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<b>let </b><font color="Maroon">f</font> be  non <a href="funct_1.html#V3">constant</a> <a href="goboard5.html#V2">standard</a> <a href="sprect_2.html#V1">clockwise_oriented</a> <a href="goboard5.html#NM1">special_circular_sequence</a>;<br/><b>let </b><font color="Maroon">G</font> be   <a href="goboard1.html#NM1">Go-board</a>;<br/>



<b>assume </b><a NAME="E1:15"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">f</font> <a href="goboard1.html#R1">is_sequence_on</a> <font color="Maroon">G</font>
 ;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:15"/><i><font color="Green">E45</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 <b>and </b><br/><a NAME="E3:15"/><i><font color="Green">E46</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <font color="Maroon">G</font>
 <b>and </b><br/><a NAME="E4:15"/><i><font color="Green">E47</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">j</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <font color="Maroon">G</font>
 <b>and </b><br/><a NAME="E5:15"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>
 <b>and </b><br/><a NAME="E6:15"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">j</font>
 ;<br/>

<a NAME="E7:15"/><i><font color="Green">E58</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">G</font> )
 
<b>by </b><i>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/>
<b>assume </b><a NAME="E8:15"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 ;<br/>

<a NAME="E9:15"/><b>then </b>
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<a NAME="E10:15"/><b>then </b><i><font color="Green">E59</font></i>: 
<font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>;<br/>
<a NAME="E11:15"/>
 <a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">f</font>,<font color="Maroon">k</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i>, , , , , , <a class="ref" href="gobrd13.html#T25">GOBRD13:25</a></i>;<br/>
<a NAME="E12:15"/><b>then </b><i><font color="Green">E60</font></i>: 
not  <a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">f</font>,<font color="Maroon">k</font>,<font color="Maroon">G</font> is <a href="jordan2c.html#V1">Bounded</a>
 
<b>by </b><i>, , <a class="ref" href="jordan1a.html#T47">JORDAN1A:47</a></i>;<br/>
<a NAME="E13:15"/><i><font color="Green">E61</font></i>: 
 <a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font> is <a href="jordan2c.html#V1">Bounded</a>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T73">JORDAN2C:73</a></i>;<br/>
<a NAME="E14:15"/><b>then </b><i><font color="Green">E62</font></i>: 
not <span class="p1">(<span class="default"><a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">f</font>,<font color="Maroon">k</font>,<font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> is <a href="jordan2c.html#V1">Bounded</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E15:15"/>
<span class="p1">(<span class="default"><a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">f</font>,<font color="Maroon">k</font>,<font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K3">RightComp</a> <font color="Maroon">f</font>
 
<b>by </b><i>, , <a class="ref" href="jordan9.html#T29">JORDAN9:29</a></i>;<br/>
<a NAME="E16:15"/><b>then </b>
not  <a href="goboard9.html#K3">RightComp</a> <font color="Maroon">f</font> is <a href="jordan2c.html#V1">Bounded</a>
 
<b>by </b><i>, <a class="ref" href="jordan2c.html#T16">JORDAN2C:16</a></i>;<br/>
<a NAME="E17:15"/><b>then </b>
not  <a href="jordan2c.html#K1">BDD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> is <a href="jordan2c.html#V1">Bounded</a>
 
<b>by </b><i><a class="ref" href="gobrd14.html#T47">GOBRD14:47</a></i>;<br/>
<b>hence </b><a NAME="E18:15"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jordan2c.html#T114">JORDAN2C:114</a></i>;<br/>


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