i><font color="Green">E101</font></i>: 
<a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K1" target="_self">`1</a> </span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span>
 <b>by </b><i><a class="ref" href="jordan.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E13:101_8"/><i><font color="Green">E102</font></i>: 
<a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K1" target="_self">`1</a> </span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="jordan.html#D4" target="_self">Def4</a></i>;<br/><b>set </b><font color="Maroon">c<sub>44</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>42</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>43</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>45</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>42</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>43</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span>;<br/><a NAME="E14:101_8"/><i><font color="Green">E103</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E16:101"><i><font color="Green">E88</font></i></a>, <a class="txt" href="jordan.html#E6:101_8"><i><font color="Green">E97</font></i></a>, <a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a></i>;<br/><a NAME="E15:101_8"/><i><font color="Green">E104</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E6:101_8"><i><font color="Green">E97</font></i></a>, <a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan.html#E17:101"><i><font color="Green">E89</font></i></a></i>;<br/><i><font color="Green">E105</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E3:101_8"><i><font color="Green">E95</font></i></a>, <a class="txt" href="jordan.html#E6:101_8"><i><font color="Green">E97</font></i></a>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>43</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E3:101_8"><i><font color="Green">E95</font></i></a>, <a class="txt" href="jordan.html#E6:101_8"><i><font color="Green">E97</font></i></a>, <a class="txt" href="jordan.html#E14:101"><i><font color="Green">E86</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>42</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>43</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="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>42</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>43</sub></font> <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="jordan.html#E15:101_8"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jordan.html#E13:101_8"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E14:101_8"><i><font color="Green">E103</font></i></a>, <a class="txt" href="jordan.html#E12:101_8"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jordan.html#E11:101_8"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jordan.html#E3:101_8"><i><font color="Green">E95</font></i></a>, <a class="txt" href="jordan.html#E6:101_8"><i><font color="Green">E97</font></i></a>, <a class="txt" href="jordan.html#E15:101"><i><font color="Green">E87</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
;<br/><a NAME="E17:101_8"/><i><font color="Green">E106</font></i>: 
0 <a href="real_1.html#K3">+</a> 0 <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>42</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>43</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="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>42</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>43</sub></font> <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="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_8_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:101_8_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>42</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>43</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="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>42</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>43</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="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:101_8_2"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>42</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>43</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>42</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>43</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="complex1.html#T2">COMPLEX1:2</a></i>;<br/><b>hence </b><a NAME="E3:101_8_2"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan.html#E9:101_8"><i><font color="Green">E99</font></i></a>, <a class="ref" href="topreal3.html#T11">TOPREAL3:11</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E19:101_8"/>
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>38</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E4:101_8"><i><font color="Green">E96</font></i></a>, <a class="txt" href="jordan.html#E6:101_8"><i><font color="Green">E97</font></i></a>, <a class="txt" href="jordan.html#E16:101_8"><i><font color="Green">E105</font></i></a>, <a class="txt" href="jordan.html#E17:101_8"><i><font color="Green">E106</font></i></a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>38</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> as  <a href="pscomp_1.html#V9">continuous</a> <a href="partfun3.html#V1">positive-yielding</a> <a href="pscomp_1.html#NM1">RealMap</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <b>by </b><i><a class="ref" href="partfun3.html#D1">PARTFUN3:def 1</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>39</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>40</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>;<br/>
<a NAME="E25:101"/><i><font color="Green">E95</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E26:101"/><i><font color="Green">E96</font></i>: 
 <a href="relset_1.html#K4">dom</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E27:101"/><i><font color="Green">E97</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E28:101"/><i><font color="Green">E98</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_9"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>41</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>assume </b><a NAME="E1:101_9"/>
<font color="Maroon">c<sub>41</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>42</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:101_9"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:101_9"/><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"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>41</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>43</sub></font>, <font color="Maroon">c<sub>44</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:101_9"/><i><font color="Green">E101</font></i>: 
( <font color="Maroon">c<sub>43</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">c<sub>44</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>43</sub></font>,<font color="Maroon">c<sub>44</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="txt" href="jordan.html#E3:101_9"><i><font color="Green">E99</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>45</sub></font> = <font color="Maroon">c<sub>43</sub></font>, <font color="Maroon">c<sub>46</sub></font> = <font color="Maroon">c<sub>44</sub></font> as   <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>by </b><i><a class="txt" href="jordan.html#E6:101_9"><i><font color="Green">E101</font></i></a></i>;<br/><b>set </b><font color="Maroon">c<sub>47</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>46</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>48</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>46</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span>;<br/><a NAME="E8:101_9"/><i><font color="Green">E102</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E20:101"><i><font color="Green">E92</font></i></a>, <a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan.html#E6:101_9"><i><font color="Green">E101</font></i></a></i>;<br/><a NAME="E9:101_9"/><i><font color="Green">E103</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan.html#E6:101_9"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jordan.html#E21:101"><i><font color="Green">E93</font></i></a></i>;<br/><a NAME="E10:101_9"/><i><font color="Green">E104</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan.html#E6:101_9"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jordan.html#E22:101"><i><font color="Green">E94</font></i></a></i>;<br/><a NAME="E11:101_9"/>
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K1" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E22"><i><font color="Green">Lemma17</font></i></a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/><a NAME="E12:101_9"/><b>then </b><i><font color="Green">E105</font></i>: 
