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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">W1</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">W2</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>









<b>assume </b><a NAME="E1:232"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">W1</font> is    <a href="glib_001.html#M4" target="_self">Subwalk</a> of <font color="Maroon">W2</font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:232_1"/>
<font color="Maroon">W1</font> <a href="glib_001.html#R1" target="_self">is_Walk_from</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 ;<br/><a NAME="E2:232_1"/><b>then </b><i><font color="Green">E40</font></i>: 
( <font color="Maroon">W1</font> <a href="glib_001.html#K3" target="_self">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">W1</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i/>;<br/><a NAME="E3:232_1"/>
<font color="Maroon">W1</font> <a href="glib_001.html#R1" target="_self">is_Walk_from</a> <font color="Maroon">W2</font> <a href="glib_001.html#K3" target="_self">.first()</a> ,<font color="Maroon">W2</font> <a href="glib_001.html#K4" target="_self">.last()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E48"><i><font color="Green">Lemma151</font></i></a>, </i>;<br/><a NAME="E4:232_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="glib_001.html#K3" target="_self">.first()</a>  &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="glib_001.html#K4" target="_self">.last()</a>  )
 <b>by </b><i><a class="txt" href="glib_001.html#E49"><i><font color="Green">Lemma152</font></i></a>, </i>;<br/><b>hence </b><a NAME="E5:232_1"/>
<font color="Maroon">W2</font> <a href="glib_001.html#R1" target="_self">is_Walk_from</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:232"/>
<font color="Maroon">W2</font> <a href="glib_001.html#R1" target="_self">is_Walk_from</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 ;<br/>

<a NAME="E4:232"/><b>then </b>
( <font color="Maroon">W2</font> <a href="glib_001.html#K3" target="_self">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">W2</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:232"/>
<font color="Maroon">W1</font> <a href="glib_001.html#R1" target="_self">is_Walk_from</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E48"><i><font color="Green">Lemma151</font></i></a>, </i>;<br/>


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