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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">Th2</font></span>: <a NAME="T2"><span class="comment"><font color="firebrick">:: GLIB_015:2</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><br/>  for <font color="Olive" title="b2">V</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Olive" title="b1">G</font> holds <br/> (  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><a href="glib_015.html#K2" title="GLIB_015:func.2">replaceVertices</a> <font color="Olive" title="b2">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">V</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><a href="glib_015.html#K2" title="GLIB_015:func.2">replaceVertices</a> <font color="Olive" title="b2">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b1">G</font> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p1">(<span class="default"><a href="glib_015.html#K2" title="GLIB_015:func.2">replaceVertices</a> <font color="Olive" title="b2">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">V</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Olive" title="b1">G</font></span>)</span> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p1">(<span class="default"><a href="glib_015.html#K2" title="GLIB_015:func.2">replaceVertices</a> <font color="Olive" title="b2">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">V</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Olive" title="b1">G</font></span>)</span> )</div></div>