( <font color="Maroon">c<sub>45</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K1" target="_self">`1</a>  &amp; <font color="Maroon">c<sub>46</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a>  )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E13:101_9"/><i><font color="Green">E106</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>
 <b>by </b><i><a class="ref" href="jordan.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E14:101_9"/><i><font color="Green">E107</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="jordan.html#D2" target="_self">Def2</a></i>;<br/><i><font color="Green">E108</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"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E6:101_9"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jordan.html#E3:101_9"><i><font color="Green">E99</font></i></a>, <a class="ref" href="seq_1.html#D4">SEQ_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"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E8:101_9"><i><font color="Green">E102</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</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"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E6:101_9"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jordan.html#E3:101_9"><i><font color="Green">E99</font></i></a>, <a class="txt" href="jordan.html#E26:101"><i><font color="Green">E96</font></i></a>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</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"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E6:101_9"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jordan.html#E3:101_9"><i><font color="Green">E99</font></i></a>, <a class="txt" href="jordan.html#E27:101"><i><font color="Green">E97</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</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>46</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</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="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>46</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</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="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E14:101_9"><i><font color="Green">E107</font></i></a>, <a class="txt" href="jordan.html#E12:101_9"><i><font color="Green">E105</font></i></a>, <a class="txt" href="jordan.html#E10:101_9"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jordan.html#E9:101_9"><i><font color="Green">E103</font></i></a>, <a class="txt" href="jordan.html#E13:101_9"><i><font color="Green">E106</font></i></a>, <a class="txt" href="jordan.html#E6:101_9"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jordan.html#E3:101_9"><i><font color="Green">E99</font></i></a>, <a class="txt" href="jordan.html#E28:101"><i><font color="Green">E98</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
;<br/><a NAME="E16:101_9"/>
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>46</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="toprns_1.html#K5">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E5:101"><i><font color="Green">E79</font></i></a>, <a class="txt" href="jordan.html#E6:101_9"><i><font color="Green">E101</font></i></a>, <a class="ref" href="topreal9.html#T8">TOPREAL9:8</a></i>;<br/><a NAME="E17:101_9"/><b>then </b><i><font color="Green">E109</font></i>: 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>46</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></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> <font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> 
 <b>by </b><i><a class="ref" href="square_1.html#T77">SQUARE_1:77</a></i>;<br/><span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>46</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></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"><font color="Maroon">c<sub>46</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>7</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>46</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>7</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="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"><font color="Maroon">c<sub>46</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</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="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>46</sub></font> <a href="euclid.html#K20">-</a> <font color="Maroon">c<sub>7</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="topreal3.html#T8">TOPREAL3:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>46</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</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="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>46</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <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="ref" href="topreal3.html#T8">TOPREAL3:8</a></i>
;<br/><a NAME="E19:101_9"/><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>46</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</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="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>46</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</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="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="jordan.html#E17:101_9"><i><font color="Green">E109</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><b>hence </b><a NAME="E20:101_9"/>
0 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>41</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E4:101_9"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jordan.html#E6:101_9"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jordan.html#E15:101_9"><i><font color="Green">E108</font></i></a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>41</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> as  <a href="pscomp_1.html#V9">continuous</a> <a href="partfun3.html#V3">nonpositive-yielding</a> <a href="pscomp_1.html#NM1">RealMap</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <b>by </b><i><a class="ref" href="partfun3.html#D3">PARTFUN3:def 3</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>42</sub></font> = <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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>43</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun3.html#K15">-</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><a href="partfun3.html#K17">sqrt</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"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>44</sub></font> = <span class="p1">(<span class="default"><a href="jordan.html#K7" target="_self">Proj2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K12">+</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"><a href="partfun3.html#K15">-</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p4">(<span class="default"><a href="partfun3.html#K17">sqrt</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>45</sub></font> = <span class="p1">(<span class="default"><a href="jordan.html#K8" target="_self">Proj2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K12">+</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"><a href="partfun3.html#K15">-</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p4">(<span class="default"><a href="partfun3.html#K17">sqrt</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>46</sub></font> = <span class="p1">(<span class="default"><a href="jordan.html#K7" target="_self">Proj2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K12">+</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"><a href="partfun3.html#K15">-</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p4">(<span class="default"><a href="partfun3.html#K17">sqrt</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span>, <font color="Maroon">c<sub>47</sub></font> = <span class="p1">(<span class="default"><a href="jordan.html#K8" target="_self">Proj2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K12">+</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"><a href="partfun3.html#K15">-</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p4">(<span class="default"><a href="partfun3.html#K17">sqrt</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>,<a href="topmetr.html#K3">R^1</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>48</sub></font> = <span class="p1"><a href="funct_3.html#K14">&lt;:</a><span class="default"><font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>47</sub></font></span><a href="funct_3.html#K14">:&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>49</sub></font> =  <a href="topreala.html#K2">R2Homeomorphism</a> ;<br/>
<a NAME="E32:101"/><i><font color="Green">E99</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> holds <span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="partfun1.html#K1">*</a> <span class="p2"><a href="funct_3.html#K14">&lt;:</a><span class="default"><font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>47</sub></font></span><a href="funct_3.html#K14">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_10"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>50</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>;<br/>

