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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G</font>;<br/>



<a NAME="E1:212"/>
( <font color="Maroon">W</font> is <a href="glib_001.html#V1" target="_self">closed</a> iff <font color="Maroon">W</font> <a href="glib_001.html#K3" target="_self">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E2:212"/><b>then </b>
( <font color="Maroon">W</font> is <a href="glib_001.html#V1" target="_self">closed</a> iff <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6" target="_self">.reverse()</a> </span>)</span> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:212"/><b>then </b>
( <font color="Maroon">W</font> is <a href="glib_001.html#V1" target="_self">closed</a> iff <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6" target="_self">.reverse()</a> </span>)</span> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6" target="_self">.reverse()</a> </span>)</span> <a href="glib_001.html#K3" target="_self">.first()</a>  )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:212"/>
( <font color="Maroon">W</font> is <a href="glib_001.html#V1" target="_self">closed</a> iff <font color="Maroon">W</font> <a href="glib_001.html#K6" target="_self">.reverse()</a>  is <a href="glib_001.html#V1" target="_self">closed</a> )
 <b>by </b><i/>;<br/>


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