<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon" title="c4">v</font> =  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E1:74_1_1"/><i><font color="Green" title="E63">A3</font></i>: 
not <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="graph_3.html#E1:74"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E2:74_1_1"/><b>then </b><i><font color="Green" title="E64">A4</font></i>: 
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E3:74_1_1"/><i><font color="Green" title="E65">A5</font></i>: 
(  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font></span>)</span> &amp;  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="graph_3.html#E1:74_1_1"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">v</font> =  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font></span>)</span></span>)</span></span>)</span> as   <a href="graph_3.html#NM2" title="GRAPH_3:NM.2">Vertex</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="graph_3.html#E2:74_1_1"><i><font color="Green" title="E64">A4</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">r1</font> =  <a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c5">v</font>;<br/>
<b>set </b><font color="Maroon" title="c7">r2</font> =  <a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c3">c2</font>,<font color="Maroon" title="c5">v</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">Rotated1</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">c'</font> where <font color="Olive" title="b1">c'</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  : (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font> &amp;  ex <font color="Olive" title="b2">vs</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b1">c'</font> &amp; <font color="Olive" title="b2">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> ) ) </span>}</span>  as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a> </span>)</span> <b>by </b><i><a class="txt" href="graph_3.html#E3:74_1_1"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="graph_3.html#T57" target="_self" title="GRAPH_3:th.57">Th57</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">Rotated2</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">c'</font> where <font color="Olive" title="b1">c'</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  : (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font> &amp;  ex <font color="Olive" title="b2">vs</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b1">c'</font> &amp; <font color="Olive" title="b2">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> ) ) </span>}</span>  as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a> </span>)</span> <b>by </b><i><a class="txt" href="graph_3.html#E3:74_1_1"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="graph_3.html#T57" target="_self" title="GRAPH_3:th.57">Th57</a></i>;<br/>
<a NAME="E7:74_1_1"/><i><font color="Green" title="E66">A6</font></i>: 
 <a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <font color="Maroon" title="c8">Rotated1</font>
 
<b>by </b><i><a class="txt" href="graph_3.html#E3:74_1_1"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="graph_3.html#D9" target="_self" title="GRAPH_3:def.9">Def9</a></i>;<br/>
<a NAME="E8:74_1_1"/><i><font color="Green" title="E67">A7</font></i>: 
 <a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c3">c2</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <font color="Maroon" title="c9">Rotated2</font>
 
<b>by </b><i><a class="txt" href="graph_3.html#E3:74_1_1"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="graph_3.html#D9" target="_self" title="GRAPH_3:def.9">Def9</a></i>;<br/>
<a NAME="E9:74_1_1"/>
 <a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">Rotated1</font>
 
<b>by </b><i><a class="txt" href="graph_3.html#E7:74_1_1"><i><font color="Green" title="E66">A6</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c10">c'</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a> <b> such that </b><br/><a NAME="E11:74_1_1"/><i><font color="Green" title="E68">A8</font></i>: 
 <a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">c'</font>
 <b>and </b><br/><a NAME="E12:74_1_1"/><i><font color="Green" title="E69">A9</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c10">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font>
 <b>and </b><br/><a NAME="E13:74_1_1"/><i><font color="Green" title="E70">A10</font></i>: 
 ex <font color="Olive" title="b1">vs</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c10">c'</font> &amp; <font color="Olive" title="b1">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> )
 ;<br/>
<a NAME="E14:74_1_1"/>
 <a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c3">c2</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Rotated2</font>
 
