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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: GLCOLO00:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G2</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><br/>  for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive" title="b4">V</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Olive" title="b1">G2</font></span>)</span><br/>  for <font color="Olive" title="b5">G1</font> being    <a href="glib_007.html#M4" title="GLIB_007:mode.4">addAdjVertexAll</a> of <font color="Olive" title="b1">G2</font>,<font color="Olive" title="b2">v</font>,<font color="Olive" title="b4">V</font><br/>  for <font color="Olive" title="b6">f1</font> being   <a href="glcolo00.html#NM1" title="GLCOLO00:NM.1">VColoring</a> of <font color="Olive" title="b5">G1</font><br/>  for <font color="Olive" title="b7">f2</font> being   <a href="glcolo00.html#NM1" title="GLCOLO00:NM.1">VColoring</a> of <font color="Olive" title="b1">G2</font>  st  not <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Olive" title="b1">G2</font> &amp; <font color="Olive" title="b6">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">f2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b3">x</font></span>)</span> &amp;  not <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b7">f2</font> &amp; <font color="Olive" title="b7">f2</font> is  <a href="glcolo00.html#V1" title="GLCOLO00:attr.1">proper</a>  holds <br/><font color="Olive" title="b6">f1</font> is  <a href="glcolo00.html#V1" title="GLCOLO00:attr.1">proper</a> </div></div>