<b>consider </b><font color="Maroon">c<sub>51</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="E2:101_10"/><i><font color="Green">E100</font></i>: 
( <font color="Maroon">c<sub>50</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>51</sub></font> &amp; <span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>50</sub></font> <a href="hidden.html#R1">=</a>  <a href="brouwer.html#K3">HC</a> <font color="Maroon">c<sub>51</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="jordan.html#E2:101"><i><font color="Green">E76</font></i></a>, <a class="txt" href="jordan.html#E1:101"><i><font color="Green">E75</font></i></a>, <a class="ref" href="jordan.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E3:101_10"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>50</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan.html#E3:101"><i><font color="Green">E77</font></i></a>, <a class="txt" href="jordan.html#E1:101"><i><font color="Green">E75</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E4:101_10"/><i><font color="Green">E102</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan.html#E4:101"><i><font color="Green">E78</font></i></a>, <a class="txt" href="jordan.html#E2:101_10"><i><font color="Green">E100</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>52</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>53</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>54</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>55</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>56</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</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>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</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"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</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="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</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="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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</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="xcmplx_0.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</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="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>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</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>;<br/>
<a NAME="E5:101_10"/>
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K1" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E22"><i><font color="Green">Lemma17</font></i></a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/>
<a NAME="E6:101_10"/><b>then </b><i><font color="Green">E103</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K1" target="_self">`1</a>  &amp; <font color="Maroon">c<sub>51</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a>  )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E7:101_10"/><i><font color="Green">E104</font></i>: 
<a href="jordan.html#K7" target="_self">Proj2_1</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="ref" href="jordan.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E8:101_10"/><i><font color="Green">E105</font></i>: 
<a href="jordan.html#K8" target="_self">Proj2_2</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span> <a href="euclid.html#K22">`2</a> 
 
<b>by </b><i><a class="ref" href="jordan.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E9:101_10"/><i><font color="Green">E106</font></i>: 
<a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K1" target="_self">`1</a> </span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="jordan.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E10:101_10"/><i><font color="Green">E107</font></i>: 
<a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K1" target="_self">`1</a> </span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="jordan.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E11:101_10"/><i><font color="Green">E108</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="jordan.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E12:101_10"/><i><font color="Green">E109</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="jordan.html#K2" target="_self">`2</a> </span>)</span> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="jordan.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E13:101_10"/><i><font color="Green">E110</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>46</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E14:101_10"/><i><font color="Green">E111</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>47</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E15:101_10"/><i><font color="Green">E112</font></i>: 
 <a href="relset_1.html#K4">dom</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"><a href="partfun3.html#K15">-</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p4">(<span class="default"><a href="partfun3.html#K17">sqrt</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E16:101_10"/><i><font color="Green">E113</font></i>: 
 <a href="relset_1.html#K4">dom</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"><a href="partfun3.html#K15">-</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p4">(<span class="default"><a href="partfun3.html#K17">sqrt</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E17:101_10"/><i><font color="Green">E114</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E18:101_10"/><i><font color="Green">E115</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E19:101_10"/><i><font color="Green">E116</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun3.html#K15">-</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><a href="partfun3.html#K17">sqrt</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"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E20:101_10"/><i><font color="Green">E117</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="partfun3.html#K15">-</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E21:101_10"/><i><font color="Green">E118</font></i>: 
 <a href="relset_1.html#K4">dom</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E22:101_10"/><i><font color="Green">E119</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E23:101_10"/><i><font color="Green">E120</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E24:101_10"/><i><font color="Green">E121</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p0"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E25:101_10"/><i><font color="Green">E122</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E26:101_10"/><i><font color="Green">E123</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E27:101_10"/><i><font color="Green">E124</font></i>: 
( <font color="Maroon">c<sub>51</sub></font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span> )
 
<b>by </b><i><a class="txt" href="jordan.html#E8:101"><i><font color="Green">E82</font></i></a>, <a class="txt" href="jordan.html#E2:101_10"><i><font color="Green">E100</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E28:101_10"/><b>then </b><i><font color="Green">E125</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E16:101"><i><font color="Green">E88</font></i></a></i>;<br/>
<a NAME="E29:101_10"/><i><font color="Green">E126</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E27:101_10"><i><font color="Green">E124</font></i></a>, <a class="txt" href="jordan.html#E17:101"><i><font color="Green">E89</font></i></a></i>;<br/>
<a NAME="E30:101_10"/><i><font color="Green">E127</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E27:101_10"><i><font color="Green">E124</font></i></a>, <a class="txt" href="jordan.html#E20:101"><i><font color="Green">E92</font></i></a></i>;<br/>
<a NAME="E31:101_10"/><i><font color="Green">E128</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E27:101_10"><i><font color="Green">E124</font></i></a>, <a class="txt" href="jordan.html#E21:101"><i><font color="Green">E93</font></i></a></i>;<br/>
<a NAME="E32:101_10"/><i><font color="Green">E129</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E27:101_10"><i><font color="Green">E124</font></i></a>, <a class="txt" href="jordan.html#E22:101"><i><font color="Green">E94</font></i></a></i>;<br/>
