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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E64">Th55</font></span>: <a NAME="T55"><span class="comment"><font color="firebrick">:: GRAPH_3:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">G</font> being   <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="b3">v</font> being   <a href="graph_3.html#NM2" title="GRAPH_3:NM.2">Vertex</a> of <font color="Olive" title="b2">G</font>  st  <a href="graph_3.html#K7" title="GRAPH_3:func.7">Degree</a> (<font color="Olive" title="b3">v</font>,<font color="Olive" title="b1">X</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; (  for <font color="Olive" title="b4">v</font> being   <a href="graph_3.html#NM2" title="GRAPH_3:NM.2">Vertex</a> of <font color="Olive" title="b2">G</font> holds   <a href="graph_3.html#K7" title="GRAPH_3:func.7">Degree</a> (<font color="Olive" title="b4">v</font>,<font color="Olive" title="b1">X</font>) is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) holds <br/> for <font color="Olive" title="b4">c</font> being    <a href="graph_3.html#M1" title="GRAPH_3:mode.1">Element</a> of <font color="Olive" title="b1">X</font> <a href="graph_3.html#K13" title="GRAPH_3:func.13">-CycleSet</a> <font color="Olive" title="b3">v</font> holds <br/> (  not <font color="Olive" title="b4">c</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b4">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">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="b4">c</font></span>)</span> )</div></div>
