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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> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:114"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="114_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:114_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font> or  not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="114_1_1"><b>suppose </b></a><a NAME="E1:114_1_1"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><a NAME="E2:114_1_1"/><b>then </b><i><font color="Green">E99</font></i>: 
 <a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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"><font color="Maroon">c<sub>4</sub></font> <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/><a NAME="E3:114_1_1"/><i><font color="Green">E100</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>4</sub></font>
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:114"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E4:114_1_1"/><i><font color="Green">E101</font></i>: 
not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:114"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E5:114_1_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:114_1_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="finseq_6.html#T75" target="_self">Th75</a></i>;<br/><a NAME="E6:114_1_1"/><b>then </b><i><font color="Green">E102</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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_6.html#E3:114_1_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="finseq_6.html#E4:114_1_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E7:114_1_1"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:114_1_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="finseq_5.html#T50">FINSEQ_5:50</a></i>;<br/><a NAME="E8:114_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_5.html#T36">FINSEQ_5:36</a></i>;<br/><a NAME="E9:114_1_1"/><b>then </b><i><font color="Green">E104</font></i>: 
not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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#E1:114"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E10:114_1_1"/><i><font color="Green">E105</font></i>: 
<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">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_6.html#T66" target="_self">Th66</a></i>;<br/><a NAME="E11:114_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E12:114_1_1"/><b>then </b><i><font color="Green">E106</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:114_1_1"><i><font color="Green">E98</font></i></a>, <a class="txt" href="finseq_6.html#E4:114_1_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="finseq_5.html#T49">FINSEQ_5:49</a></i>;<br/><a NAME="E13:114_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="finseq_6.html#T84" target="_self">Th84</a></i>;<br/><a NAME="E14:114_1_1"/><b>then </b><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>by </b><i><a class="txt" href="finseq_6.html#E6:114_1_1"><i><font color="Green">E102</font></i></a>, <a class="txt" href="finseq_6.html#E10:114_1_1"><i><font color="Green">E105</font></i></a>, <a class="txt" href="finseq_6.html#E12:114_1_1"><i><font color="Green">E106</font></i></a>, <a class="ref" href="finseq_5.html#T10">FINSEQ_5:10</a></i>;<br/><div><i><font color="Green">E108</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:114_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><a NAME="E2:114_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:114_1_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="finseq_4.html#T31">FINSEQ_4:31</a></i>;<br/><b>hence </b><a NAME="E3:114_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:114_1_1"><i><font color="Green">E98</font></i></a>, <a class="txt" href="finseq_6.html#E3:114_1_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="finseq_6.html#E4:114_1_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="finseq_5.html#T49">FINSEQ_5:49</a></i>;<br/></div><b>end;</b></div><a NAME="E16:114_1_1"/><b>then </b><i><font color="Green">E109</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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="finseq_6.html#E3:114_1_1"><i><font color="Green">E100</font></i></a>, <a class="ref" href="finseq_6.html#T83" target="_self">Th83</a></i>;<br/><a NAME="E17:114_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</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#E6:114_1_1"><i><font color="Green">E102</font></i></a>, <a class="txt" href="finseq_6.html#E14:114_1_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="finseq_6.html#T83" target="_self">Th83</a></i>;<br/><a NAME="E18:114_1_1"/><b>then </b><i><font color="Green">E110</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_6.html#E9:114_1_1"><i><font color="Green">E104</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E19:114_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_6.html#T107" target="_self">Th107</a></i>;<br/><b>hence </b> <a href="finseq_6.html#K1" target="_self">Rotate</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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></span>)</span> <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#E2:114_1_1"><i><font color="Green">E99</font></i></a>, <a class="txt" href="finseq_6.html#E16:114_1_1"><i><font color="Green">E109</font></i></a>, <a class="ref" href="finseq_6.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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>4</sub></font> <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></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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></span>)</span> <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#E6:114_1_1"><i><font color="Green">E102</font></i></a>, <a class="ref" href="finseq_6.html#T69" target="_self">Th69</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</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>4</sub></font> <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></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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></span>)</span> <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#E1:114"><i><font color="Green">E97</font></i></a>, <a class="txt" href="finseq_6.html#E1:114_1_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="finseq_6.html#T76" target="_self">Th76</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</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>4</sub></font> <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></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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#E6:114_1_1"><i><font color="Green">E102</font></i></a>, <a class="ref" href="finseq_6.html#T71" target="_self">Th71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</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>4</sub></font> <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></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E6:114_1_1"><i><font color="Green">E102</font></i></a>, <a class="txt" href="finseq_6.html#E14:114_1_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="finseq_6.html#T65" target="_self">Th65</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <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> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E18:114_1_1"><i><font color="Green">E110</font></i></a>, <a class="ref" href="finseq_6.html#T72" target="_self">Th72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E7:114_1_1"><i><font color="Green">E103</font></i></a>, <a class="ref" href="finseq_6.html#T82" target="_self">Th82</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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>4</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_5.html#K1">-:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:114_1_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="finseq_6.html#T81" target="_self">Th81</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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>4</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#E3:114_1_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="finseq_6.html#E15:114_1_1"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_6.html#T65" target="_self">Th65</a></i>
<br/>.= 
 <a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="finseq_6.html#E3:114_1_1"><i><font color="Green">E100</font></i></a>, <a class="ref" href="finseq_6.html#D2" target="_self">Def2</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="114_1_2"><b>suppose </b></a><a NAME="E1:114_1_2"/>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:114_1_2"/>
 <a href="finseq_6.html#K1" target="_self">Rotate</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_6.html#K1" target="_self">Rotate</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="finseq_6.html#D2" target="_self">Def2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