<i><font color="Green">E130</font></i>: <font color="Maroon">c<sub>38</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E13:101"><i><font color="Green">E85</font></i></a>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E17:101_10"><i><font color="Green">E114</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>51</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="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>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <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="jordan.html#E29:101_10"><i><font color="Green">E126</font></i></a>, <a class="txt" href="jordan.html#E10:101_10"><i><font color="Green">E107</font></i></a>, <a class="txt" href="jordan.html#E6:101_10"><i><font color="Green">E103</font></i></a>, <a class="txt" href="jordan.html#E28:101_10"><i><font color="Green">E125</font></i></a>, <a class="txt" href="jordan.html#E9:101_10"><i><font color="Green">E106</font></i></a>, <a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E18:101_10"><i><font color="Green">E115</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
;<br/>
<a NAME="E34:101_10"/><i><font color="Green">E131</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E22:101_10"><i><font color="Green">E119</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>;<br/>
<a NAME="E35:101_10"/><i><font color="Green">E132</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E23:101_10"><i><font color="Green">E120</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>;<br/>
<a NAME="E36:101_10"/><i><font color="Green">E133</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E21:101_10"><i><font color="Green">E118</font></i></a>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>;<br/>
<a NAME="E37:101_10"/><i><font color="Green">E134</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"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R1">=</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>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> 
 
<b>by </b><i><a class="txt" href="jordan.html#E28:101_10"><i><font color="Green">E125</font></i></a>, <a class="txt" href="jordan.html#E9:101_10"><i><font color="Green">E106</font></i></a>, <a class="txt" href="jordan.html#E31:101_10"><i><font color="Green">E128</font></i></a>, <a class="txt" href="jordan.html#E11:101_10"><i><font color="Green">E108</font></i></a>, <a class="txt" href="jordan.html#E36:101_10"><i><font color="Green">E133</font></i></a>, <a class="txt" href="jordan.html#E34:101_10"><i><font color="Green">E131</font></i></a>, <a class="txt" href="jordan.html#E35:101_10"><i><font color="Green">E132</font></i></a>, <a class="txt" href="jordan.html#E29:101_10"><i><font color="Green">E126</font></i></a>, <a class="txt" href="jordan.html#E10:101_10"><i><font color="Green">E107</font></i></a>, <a class="txt" href="jordan.html#E6:101_10"><i><font color="Green">E103</font></i></a>, <a class="txt" href="jordan.html#E32:101_10"><i><font color="Green">E129</font></i></a>, <a class="txt" href="jordan.html#E12:101_10"><i><font color="Green">E109</font></i></a>, <a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E25:101_10"><i><font color="Green">E122</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>;<br/>
<i><font color="Green">E135</font></i>: <font color="Maroon">c<sub>41</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E25:101"><i><font color="Green">E95</font></i></a>, <a class="ref" href="seq_1.html#D4">SEQ_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"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E30:101_10"><i><font color="Green">E127</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</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"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E26:101"><i><font color="Green">E96</font></i></a>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</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"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E27:101"><i><font color="Green">E97</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</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>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</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="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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</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="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E12:101_10"><i><font color="Green">E109</font></i></a>, <a class="txt" href="jordan.html#E6:101_10"><i><font color="Green">E103</font></i></a>, <a class="txt" href="jordan.html#E32:101_10"><i><font color="Green">E129</font></i></a>, <a class="txt" href="jordan.html#E31:101_10"><i><font color="Green">E128</font></i></a>, <a class="txt" href="jordan.html#E11:101_10"><i><font color="Green">E108</font></i></a>, <a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E28:101"><i><font color="Green">E98</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
;<br/>
<a NAME="E39:101_10"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="partfun3.html#K17">sqrt</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"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b><i><font color="Green">E136</font></i>: <span class="p1">(<span class="default"><a href="partfun3.html#K17">sqrt</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"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> = 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="ref" href="partfun3.html#D5">PARTFUN3:def 5</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E24:101_10"><i><font color="Green">E121</font></i></a>, <a class="ref" href="seq_1.html#D4">SEQ_1:def 4</a></i>
<br/>.= 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</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"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</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="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.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"><span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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="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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E33:101_10"><i><font color="Green">E130</font></i></a>, <a class="txt" href="jordan.html#E37:101_10"><i><font color="Green">E134</font></i></a>, <a class="txt" href="jordan.html#E38:101_10"><i><font color="Green">E135</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E26:101_10"><i><font color="Green">E123</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
;<br/>
<a NAME="E41:101_10"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K15">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><a href="partfun3.html#K17">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b><i><font color="Green">E137</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K15">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><a href="partfun3.html#K17">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K15">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><a href="partfun3.html#K17">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K5">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="ref" href="rfunct_1.html#D4">RFUNCT_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K15">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><a href="partfun3.html#K17">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K15">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K17">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</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="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>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</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>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E19:101_10"><i><font color="Green">E116</font></i></a>, <a class="txt" href="jordan.html#E33:101_10"><i><font color="Green">E130</font></i></a>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</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>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</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"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</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="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</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="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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</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="xcmplx_0.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</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="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>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</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>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E28:101_10"><i><font color="Green">E125</font></i></a>, <a class="txt" href="jordan.html#E9:101_10"><i><font color="Green">E106</font></i></a>, <a class="txt" href="jordan.html#E6:101_10"><i><font color="Green">E103</font></i></a>, <a class="txt" href="jordan.html#E31:101_10"><i><font color="Green">E128</font></i></a>, <a class="txt" href="jordan.html#E11:101_10"><i><font color="Green">E108</font></i></a>, <a class="txt" href="jordan.html#E34:101_10"><i><font color="Green">E131</font></i></a>, <a class="txt" href="jordan.html#E29:101_10"><i><font color="Green">E126</font></i></a>, <a class="txt" href="jordan.html#E10:101_10"><i><font color="Green">E107</font></i></a>, <a class="txt" href="jordan.html#E32:101_10"><i><font color="Green">E129</font></i></a>, <a class="txt" href="jordan.html#E12:101_10"><i><font color="Green">E109</font></i></a>, <a class="txt" href="jordan.html#E35:101_10"><i><font color="Green">E132</font></i></a>, <a class="txt" href="jordan.html#E36:101_10"><i><font color="Green">E133</font></i></a>, <a class="txt" href="jordan.html#E40:101_10"><i><font color="Green">E136</font></i></a>, <a class="txt" href="jordan.html#E20:101_10"><i><font color="Green">E117</font></i></a>, <a class="ref" href="seq_1.html#D7">SEQ_1:def 7</a></i>
