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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E35">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: GLIB_008:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G1</font> being   <a href="glib_000.html#V2" title="GLIB_000:attr.2">_finite</a>   non  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><br/>  for <font color="Olive" title="b2">G2</font> being   non  <a href="glib_000.html#V9" title="GLIB_000:attr.9">spanning</a>   <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>   <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Olive" title="b1">G1</font>  ex <font color="Olive" title="b3">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">G1</font> st <br/>( <font color="Olive" title="b3">v</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  &amp;  not <font color="Olive" title="b3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Olive" title="b2">G2</font> )</div></div>
