<?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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W1</font>, <font color="Olive" title="b2">W2</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">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="Olive" title="b2">W2</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">W1</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Olive" title="b2">W2</font></span>)</span> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">W1</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">W2</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">P</font>, <font color="Maroon" title="c3">H</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">P</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="c3">H</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span> )</span><br/>



<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c3">H</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="c2">P</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span></span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="chord.html#E1:31"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="glib_001.html#T86" title="GLIB_001:th.86">GLIB_001:86</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a> </span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
