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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:111"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1"><b>suppose </b></a><a NAME="E1:111_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:111_1_1"/>
 <a href="finseq_6.html#K1" target="_self">Rotate</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_6.html#T103" target="_self">Th103</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_2"><b>suppose </b></a><a NAME="E1:111_1_2"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:111_1_2"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="finseq_6.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E3:111_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b> <a href="finseq_6.html#K1" target="_self">Rotate</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>,<font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_6.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:111"><i><font color="Green">E95</font></i></a>, <a class="txt" href="finseq_6.html#E1:111_1_2"><i><font color="Green">E96</font></i></a>, <a class="ref" href="finseq_6.html#T59" target="_self">Th59</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:111"><i><font color="Green">E95</font></i></a>, <a class="txt" href="finseq_6.html#E1:111_1_2"><i><font color="Green">E96</font></i></a>, <a class="ref" href="finseq_6.html#T55" target="_self">Th55</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_6.html#T51" target="_self">Th51</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

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