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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E48">Th45</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: GLPACY00:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being   non  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><br/>  for <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">C</font><br/>  for <font color="Olive" title="b4">e</font> being   <a href="glib_008.html#NM1" title="GLIB_008:NM.1">Edge</a> of <font color="Olive" title="b1">C</font>  st <font color="Olive" title="b4">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Olive" title="b1">C</font> holds <br/> ex <font color="Olive" title="b5">P</font> being   <a href="glib_000.html#V2" title="GLIB_000:attr.2">_finite</a>   non  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> st <br/>(  not <font color="Olive" title="b4">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b5">P</font> &amp; <font color="Olive" title="b1">C</font> is    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of <font color="Olive" title="b5">P</font>,<font color="Olive" title="b2">v1</font>,<font color="Olive" title="b4">e</font>,<font color="Olive" title="b3">v2</font> &amp;  <a href="glib_006.html#K6" title="GLIB_006:func.6">Endvertices</a> <font color="Olive" title="b5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> )</div></div>
