<?xml version="1.0"?>
<div class="add">

<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">W1</font>, <font color="Maroon" title="c3">W2</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>









<b>assume </b><a NAME="E1:232"/><i><font color="Green" title="E151">A1</font></i>: 
<font color="Maroon" title="c2">W1</font> is    <a href="glib_001.html#M4" title="GLIB_001:mode.4">Subwalk</a> of <font color="Maroon" title="c3">W2</font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:232_1"/>
<font color="Maroon" title="c2">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>
 ;<br/><a NAME="E2:232_1"/><b>then </b><i><font color="Green" title="E152">A2</font></i>: 
( <font color="Maroon" title="c2">W1</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="c4">x</font> &amp; <font color="Maroon" title="c2">W1</font> <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="c5">y</font> )
 <b>by </b><i><a class="ref" href="glib_001.html#D23" target="_self" title="GLIB_001:def.23">Def23</a></i>;<br/><a NAME="E3:232_1"/>
<font color="Maroon" title="c2">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> ,<font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E1:232"><i><font color="Green" title="E151">A1</font></i></a>, <a class="ref" href="glib_001.html#D32" target="_self" title="GLIB_001:def.32">Def32</a></i>;<br/><a NAME="E4:232_1"/><b>then </b>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  )
 <b>by </b><i><a class="txt" href="glib_001.html#E2:232_1"><i><font color="Green" title="E152">A2</font></i></a>, <a class="ref" href="glib_001.html#D23" target="_self" title="GLIB_001:def.23">Def23</a></i>;<br/><b>hence </b><a NAME="E5:232_1"/>
<font color="Maroon" title="c3">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>
 <b>by </b><i><a class="ref" href="glib_001.html#D23" target="_self" title="GLIB_001:def.23">Def23</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:232"/>
<font color="Maroon" title="c3">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>
 ;<br/>

<a NAME="E4:232"/><b>then </b>
( <font color="Maroon" title="c3">W2</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="c4">x</font> &amp; <font color="Maroon" title="c3">W2</font> <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="c5">y</font> )
 
<b>by </b><i><a class="ref" href="glib_001.html#D23" target="_self" title="GLIB_001:def.23">Def23</a></i>;<br/>
<b>hence </b><a NAME="E5:232"/>
<font color="Maroon" title="c2">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:232"><i><font color="Green" title="E151">A1</font></i></a>, <a class="ref" href="glib_001.html#D32" target="_self" title="GLIB_001:def.32">Def32</a></i>;<br/>


</div>