;<br/>
<i><font color="Green">E138</font></i>: <font color="Maroon">c<sub>46</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K7" target="_self">Proj2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="partfun3.html#K15">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><a href="partfun3.html#K17">sqrt</a> <span class="p0">(<span class="default"><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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E13:101_10"><i><font color="Green">E110</font></i></a>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="partfun3.html#K15">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><a href="partfun3.html#K17">sqrt</a> <span class="p0">(<span class="default"><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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E27:101_10"><i><font color="Green">E124</font></i></a>, <a class="txt" href="jordan.html#E18:101"><i><font color="Green">E90</font></i></a>, <a class="txt" href="jordan.html#E7:101_10"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jordan.html#E6:101_10"><i><font color="Green">E103</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</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"><a href="real_1.html#K1">-</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>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="square_1.html#K6">sqrt</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p0">(<span class="default"><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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</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="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>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.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"><span class="p5">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</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="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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</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="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</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="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E28:101_10"><i><font color="Green">E125</font></i></a>, <a class="txt" href="jordan.html#E9:101_10"><i><font color="Green">E106</font></i></a>, <a class="txt" href="jordan.html#E6:101_10"><i><font color="Green">E103</font></i></a>, <a class="txt" href="jordan.html#E42:101_10"><i><font color="Green">E137</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E15:101_10"><i><font color="Green">E112</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
;<br/>
<i><font color="Green">E139</font></i>: <font color="Maroon">c<sub>47</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K8" target="_self">Proj2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="partfun3.html#K15">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><a href="partfun3.html#K17">sqrt</a> <span class="p0">(<span class="default"><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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E14:101_10"><i><font color="Green">E111</font></i></a>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="partfun3.html#K15">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p5">(<span class="default"><a href="partfun3.html#K17">sqrt</a> <span class="p0">(<span class="default"><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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14">(#)</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"><a href="jordan.html#K3" target="_self">diffX2_1</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" target="_self">diffX1_X2_1</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K12">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" target="_self">diffX2_2</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p5"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K13">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>38</sub></font> <a href="partfun3.html#K14">(#)</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K20">/</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="partfun3.html#K14">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" target="_self">diffX1_X2_2</a>  <a href="pscomp_1.html#K12">||</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E27:101_10"><i><font color="Green">E124</font></i></a>, <a class="txt" href="jordan.html#E19:101"><i><font color="Green">E91</font></i></a>, <a class="txt" href="jordan.html#E8:101_10"><i><font color="Green">E105</font></i></a>, <a class="txt" href="jordan.html#E6:101_10"><i><font color="Green">E103</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</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"><a href="real_1.html#K1">-</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>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="square_1.html#K6">sqrt</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p0">(<span class="default"><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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</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="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>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.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"><span class="p5">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</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="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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</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="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</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="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E29:101_10"><i><font color="Green">E126</font></i></a>, <a class="txt" href="jordan.html#E10:101_10"><i><font color="Green">E107</font></i></a>, <a class="txt" href="jordan.html#E6:101_10"><i><font color="Green">E103</font></i></a>, <a class="txt" href="jordan.html#E42:101_10"><i><font color="Green">E137</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan.html#E16:101_10"><i><font color="Green">E113</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
;<br/>
<a NAME="E45:101_10"/>
<font color="Maroon">c<sub>51</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E2:101_10"><i><font color="Green">E100</font></i></a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>50</sub></font> = 
