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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="101_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:101_1_1_1"/>
(  not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> or ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> &amp; <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> <a href="finseq_4.html#K4">/.</a> 1 ) or ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> 1 ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="101_1_1_1_1"><b>suppose </b></a><a NAME="E1:101_1_1_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:101_1_1_1_1"/>
 <a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="finseq_6.html#V1" target="_self">circular</a>
 <b>by </b><i><a class="ref" href="finseq_6.html#D2" target="_self">Def2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="101_1_1_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:101_1_1_1_2"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:101_1_1_1_2"/><i><font color="Green">E91</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> <a href="finseq_4.html#K4">/.</a> 1
 ;<br/><div class="add"><a NAME="E3:101_1_1_1_2"/><i><font color="Green">E92</font></i>: 
 <a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:101_1_1_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="finseq_6.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E4:101_1_1_1_2"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 )
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:101_1_1_1_2"><i><font color="Green">E90</font></i></a>, <a class="txt" href="finseq_6.html#E2:101_1_1_1_2"><i><font color="Green">E91</font></i></a>, <a class="ref" href="finseq_4.html#T31">FINSEQ_4:31</a>, <a class="ref" href="finseq_5.html#T41">FINSEQ_5:41</a></i>;<br/><a NAME="E5:101_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E6:101_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E7:101_1_1_1_2"/><b>then </b><i><font color="Green">E93</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:101_1_1_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="finseq_5.html#T45">FINSEQ_5:45</a></i>;<br/><a NAME="E8:101_1_1_1_2"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E9:101_1_1_1_2"/><b>then </b><i><font color="Green">E94</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>;<br/><a NAME="E10:101_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E11:101_1_1_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="finseq_6.html#E7:101_1_1_1_2"><i><font color="Green">E93</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E12:101_1_1_1_2"/><b>then </b><i><font color="Green">E95</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E13:101_1_1_1_2"/>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_5.html#T6">FINSEQ_5:6</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1
<b>by </b><i><a class="txt" href="finseq_6.html#E3:101_1_1_1_2"><i><font color="Green">E92</font></i></a>, <a class="ref" href="finseq_4.html#T83">FINSEQ_4:83</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="finseq_5.html#T56">FINSEQ_5:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:101_1_1_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="finseq_5.html#T48">FINSEQ_5:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:101_1_1_1_2"><i><font color="Green">E90</font></i></a>, <a class="txt" href="finseq_6.html#E9:101_1_1_1_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="finseq_5.html#T45">FINSEQ_5:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E12:101_1_1_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="finseq_5.html#T30">FINSEQ_5:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E12:101_1_1_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="finseq_4.html#T84">FINSEQ_4:84</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E3:101_1_1_1_2"><i><font color="Green">E92</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="finseq_6.html#D1" target="_self">FINSEQ_6:def 1</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="101_1_1_1_3"><b>suppose </b></a><a NAME="E1:101_1_1_1_3"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> 1 )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:101_1_1_1_3"/>
 <a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="finseq_6.html#V1" target="_self">circular</a>
 <b>by </b><i><a class="ref" href="finseq_6.html#T95" target="_self">Th95</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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