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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: GRAPH_3:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a> holds <br/> ( <font color="Olive" title="b1">G</font> is  <a href="graph_1.html#V5" title="GRAPH_1:attr.5">connected</a>  iff  for <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</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">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">v2</font> holds <br/> ex <font color="Olive" title="b4">c</font> being    <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Olive" title="b1">G</font> ex <font color="Olive" title="b5">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">G</font> st <br/>(  not <font color="Olive" title="b4">c</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Olive" title="b5">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b5">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v1</font> &amp; <font color="Olive" title="b5">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">vs</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v2</font> ) )</div></div>