<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>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</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"><a href="real_1.html#K1">-</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>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p0">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</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"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</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="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.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"><span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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="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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</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="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</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"><a href="real_1.html#K1">-</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>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p0">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</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"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</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="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.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"><span class="p1">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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="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>51</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</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>8</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</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="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>51</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="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>51</sub></font> <a href="euclid.html#K22">`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="jordan.html#E2:101_10"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jordan.html#E3:101_10"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jordan.html#E6:101"><i><font color="Green">E80</font></i></a>, <a class="txt" href="jordan.html#E7:101"><i><font color="Green">E81</font></i></a>, <a class="txt" href="jordan.html#E1:101"><i><font color="Green">E75</font></i></a>, <a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan.html#E5:101"><i><font color="Green">E79</font></i></a>, <a class="ref" href="brouwer.html#T8">BROUWER:8</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>46</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>47</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="txt" href="jordan.html#E43:101_10"><i><font color="Green">E138</font></i></a>, <a class="txt" href="jordan.html#E44:101_10"><i><font color="Green">E139</font></i></a></i>
<br/>.= 
<a href="topreala.html#K2">R2Homeomorphism</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>46</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>47</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="topreala.html#D2">TOPREALA:def 2</a></i>
<br/>.= 
<a href="topreala.html#K2">R2Homeomorphism</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="funct_3.html#K14">&lt;:</a><span class="default"><font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>47</sub></font></span><a href="funct_3.html#K14">:&gt;</a></span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E13:101_10"><i><font color="Green">E110</font></i></a>, <a class="txt" href="jordan.html#E14:101_10"><i><font color="Green">E111</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_3.html#T69">FUNCT_3:69</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="partfun1.html#K1">*</a> <span class="p2"><a href="funct_3.html#K14">&lt;:</a><span class="default"><font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>47</sub></font></span><a href="funct_3.html#K14">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>50</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="txt" href="jordan.html#E4:101_10"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E2:101_10"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
;<br/><br/>


</div><b>end;</b></div>
<a NAME="E33:101"/>
( <font color="Maroon">c<sub>46</sub></font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">c<sub>47</sub></font> is <a href="pre_topc.html#V5">continuous</a> )
 
<b>by </b><i><a class="ref" href="topreal6.html#T83">TOPREAL6:83</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>50</sub></font> = <span class="p1"><a href="funct_3.html#K14">&lt;:</a><span class="default"><font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>47</sub></font></span><a href="funct_3.html#K14">:&gt;</a></span> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>,<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><a href="topmetr.html#K3">R^1</a> ,<a href="topmetr.html#K3">R^1</a> </span><a href="borsuk_1.html#K5">:]</a></span> <b>by </b><i><a class="ref" href="yellow12.html#T41">YELLOW12:41</a></i>;<br/>
<a NAME="E35:101"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span><br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> st <span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a> holds <br/>ex <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Olive">b<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>2</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_11"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>51</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>52</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:101_11"/><i><font color="Green">E100</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>51</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>52</sub></font>
 <b>and </b><br/><a NAME="E2:101_11"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>52</sub></font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>53</sub></font> = <font color="Maroon">c<sub>51</sub></font>, <font color="Maroon">c<sub>54</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <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>by </b><i><a class="ref" href="topmetr.html#T2">TOPMETR:2</a></i>;<br/>
<a NAME="E4:101_11"/><i><font color="Green">E102</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan.html#E4:101"><i><font color="Green">E78</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>55</sub></font> being   <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><b> such that </b><br/><a NAME="E6:101_11"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>55</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E7:101_11"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>55</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>52</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E2:101_11"><i><font color="Green">E101</font></i></a>, <a class="ref" href="tops_2.html#T32">TOPS_2:32</a></i>;<br/>
<a NAME="E8:101_11"/><i><font color="Green">E105</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>51</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>51</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E32:101"><i><font color="Green">E99</font></i></a></i>;<br/>
<a NAME="E9:101_11"/>
<a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a>  <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 
<b>by </b><i><a class="ref" href="tops_2.html#T70">TOPS_2:70</a>, <a class="ref" href="topreala.html#T56">TOPREALA:56</a></i>;<br/>
<a NAME="E10:101_11"/><b>then </b><i><font color="Green">E106</font></i>: 
<span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>55</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E6:101_11"><i><font color="Green">E103</font></i></a>, <a class="ref" href="topgrp_1.html#T25">TOPGRP_1:25</a></i>;<br/>
<a NAME="E11:101_11"/><i><font color="Green">E107</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>50</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E12:101_11"/><i><font color="Green">E108</font></i>: 
 <a href="relset_1.html#K4">dom</a> <a href="topreala.html#K2">R2Homeomorphism</a>  <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><a href="topmetr.html#K3">R^1</a> ,<a href="topmetr.html#K3">R^1</a> </span><a href="borsuk_1.html#K5">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E13:101_11"/><b>then </b><i><font color="Green">E109</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>50</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <a href="topreala.html#K2">R2Homeomorphism</a> 
 
;<br/>
<a NAME="E14:101_11"/><b>then </b><i><font color="Green">E110</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>50</sub></font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>
<a NAME="E15:101_11"/><i><font color="Green">E111</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <a href="topreala.html#K2">R2Homeomorphism</a>  <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> &amp;  <a href="topreala.html#K2">R2Homeomorphism</a>  is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i><a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a>, <a class="ref" href="topreala.html#T56">TOPREALA:56</a></i>;<br/>
<i><font color="Green">E112</font></i>: <span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <a href="topreala.html#K2">R2Homeomorphism</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <a href="topreala.html#K2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font>
<b>by </b><i><a class="txt" href="jordan.html#E15:101_11"><i><font color="Green">E111</font></i></a>, <a class="ref" href="tops_2.html#T65">TOPS_2:65</a></i>
;<br/>
<a NAME="E17:101_11"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <a href="topreala.html#K2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <a href="topreala.html#K2">R2Homeomorphism</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<a NAME="E18:101_11"/><b>then </b><i><font color="Green">E113</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <a href="topreala.html#K2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>50</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E13:101_11"><i><font color="Green">E109</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>
