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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> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:6"/><i><font color="Green">E6</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>2</sub></font>
 <b>and </b><br/><a NAME="E2:6"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>and </b><br/><a NAME="E3:6"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E4:6"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:6_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font> )
 </span><b>by </b><i><a class="txt" href="sprect_5.html#E4:6"><i><font color="Green">E9</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1_1"><b>suppose </b></a><a NAME="E1:6_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:6_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K5">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K5">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E1:6"><i><font color="Green">E6</font></i></a>, <a class="txt" href="sprect_5.html#E2:6"><i><font color="Green">E7</font></i></a>, <a class="txt" href="sprect_5.html#E3:6"><i><font color="Green">E8</font></i></a>, <a class="ref" href="sprect_5.html#T5" target="_self">Th5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1_2"><b>suppose </b></a><a NAME="E1:6_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:6_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K5">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K5">..</a> <span class="p1">(<span class="default"><a href="finseq_6.html#K1">Rotate</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_5.html#E2:6"><i><font color="Green">E7</font></i></a>, <a class="ref" href="finseq_5.html#T10">FINSEQ_5:10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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