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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">g</font> be  <a href="finseq_6.html#V1">circular</a>  <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:7"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E2:7"/><i><font color="Green">E32</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>and </b><br/><a NAME="E3:7"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font>
 ;<br/>

<a NAME="E4:7"/><i><font color="Green">E35</font></i>: 
not <font color="Maroon">g</font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<a NAME="E5:7"/>
<font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">g</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#T31">FINSEQ_4:31</a></i>;<br/>
<a NAME="E6:7"/><b>then </b>
<font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font>
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<b>then </b><font color="Maroon">p</font> = 
<font color="Maroon">g</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_5.html#T41">FINSEQ_5:41</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="finseq_4.html#K4">/.</a> 1
<b>by </b><i><a class="ref" href="finseq_6.html#D1">FINSEQ_6:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E8:7"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="finseq_6.html#T47">FINSEQ_6:47</a></i>;<br/>


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