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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="goboard5.html#NM1">special_circular_sequence</a>;<br/>

<b>set </b><font color="Maroon">G</font> =  <a href="goboard2.html#K3">GoB</a> <font color="Maroon">f</font>;<br/>
<a NAME="E1:30"/><i><font color="Green">E35</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">f</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="ref" href="goboard7.html#T35">GOBOARD7:35</a></i>;<br/>
<a NAME="E2:30"/><i><font color="Green">E36</font></i>: 
 <a href="jordan5d.html#K7">i_w_n</a> <font color="Maroon">f</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan5d.html#T47">JORDAN5D:47</a></i>;<br/>
<a NAME="E3:30"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">f</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan5d.html#K7">i_w_n</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K29">N-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan5d.html#D7">JORDAN5D:def 7</a></i>;<br/>
<a NAME="E4:30"/><i><font color="Green">E38</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="jordan5d.html#K8">i_e_n</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="jordan5d.html#T47">JORDAN5D:47</a></i>;<br/>
<a NAME="E5:30"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">f</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan5d.html#K8">i_e_n</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K30">N-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan5d.html#D8">JORDAN5D:def 8</a></i>;<br/>
<a NAME="E6:30"/><i><font color="Green">E64</font></i>: 
<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">f</font></span>)</span></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K30">N-max</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="ref" href="sprect_2.html#T55">SPRECT_2:55</a></i>;<br/>
<a NAME="E7:30"/><b>then </b><i><font color="Green">E65</font></i>: 
 <a href="jordan5d.html#K7">i_w_n</a> <font color="Maroon">f</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="jordan5d.html#K8">i_e_n</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="jordan5d.html#D7">JORDAN5D:def 7</a></i>;<br/>
<b>assume </b><a NAME="E8:30"/>
 <a href="jordan5d.html#K7">i_w_n</a> <font color="Maroon">f</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="jordan5d.html#K8">i_e_n</a> <font color="Maroon">f</font>
 ;<br/>

<a NAME="E9:30"/><b>then </b>
 <a href="jordan5d.html#K7">i_w_n</a> <font color="Maroon">f</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="jordan5d.html#K8">i_e_n</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<b>hence </b><a NAME="E10:30"/>
contradiction
 <b>by </b><i>, , , , , , <a class="ref" href="goboard5.html#T4">GOBOARD5:4</a></i>;<br/>


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