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<b>let </b><font color="Maroon" title="c1">f</font> be  non <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> <a href="goboard5.html#V2" title="GOBOARD5:attr.2">standard</a> <a href="goboard5.html#NM1" title="GOBOARD5:NM.1">special_circular_sequence</a>;<br/>

<b>assume </b><a NAME="E1:55"/><i><font color="Green" title="E39">A1</font></i>: 
 <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon" title="c2">g</font> =  <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>;<br/>
<a NAME="E2:55"/><i><font color="Green" title="E40">A2</font></i>: 
 <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="revrot_1.html#T33" title="REVROT_1:th.33">REVROT_1:33</a></i>;<br/>
<b>assume </b><a NAME="E3:55"/>
not <font color="Maroon" title="c1">f</font> is <a href="sprect_2.html#V1" title="SPRECT_2:attr.1">clockwise_oriented</a>
 ;<br/>

<a NAME="E4:55"/><b>then </b>
not  <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">N-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> is <a href="sprect_2.html#V1" title="SPRECT_2:attr.1">clockwise_oriented</a>
 
<b>by </b><i><a class="ref" href="jordan1h.html#T48" target="_self" title="JORDAN1H:th.48">Th48</a></i>;<br/>
<a NAME="E5:55"/><b>then </b><i><font color="Green" title="E41">A3</font></i>: 
 <a href="goboard9.html#K1" title="GOBOARD9:func.1">Rev</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> is <a href="sprect_2.html#V1" title="SPRECT_2:attr.1">clockwise_oriented</a>
 
<b>by </b><i><a class="ref" href="revrot_1.html#T38" title="REVROT_1:th.38">REVROT_1:38</a></i>;<br/>
 <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> = 
 <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p2">(<span class="default"><a href="goboard9.html#K1" title="GOBOARD9:func.1">Rev</a> <span class="p3">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c1">f</font>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">N-min</a> <span class="p5">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan1h.html#E2:55"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="sppol_2.html#T22" title="SPPOL_2:th.22">SPPOL_2:22</a></i>
<br/>.= 
 <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <span class="p1">(<span class="default"><a href="goboard9.html#K1" title="GOBOARD9:func.1">Rev</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c1">f</font>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">N-min</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan1h.html#E5:55"><i><font color="Green" title="E41">A3</font></i></a>, <a class="ref" href="gobrd14.html#T46" title="GOBRD14:th.46">GOBRD14:46</a></i>
<br/>.= 
 <a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">N-min</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="goboard9.html#T26" title="GOBOARD9:th.26">GOBOARD9:26</a></i>
<br/>.= 
 <a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <font color="Maroon" title="c1">f</font>
<b>by </b><i><a class="ref" href="revrot_1.html#T37" title="REVROT_1:th.37">REVROT_1:37</a></i>
;<br/>
<b>hence </b><a NAME="E7:55"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan1h.html#E1:55"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="sprect_4.html#T7" title="SPRECT_4:th.7">SPRECT_4:7</a></i>;<br/>


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