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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">W</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:210_1"/>
<font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>
 ;<br/><a NAME="E2:210_1"/><b>then </b>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
 <b>by </b><i><a class="ref" href="glib_001.html#D24" target="_self" title="GLIB_001:def.24">Def24</a></i>;<br/><b>hence </b><a NAME="E3:210_1"/>
<font color="Maroon" title="c2">W</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="Maroon" title="c2">W</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="Maroon" title="c2">W</font></span>)</span>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:210"/>
<font color="Maroon" title="c2">W</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="Maroon" title="c2">W</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="Maroon" title="c2">W</font></span>)</span>
 ;<br/>

<a NAME="E3:210"/><b>then </b>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
 
;<br/>
<b>hence </b><a NAME="E4:210"/>
<font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D24" target="_self" title="GLIB_001:def.24">Def24</a></i>;<br/>


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