<b>by </b><i><a class="txt" href="graph_3.html#E8:74_1_1"><i><font color="Green" title="E67">A7</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">c''</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a> <b> such that </b><br/><a NAME="E16:74_1_1"/><i><font color="Green" title="E71">A11</font></i>: 
 <a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c3">c2</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c''</font>
 <b>and </b><br/><a NAME="E17:74_1_1"/><i><font color="Green" title="E72">A12</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c11">c''</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font>
 <b>and </b><br/><a NAME="E18:74_1_1"/><i><font color="Green" title="E73">A13</font></i>: 
 ex <font color="Olive" title="b1">vs</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c11">c''</font> &amp; <font color="Olive" title="b1">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> )
 ;<br/>
<b>consider </b><font color="Maroon" title="c12">vs1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E20:74_1_1"/><i><font color="Green" title="E74">A14</font></i>: 
( <font color="Maroon" title="c12">vs1</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c10">c'</font> &amp; <font color="Maroon" title="c12">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> )
 <b>by </b><i><a class="txt" href="graph_3.html#E13:74_1_1"><i><font color="Green" title="E70">A10</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c13">vs2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E22:74_1_1"/><i><font color="Green" title="E75">A15</font></i>: 
( <font color="Maroon" title="c13">vs2</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c11">c''</font> &amp; <font color="Maroon" title="c13">vs2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> )
 <b>by </b><i><a class="txt" href="graph_3.html#E18:74_1_1"><i><font color="Green" title="E73">A13</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c14">c'1</font> = <font color="Maroon" title="c10">c'</font> as  <a href="msscyc_1.html#V1" title="MSSCYC_1:attr.1">cyclic</a> <a href="graph_1.html#NM4" title="GRAPH_1:NM.4">Path</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="graph_3.html#D8" target="_self" title="GRAPH_3:def.8">Def8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">c'2</font> = <font color="Maroon" title="c11">c''</font> as  <a href="msscyc_1.html#V1" title="MSSCYC_1:attr.1">cyclic</a> <a href="graph_1.html#NM4" title="GRAPH_1:NM.4">Path</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="graph_3.html#D8" target="_self" title="GRAPH_3:def.8">Def8</a></i>;<br/>
<a NAME="E25:74_1_1"/><i><font color="Green" title="E76">A16</font></i>: 
<font color="Maroon" title="c13">vs2</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c15">c'2</font>
 
<b>by </b><i><a class="txt" href="graph_3.html#E22:74_1_1"><i><font color="Green" title="E75">A15</font></i></a></i>;<br/>
<a NAME="E26:74_1_1"/>
<font color="Maroon" title="c12">vs1</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c14">c'1</font>
 
<b>by </b><i><a class="txt" href="graph_3.html#E20:74_1_1"><i><font color="Green" title="E74">A14</font></i></a></i>;<br/>
<a NAME="E27:74_1_1"/><b>then </b><i><font color="Green" title="E77">A17</font></i>: 
<font color="Maroon" title="c12">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">vs1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="msscyc_1.html#T6" title="MSSCYC_1:th.6">MSSCYC_1:6</a></i>;<br/>
<a NAME="E28:74_1_1"/><i><font color="Green" title="E78">A18</font></i>: 
(  <a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">c'1</font> &amp;  <a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c3">c2</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">c'2</font> )
 
<b>by </b><i><a class="txt" href="graph_3.html#E11:74_1_1"><i><font color="Green" title="E68">A8</font></i></a>, <a class="txt" href="graph_3.html#E16:74_1_1"><i><font color="Green" title="E71">A11</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c16">c</font> = <span class="p1">(<span class="default"><a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c3">c2</font>,<font color="Maroon" title="c5">v</font></span>)</span> as   <a href="graph_1.html#NM4" title="GRAPH_1:NM.4">Path</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="graph_3.html#E2:74"><i><font color="Green" title="E62">A2</font></i></a>, <a class="txt" href="graph_3.html#E12:74_1_1"><i><font color="Green" title="E69">A9</font></i></a>, <a class="txt" href="graph_3.html#E17:74_1_1"><i><font color="Green" title="E72">A12</font></i></a>, <a class="txt" href="graph_3.html#E20:74_1_1"><i><font color="Green" title="E74">A14</font></i></a>, <a class="txt" href="graph_3.html#E22:74_1_1"><i><font color="Green" title="E75">A15</font></i></a>, <a class="txt" href="graph_3.html#E27:74_1_1"><i><font color="Green" title="E77">A17</font></i></a>, <a class="ref" href="graph_3.html#T9" target="_self" title="GRAPH_3:th.9">Th9</a></i>;<br/>
<b>set </b><font color="Maroon" title="c17">vs12</font> = <font color="Maroon" title="c12">vs1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c13">vs2</font>;<br/>
<a NAME="E30:74_1_1"/><i><font color="Green" title="E79">A19</font></i>: 
<font color="Maroon" title="c12">vs1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c13">vs2</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c16">c</font>
 
