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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: GRAPH_3:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="graph_1.html#V5" title="GRAPH_1:attr.5">connected</a>  <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a><br/>  for <font color="Olive" title="b2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">v</font> being   <a href="graph_3.html#NM2" title="GRAPH_3:NM.2">Vertex</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b2">X</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b1">G</font> &amp;  not <font color="Olive" title="b3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <font color="Olive" title="b2">X</font> holds <br/> ex <font color="Olive" title="b4">v9</font> being   <a href="graph_3.html#NM2" title="GRAPH_3:NM.2">Vertex</a> of <font color="Olive" title="b1">G</font> ex <font color="Olive" title="b5">e</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b1">G</font> st <br/>( <font color="Olive" title="b4">v9</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">G</font> <a href="graph_3.html#K1" title="GRAPH_3:func.1">-VSet</a> <font color="Olive" title="b2">X</font> &amp;  not <font color="Olive" title="b5">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">X</font> &amp; ( <font color="Olive" title="b4">v9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Olive" title="b1">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">e</font> or <font color="Olive" title="b4">v9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Olive" title="b1">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">e</font> ) )</div></div>
