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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E65">Th56</font></span>: <a NAME="T56"><span class="comment"><font color="firebrick">:: GRAPH_3:56</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="graph_1.html#V5" title="GRAPH_1:attr.5">connected</a>   <a href="graph_1.html#V6" title="GRAPH_1:attr.6">finite</a>  <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a><br/>  for <font color="Olive" title="b2">c</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Olive" title="b1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>   st  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b1">G</font> &amp;  not <font color="Olive" title="b2">c</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  holds <br/><span class="p1"> { <span class="default"> <font color="Olive" title="b3">v9</font> where <font color="Olive" title="b3">v9</font> is   <a href="graph_3.html#NM2" title="GRAPH_3:NM.2">Vertex</a> of <font color="Olive" title="b1">G</font> : ( <font color="Olive" title="b3">v9</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">c</font></span>)</span> &amp;  <a href="graph_1.html#K10" title="GRAPH_1:func.10">Degree</a> <font color="Olive" title="b3">v9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="graph_3.html#K7" title="GRAPH_3:func.7">Degree</a> (<font color="Olive" title="b3">v9</font>,<span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">c</font></span>)</span>) ) </span> } </span>  is   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  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">G</font></div></div>
