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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">Walk</a> of <font color="Maroon">G</font>, <font color="Maroon">W2</font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:28"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">W1</font> is <a href="glib_001.html#V3">trivial</a> &amp; <font color="Maroon">W1</font> <a href="glib_001.html#K4">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="glib_001.html#K3">.first()</a>  )
 ;<br/>

<a NAME="E2:28"/><i><font color="Green">E36</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i>, <a class="ref" href="glib_001.html#T127">GLIB_001:127</a></i>;<br/>
<a NAME="E3:28"/><b>then </b><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7">.append</a> <font color="Maroon">W2</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="glib_001.html#T29">GLIB_001:29</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:28_1"/><i><font color="Green">E39</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7">.append</a> <font color="Maroon">W2</font></span>)</span> )
 ;<br/><a NAME="E2:28_1"/><i><font color="Green">E40</font></i>: 
1 <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E3:28_1"/>
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T46">XREAL_1:46</a></i>;<br/><a NAME="E4:28_1"/><b>then </b><i><font color="Green">E42</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font> )
 <b>by </b><i>, , , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>reconsider </b><font color="Maroon">k1</font> = <font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> 1 as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E6:28_1"/>
<span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <font color="Maroon">k1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , , <a class="ref" href="glib_001.html#T34">GLIB_001:34</a></i>;<br/><b>hence </b><a NAME="E7:28_1"/>
<span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7">.append</a> <font color="Maroon">W2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:28"/>
<font color="Maroon">W1</font> <a href="glib_001.html#K7">.append</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


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