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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: GLIB_014:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>  st <font color="Olive" title="b1">G1</font> <a href="glib_014.html#R1" title="GLIB_014:pred.1">tolerates</a> <font color="Olive" title="b2">G2</font> holds <br/>( <font color="Olive" title="b3">G</font> is    <a href="glib_014.html#M2" title="GLIB_014:mode.2">GraphUnion</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font> iff (  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Olive" title="b3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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">G1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <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="b2">G2</font></span>)</span> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b1">G1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b2">G2</font></span>)</span> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Olive" title="b3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">G1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="b2">G2</font></span>)</span> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Olive" title="b3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">G1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="b2">G2</font></span>)</span> ) )</div></div>
