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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<a NAME="E1:67"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#R1" target="_self">is_Walk_from</a> <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K3" target="_self">.first()</a> ,<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> 
 
<b>by </b><i><a class="ref" href="glib_001.html#D23" target="_self">Def23</a></i>;<br/>
<a NAME="E2:67"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K9" target="_self">.remove</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#R1" target="_self">is_Walk_from</a> <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K3" target="_self">.first()</a> ,<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> 
 
<b>by </b><i><a class="txt" href="glib_001.html#E66"><i><font color="Green">Lemma58</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:67"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K9" target="_self">.remove</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_001.html#K3" target="_self">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K3" target="_self">.first()</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K9" target="_self">.remove</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a>  )
 <b>by </b><i><a class="ref" href="glib_001.html#D23" target="_self">Def23</a></i>;<br/>


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