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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>;<br/>



<a NAME="E1:100"/><i><font color="Green" title="E90">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="100_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:100_1"/>
(  not <font color="Maroon" title="c2">f</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c2">f</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="100_1_1"><b>suppose </b></a><a NAME="E1:100_1_1"/><i><font color="Green" title="E91">A2</font></i>: 
not <font color="Maroon" title="c2">f</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><div class="add"><a NAME="E2:100_1_1"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f</font>
 <b>by </b><i><a class="ref" href="finseq_6.html#T46" target="_self" title="FINSEQ_6:th.46">Th46</a></i>;<br/><b>hence </b> <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_5.html#K2" title="FINSEQ_5:func.2">:-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span>)</span> <a href="rfinseq.html#K1" title="RFINSEQ:func.1">/^</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_6.html#D2" target="_self" title="FINSEQ_6:def.2">Def2</a></i>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_5.html#K1" title="FINSEQ_5:func.1">-:</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span>)</span> <a href="rfinseq.html#K1" title="RFINSEQ:func.1">/^</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:100_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="ref" href="finseq_6.html#T48" target="_self" title="FINSEQ_6:th.48">Th48</a></i>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="rfinseq.html#K1" title="RFINSEQ:func.1">/^</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:100_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="ref" href="finseq_6.html#T48" target="_self" title="FINSEQ_6:th.48">Th48</a></i>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="finseq_6.html#E1:100"><i><font color="Green" title="E90">A1</font></i></a>, <a class="ref" href="finseq_5.html#T35" title="FINSEQ_5:th.35">FINSEQ_5:35</a></i>
<br/>.= 
<font color="Maroon" title="c2">f</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="100_1_2"><b>suppose </b></a><a NAME="E1:100_1_2"/>
<font color="Maroon" title="c2">f</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:100_1_2"/>
 <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font>
 <b>by </b><i><a class="ref" href="finseq_6.html#D2" target="_self" title="FINSEQ_6:def.2">Def2</a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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