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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E60">Th53</font></span>: <a NAME="T53"><span class="comment"><font color="firebrick">:: GRAPH_3:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a><br/>  for <font color="Olive" title="b2">c1</font>, <font color="Olive" title="b3">c2</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 <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">c1</font></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</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="b3">c2</font></span>)</span> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">c1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">c2</font> &amp; ( <font color="Olive" title="b2">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Olive" title="b3">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) holds <br/> not  <a href="graph_3.html#K11" title="GRAPH_3:func.11">CatCycles</a> (<font color="Olive" title="b2">c1</font>,<font color="Olive" title="b3">c2</font>) is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </div></div>
