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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E60">Th83</font></span>: <a NAME="T83"><span class="comment"><font color="firebrick">:: GLIB_015:83</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="glib_000.html#V12" title="GLIB_000:attr.12">Graph-yielding</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">F</font> holds  <span class="p1">(<span class="default"><a href="glib_015.html#K4" title="GLIB_015:func.4">the_Vertices_of</a> <span class="p2">(<span class="default"><a href="glib_015.html#K9" title="GLIB_015:func.9">canGFDistinction</a> <font color="Olive" title="b1">F</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p4">(<span class="default"><a href="glib_015.html#K4" title="GLIB_015:func.4">the_Vertices_of</a> <font color="Olive" title="b1">F</font></span>)</span>,<font color="Olive" title="b2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_015.html#K4" title="GLIB_015:func.4">the_Vertices_of</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></div></div>
