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<b>let </b><font color="Maroon">G</font> be   <a href="graph_1.html#NM1">Graph</a>;<br/><b>let </b><font color="Maroon">c</font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">G</font> <a href="graph_3.html#K9" target="_self">-CycleSet</a> ;<br/><b>let </b><font color="Maroon">v</font> be   <a href="graph_3.html#NM2">Vertex</a> of <font color="Maroon">G</font>;<br/>





<b>assume </b><a NAME="E1:73"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="graph_3.html#K1" target="_self">-VSet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">Rotated</font> = <span class="p1">{<span class="default"> <font color="Olive">c'</font> where <font color="Olive">c'</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">G</font> <a href="graph_3.html#K9" target="_self">-CycleSet</a>  : (  <a href="relat_1.html#K2">rng</a> <font color="Olive">c'</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c</font> &amp;  ex <font color="Olive">vs</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">G</font> st <br/>( <font color="Olive">vs</font> <a href="graph_2.html#R1">is_vertex_seq_of</a> <font color="Olive">c'</font> &amp; <font color="Olive">vs</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> ) ) </span>}</span>  as  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_3.html#K9" target="_self">-CycleSet</a> </span>)</span> <b>by </b><i/>;<br/>
<a NAME="E3:73"/>
 <a href="graph_3.html#K10" target="_self">Rotate</a> <font color="Maroon">c</font>,<font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="subset_1.html#K10">choose</a> <font color="Maroon">Rotated</font>
 
<b>by </b><i><a class="ref" href="graph_3.html#T3" target="_self">Th3</a>, </i>;<br/>
<a NAME="E4:73"/><b>then </b>
 <a href="graph_3.html#K10" target="_self">Rotate</a> <font color="Maroon">c</font>,<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Rotated</font>
 
;<br/>
<b>then consider </b><font color="Maroon">c'</font> being    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">G</font> <a href="graph_3.html#K9" target="_self">-CycleSet</a> <b> such that </b><br/><a NAME="E6:73"/><i><font color="Green">E32</font></i>: 
(  <a href="graph_3.html#K10" target="_self">Rotate</a> <font color="Maroon">c</font>,<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c'</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c'</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c</font> &amp;  ex <font color="Olive">vs</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">G</font> st <br/>( <font color="Olive">vs</font> <a href="graph_2.html#R1">is_vertex_seq_of</a> <font color="Maroon">c'</font> &amp; <font color="Olive">vs</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> ) )
 ;<br/>
<b>thus </b><a NAME="E7:73"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="graph_3.html#K10" target="_self">Rotate</a> <font color="Maroon">c</font>,<font color="Maroon">v</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="txt" href="graph_3.html#E5"><i><font color="Green">Lemma62</font></i></a></i>;<br/>


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