<b>by </b><i><a class="txt" href="graph_3.html#E20:74_1_1"><i><font color="Green" title="E74">A14</font></i></a>, <a class="txt" href="graph_3.html#E22:74_1_1"><i><font color="Green" title="E75">A15</font></i></a>, <a class="txt" href="graph_3.html#E27:74_1_1"><i><font color="Green" title="E77">A17</font></i></a>, <a class="txt" href="graph_3.html#E28:74_1_1"><i><font color="Green" title="E78">A18</font></i></a>, <a class="ref" href="graph_2.html#T47" title="GRAPH_2:th.47">GRAPH_2:47</a></i>;<br/>
<a NAME="E31:74_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">vs1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">c'</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="txt" href="graph_3.html#E20:74_1_1"><i><font color="Green" title="E74">A14</font></i></a>, <a class="ref" href="graph_2.html#D7" title="GRAPH_2:def.7">GRAPH_2:def 7</a></i>;<br/>
<a NAME="E32:74_1_1"/><b>then </b><i><font color="Green" title="E80">A20</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">vs1</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E33:74_1_1"/>
not  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="graph_3.html#E3:74_1_1"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="graph_3.html#T21" target="_self" title="GRAPH_3:th.21">Th21</a></i>;<br/>
<a NAME="E34:74_1_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">c''</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="graph_3.html#E17:74_1_1"><i><font color="Green" title="E72">A12</font></i></a>, <a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>;<br/>
<a NAME="E35:74_1_1"/><b>then </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">c''</font>
 
;<br/>
<a NAME="E36:74_1_1"/><b>then </b>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">c''</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E37:74_1_1"/><b>then </b><i><font color="Green" title="E81">A21</font></i>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">vs2</font>
 
<b>by </b><i><a class="txt" href="graph_3.html#E22:74_1_1"><i><font color="Green" title="E75">A15</font></i></a>, <a class="ref" href="graph_2.html#D7" title="GRAPH_2:def.7">GRAPH_2:def 7</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">vs1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c13">vs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c12">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="graph_3.html#E32:74_1_1"><i><font color="Green" title="E80">A20</font></i></a>, <a class="ref" href="graph_2.html#T14" title="GRAPH_2:th.14">GRAPH_2:14</a></i>
<br/>.= 
<font color="Maroon" title="c13">vs2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">vs2</font></span>)</span>
<b>by </b><i><a class="txt" href="graph_3.html#E20:74_1_1"><i><font color="Green" title="E74">A14</font></i></a>, <a class="txt" href="graph_3.html#E22:74_1_1"><i><font color="Green" title="E75">A15</font></i></a>, <a class="txt" href="graph_3.html#E25:74_1_1"><i><font color="Green" title="E76">A16</font></i></a>, <a class="ref" href="msscyc_1.html#T6" title="MSSCYC_1:th.6">MSSCYC_1:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">vs1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c13">vs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">vs1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c13">vs2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="graph_3.html#E37:74_1_1"><i><font color="Green" title="E81">A21</font></i></a>, <a class="ref" href="graph_2.html#T16" title="GRAPH_2:th.16">GRAPH_2:16</a></i>
;<br/>
<a NAME="E39:74_1_1"/><b>then </b>
<font color="Maroon" title="c16">c</font> is <a href="msscyc_1.html#V1" title="MSSCYC_1:attr.1">cyclic</a>
 
<b>by </b><i><a class="txt" href="graph_3.html#E30:74_1_1"><i><font color="Green" title="E79">A19</font></i></a>, <a class="ref" href="msscyc_1.html#D2" title="MSSCYC_1:def.2">MSSCYC_1:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c18">c</font> = <font color="Maroon" title="c16">c</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  <b>by </b><i><a class="ref" href="graph_3.html#D8" target="_self" title="GRAPH_3:def.8">Def8</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c18">c</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c5">v</font>
;<br/>

<b>thus </b><a NAME="E41:74_1_1"/>
( <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">c1</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p3">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c2</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c18">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="graph_3.html#K10" title="GRAPH_3:func.10">Rotate</a> <font color="Maroon" title="c3">c2</font>,<font color="Maroon" title="c5">v</font></span>)</span> )
 ;<br/>


</div>
