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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="funct_1.html#V3">constant</a> <a href="goboard5.html#V2">standard</a> <a href="goboard5.html#NM1">special_circular_sequence</a>;<br/>

<b>assume </b><a NAME="E1:56"/><i><font color="Green">E39</font></i>: 
 <a href="goboard9.html#K2">LeftComp</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="jordan2c.html#K2">UBD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E2:56"/><i><font color="Green">E40</font></i>: 
 <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="revrot_1.html#T33">REVROT_1:33</a></i>;<br/>
<b>assume </b><a NAME="E3:56"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="sprect_2.html#V1">clockwise_oriented</a>
 ;<br/>

<a NAME="E4:56"/><b>then </b>
not  <a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> is <a href="sprect_2.html#V1">clockwise_oriented</a>
 
<b>by </b><i><a class="ref" href="jordan1h.html#T48" target="_self">Th48</a></i>;<br/>
<a NAME="E5:56"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="goboard9.html#K1">Rev</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> is <a href="sprect_2.html#V1">clockwise_oriented</a>
 
<b>by </b><i><a class="ref" href="revrot_1.html#T38">REVROT_1:38</a></i>;<br/>
 <a href="jordan2c.html#K2">UBD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
 <a href="jordan2c.html#K2">UBD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="goboard9.html#K1">Rev</a> <span class="p3">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan1h.html#E2:56"><i><font color="Green">E40</font></i></a>, <a class="ref" href="sppol_2.html#T22">SPPOL_2:22</a></i>
<br/>.= 
 <a href="goboard9.html#K2">LeftComp</a> <span class="p1">(<span class="default"><a href="goboard9.html#K1">Rev</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan1h.html#E5:56"><i><font color="Green">E41</font></i></a>, <a class="ref" href="gobrd14.html#T46">GOBRD14:46</a></i>
<br/>.= 
 <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K29">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="goboard9.html#T26">GOBOARD9:26</a></i>
<br/>.= 
 <a href="goboard9.html#K3">RightComp</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="revrot_1.html#T37">REVROT_1:37</a></i>
;<br/>
<b>hence </b><a NAME="E7:56"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan1h.html#E1:56"><i><font color="Green">E39</font></i></a>, <a class="ref" href="sprect_4.html#T7">SPRECT_4:7</a></i>;<br/>


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