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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/>



<a NAME="E1:212"/>
( <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> iff <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/>
<a NAME="E2:212"/><b>then </b>
( <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> iff <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</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#T23" target="_self" title="GLIB_001:th.23">Th23</a></i>;<br/>
<a NAME="E3:212"/><b>then </b>
( <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> iff <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  )
 
<b>by </b><i><a class="ref" href="glib_001.html#T23" target="_self" title="GLIB_001:th.23">Th23</a></i>;<br/>
<b>hence </b><a NAME="E4:212"/>
( <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> iff <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a>  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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