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



<b>set </b><font color="Maroon">W</font> = <font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font>;<br/>
<b>assume </b><a NAME="E1:44"/>
<font color="Maroon">W1</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="glib_001.html#K3" target="_self">.first()</a> 
 ;<br/>

<a NAME="E2:44"/><b>then </b><i><font color="Green">E39</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" target="_self">.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> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font></span>)</span> <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/>;<br/>
<a NAME="E3:44"/><i><font color="Green">E40</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font> )
 
<b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/>
<a NAME="E4:44"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/>
<b>hence </b><a NAME="E5:44"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</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" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span>
 ;<br/>

<a NAME="E6:44"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i>, , <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/>
<b>hence </b><a NAME="E7:44"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</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" target="_self">.append</a> <font color="Maroon">W2</font></span>)</span>
 ;<br/>


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