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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E67">Th57</font></span>: <a NAME="T57"><span class="comment"><font color="firebrick">:: GRAPH_3:57</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>  &amp; (  for <font color="Olive" title="b3">v</font> being   <a href="graph_3.html#NM2" title="GRAPH_3:NM.2">Vertex</a> of <font color="Olive" title="b1">G</font> holds   <a href="graph_1.html#K10" title="GRAPH_1:func.10">Degree</a> <font color="Olive" title="b3">v</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) holds <br/>(  not  <a href="graph_3.html#K14" title="GRAPH_3:func.14">ExtendCycle</a> <font color="Olive" title="b2">c</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</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> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p2">(<span class="default"><a href="graph_3.html#K14" title="GRAPH_3:func.14">ExtendCycle</a> <font color="Olive" title="b2">c</font></span>)</span></span>)</span> )</div></div>
