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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E61">Th80</font></span>: <a NAME="T80"><span class="comment"><font color="firebrick">:: GLIB_012:80</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G1</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><br/>  for <font color="Olive" title="b2">G2</font> being   <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> holds <br/> ( <font color="Olive" title="b2">G2</font> is    <a href="glib_012.html#M4" title="GLIB_012:mode.4">DGraphComplement</a> of <font color="Olive" title="b1">G1</font> iff (  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Olive" title="b2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Olive" title="b1">G1</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b2">G2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b1">G1</font> &amp; (  for <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">G1</font>  st <font color="Olive" title="b3">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">w</font> holds <br/>(  ex <font color="Olive" title="b5">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b5">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font>,<font color="Olive" title="b1">G1</font> iff  for <font color="Olive" title="b5">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds  not <font color="Olive" title="b5">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font>,<font color="Olive" title="b2">G2</font> ) ) ) )</div></div>
