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<b>let </b><font color="Maroon">G</font> be   <a href="glib_003.html#NM1">WGraph</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>set </b><font color="Maroon">W</font> = <font color="Maroon">G</font> <a href="glib_001.html#K2">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font>;<br/>
<b>assume </b><a NAME="E1:162"/>
<font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G</font>
 ;<br/>

<a NAME="E2:162"/><b>then </b><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K2">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font></span>)</span> <a href="glib_001.html#K12">.edgeSeq()</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="glib_001.html#T84">GLIB_001:84</a></i>;<br/>
<a NAME="E3:162"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K2">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font></span>)</span> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E4:162"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K2">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font></span>)</span> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E5:162"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K2">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font></span>)</span> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="162_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:162_1"/><i><font color="Green">E52</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K2">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font></span>)</span> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span> )
 ;<br/><a NAME="E2:162_1"/><b>then </b><i><font color="Green">E55</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K2">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font></span>)</span> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="glib_003.html#E2:162"><i><font color="Green">E30</font></i></a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:162"/>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K2">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font></span>)</span> <a href="glib_003.html#K8" target="_self">.weightSeq()</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="glib_003.html#E4:162"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


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