<a NAME="E19:101_11"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>50</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <a href="topreala.html#K2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>50</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="101_11_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>56</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:101_11_2"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>56</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>50</sub></font>
 ;<br/>

<a NAME="E2:101_11_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>50</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>56</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>50</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E1:101_11_2"><i><font color="Green">E114</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <a href="topreala.html#K2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>56</sub></font> = 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <a href="topreala.html#K2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>56</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E1:101_11_2"><i><font color="Green">E114</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">c<sub>50</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>56</sub></font>
<b>by </b><i><a class="txt" href="jordan.html#E12:101_11"><i><font color="Green">E108</font></i></a>, <a class="txt" href="jordan.html#E2:101_11_2"><i><font color="Green">E115</font></i></a>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E20:101_11"/><b>then </b><i><font color="Green">E114</font></i>: 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <a href="topreala.html#K2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>50</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E18:101_11"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>
<a NAME="E21:101_11"/>
<span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>54</sub></font>,<font color="Maroon">c<sub>53</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>55</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E1:101_11"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jordan.html#E7:101_11"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jordan.html#E8:101_11"><i><font color="Green">E105</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E22:101_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>54</sub></font>,<font color="Maroon">c<sub>53</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>55</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/>
<a NAME="E23:101_11"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>54</sub></font>,<font color="Maroon">c<sub>53</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>55</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E4:101_11"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E14:101_11"><i><font color="Green">E110</font></i></a>, <a class="txt" href="jordan.html#E11:101_11"><i><font color="Green">E107</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>56</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span><b> such that </b><br/><a NAME="E25:101_11"/><i><font color="Green">E115</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>54</sub></font>,<font color="Maroon">c<sub>53</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>56</sub></font>
 <b>and </b><br/><a NAME="E26:101_11"/><i><font color="Green">E116</font></i>: 
<font color="Maroon">c<sub>56</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E27:101_11"/><i><font color="Green">E117</font></i>: 
<font color="Maroon">c<sub>50</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>56</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>55</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E4:101_11"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan.html#E10:101_11"><i><font color="Green">E106</font></i></a>, <a class="txt" href="jordan.html#E16:101_11"><i><font color="Green">E112</font></i></a>, <a class="txt" href="jordan.html#E20:101_11"><i><font color="Green">E114</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="ref" href="jgraph_2.html#T20">JGRAPH_2:20</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>57</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span><b> such that </b><br/><a NAME="E29:101_11"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">c<sub>57</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E30:101_11"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">c<sub>57</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>56</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E26:101_11"><i><font color="Green">E116</font></i></a>, <a class="ref" href="tops_2.html#T32">TOPS_2:32</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>58</sub></font> being   <a href="struct_0.html#NM3">Subset-Family</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span><b> such that </b><br/><a NAME="E32:101_11"/><i><font color="Green">E120</font></i>: 
<font color="Maroon">c<sub>57</sub></font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>58</sub></font>
 <b>and </b><br/><a NAME="E33:101_11"/><i><font color="Green">E121</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>58</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <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> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="borsuk_1.html#K6">:]</a></span> &amp; <font color="Olive">b<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">b<sub>3</sub></font> is <a href="pre_topc.html#V3">open</a> )
 <b>by </b><i><a class="txt" href="jordan.html#E29:101_11"><i><font color="Green">E118</font></i></a>, <a class="ref" href="borsuk_1.html#T45">BORSUK_1:45</a></i>;<br/>
<a NAME="E34:101_11"/>
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>54</sub></font>,<font color="Maroon">c<sub>53</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>57</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E30:101_11"><i><font color="Green">E119</font></i></a>, <a class="txt" href="jordan.html#E25:101_11"><i><font color="Green">E115</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>59</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E36:101_11"/><i><font color="Green">E122</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>54</sub></font>,<font color="Maroon">c<sub>53</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>59</sub></font>
 <b>and </b><br/><a NAME="E37:101_11"/><i><font color="Green">E123</font></i>: 
<font color="Maroon">c<sub>59</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>58</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E32:101_11"><i><font color="Green">E120</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>60</sub></font>, <font color="Maroon">c<sub>61</sub></font> being   <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><b> such that </b><br/><a NAME="E39:101_11"/><i><font color="Green">E124</font></i>: 
<font color="Maroon">c<sub>59</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">c<sub>60</sub></font>,<font color="Maroon">c<sub>61</sub></font></span><a href="borsuk_1.html#K6">:]</a></span>
 <b>and </b><br/><a NAME="E40:101_11"/>
<font color="Maroon">c<sub>60</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E41:101_11"/><i><font color="Green">E125</font></i>: 
<font color="Maroon">c<sub>61</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="txt" href="jordan.html#E33:101_11"><i><font color="Green">E121</font></i></a>, <a class="txt" href="jordan.html#E37:101_11"><i><font color="Green">E123</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>62</sub></font> = <font color="Maroon">c<sub>59</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>63</sub></font> = <font color="Maroon">c<sub>61</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p3">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span></span>)</span> as  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <b>by </b><i><a class="txt" href="jordan.html#E41:101_11"><i><font color="Green">E125</font></i></a>, <a class="ref" href="tops_2.html#T32">TOPS_2:32</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>63</sub></font>
;<br/>

<a NAME="E43:101_11"/>
<font color="Maroon">c<sub>51</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>61</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E36:101_11"><i><font color="Green">E122</font></i></a>, <a class="txt" href="jordan.html#E39:101_11"><i><font color="Green">E124</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>hence </b><a NAME="E44:101_11"/>
