<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E134">Th148</font></span>: <a NAME="T148"><span class="comment"><font color="firebrick">:: GLCOLO00:148</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">t</font> being    <a href="glcolo00.html#M1" title="GLCOLO00:mode.1">TColoring</a> of <font color="Olive" title="b1">G</font> holds <br/> ( <font color="Olive" title="b2">t</font> is  <a href="glcolo00.html#V7" title="GLCOLO00:attr.7">proper</a>  iff  for <font color="Olive" title="b3">e1</font>, <font color="Olive" title="b4">e2</font>, <font color="Olive" title="b5">v</font>, <font color="Olive" title="b6">w1</font>, <font color="Olive" title="b7">w2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b5">v</font>,<font color="Olive" title="b6">w1</font>,<font color="Olive" title="b1">G</font> &amp; <font color="Olive" title="b4">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b5">v</font>,<font color="Olive" title="b7">w2</font>,<font color="Olive" title="b1">G</font> holds <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="glcolo00.html#K7" title="GLCOLO00:func.7">_V</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="glcolo00.html#K7" title="GLCOLO00:func.7">_V</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">w1</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="glcolo00.html#K7" title="GLCOLO00:func.7">_V</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="glcolo00.html#K8" title="GLCOLO00:func.8">_E</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">e1</font> &amp; ( <font color="Olive" title="b3">e1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">e2</font> implies <span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="glcolo00.html#K8" title="GLCOLO00:func.8">_E</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">e1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="glcolo00.html#K8" title="GLCOLO00:func.8">_E</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">e2</font> ) ) )</div></div>