<font color="Maroon">c<sub>51</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>63</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>

<b>thus </b><a NAME="E45:101_11"/>
<font color="Maroon">c<sub>63</sub></font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>64</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E46:101_11"/>
<font color="Maroon">c<sub>64</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>63</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>65</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span><b> such that </b><br/><a NAME="E48:101_11"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">c<sub>65</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>63</sub></font>
 <b>and </b><br/><a NAME="E49:101_11"/><i><font color="Green">E127</font></i>: 
<font color="Maroon">c<sub>64</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>65</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E2:101"><i><font color="Green">E76</font></i></a>, <a class="ref" href="funct_2.html#T116">FUNCT_2:116</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>66</sub></font> = <font color="Maroon">c<sub>65</sub></font>, <font color="Maroon">c<sub>67</sub></font> = <font color="Maroon">c<sub>54</sub></font> as   <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>by </b><i><a class="ref" href="topmetr.html#T2">TOPMETR:2</a></i>;<br/>
<a NAME="E51:101_11"/><i><font color="Green">E128</font></i>: 
<font color="Maroon">c<sub>65</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>61</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E48:101_11"><i><font color="Green">E126</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E52:101_11"/><i><font color="Green">E129</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>65</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E9:101"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan.html#E4:101"><i><font color="Green">E78</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E53:101_11"/>
<font color="Maroon">c<sub>67</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>60</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E36:101_11"><i><font color="Green">E122</font></i></a>, <a class="txt" href="jordan.html#E39:101_11"><i><font color="Green">E124</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E54:101_11"/><b>then </b>
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>67</sub></font>,<font color="Maroon">c<sub>65</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>59</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E39:101_11"><i><font color="Green">E124</font></i></a>, <a class="txt" href="jordan.html#E51:101_11"><i><font color="Green">E128</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E55:101_11"/><b>then </b>
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>67</sub></font>,<font color="Maroon">c<sub>65</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>59</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E52:101_11"><i><font color="Green">E129</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E56:101_11"/><b>then </b><i><font color="Green">E130</font></i>: 
<font color="Maroon">c<sub>50</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>67</sub></font>,<font color="Maroon">c<sub>66</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>50</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>59</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p3">(<span class="default"><span class="p4"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p5">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p5">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/>
<a NAME="E57:101_11"/><i><font color="Green">E131</font></i>: 
<a href="topreala.html#K2">R2Homeomorphism</a>  <a href="funct_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> <a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> 
 
<b>by </b><i><a class="txt" href="jordan.html#E15:101_11"><i><font color="Green">E111</font></i></a>, <a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>;<br/>
<a NAME="E58:101_11"/><i><font color="Green">E132</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E15:101_11"><i><font color="Green">E111</font></i></a>, <a class="ref" href="tops_2.html#T62">TOPS_2:62</a></i>;<br/>
<a NAME="E59:101_11"/><i><font color="Green">E133</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>66</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E2:101"><i><font color="Green">E76</font></i></a>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/>
<a NAME="E60:101_11"/>
<font color="Maroon">c<sub>59</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>57</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E32:101_11"><i><font color="Green">E120</font></i></a>, <a class="txt" href="jordan.html#E37:101_11"><i><font color="Green">E123</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E61:101_11"/><b>then </b>
<font color="Maroon">c<sub>59</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>57</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/>
<a NAME="E62:101_11"/><b>then </b>
<font color="Maroon">c<sub>50</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>59</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p3">(<span class="default"><span class="p4"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p5">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p5">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p4"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>50</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>56</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E30:101_11"><i><font color="Green">E119</font></i></a>, <a class="ref" href="relat_1.html#T156">RELAT_1:156</a></i>;<br/>
<a NAME="E63:101_11"/><b>then </b>
<font color="Maroon">c<sub>50</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>67</sub></font>,<font color="Maroon">c<sub>66</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>50</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>56</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E56:101_11"><i><font color="Green">E130</font></i></a></i>;<br/>
<a NAME="E64:101_11"/><b>then </b>
<a href="topreala.html#K2">R2Homeomorphism</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>50</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>67</sub></font>,<font color="Maroon">c<sub>66</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span> <a href="hidden.html#R2">in</a> <a href="topreala.html#K2">R2Homeomorphism</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>55</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E27:101_11"><i><font color="Green">E117</font></i></a>, <a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/>
<a NAME="E65:101_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>67</sub></font>,<font color="Maroon">c<sub>66</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <a href="topreala.html#K2">R2Homeomorphism</a>  <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>55</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E52:101_11"><i><font color="Green">E129</font></i></a>, <a class="txt" href="jordan.html#E12:101"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>
<a NAME="E66:101_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreala.html#K2">R2Homeomorphism</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>67</sub></font>,<font color="Maroon">c<sub>66</sub></font></span><a href="borsuk_1.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>55</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E15:101_11"><i><font color="Green">E111</font></i></a>, <a class="txt" href="jordan.html#E58:101_11"><i><font color="Green">E132</font></i></a>, <a class="txt" href="jordan.html#E57:101_11"><i><font color="Green">E131</font></i></a>, <a class="ref" href="partfun3.html#T1">PARTFUN3:1</a></i>;<br/>
<a NAME="E67:101_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>65</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>55</sub></font>
 
<b>by </b><i><a class="txt" href="jordan.html#E32:101"><i><font color="Green">E99</font></i></a></i>;<br/>
<b>hence </b><a NAME="E68:101_11"/>
<font color="Maroon">c<sub>64</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>52</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E7:101_11"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jordan.html#E49:101_11"><i><font color="Green">E127</font></i></a>, <a class="txt" href="jordan.html#E59:101_11"><i><font color="Green">E133</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E36:101"/>
 <a href="jordan.html#K10" target="_self">RotateCircle</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="txt" href="jordan.html#E2:101"><i><font color="Green">E76</font></i></a>, <a class="ref" href="jgraph_2.html#T20">JGRAPH_2:20</a></i>;<br/>


</div>
