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



<b>set </b><font color="Maroon">W1</font> = <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6">.reverse()</a> </span>)</span> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> ;<br/>
<b>set </b><font color="Maroon">W2</font> =  <a href="finseq_5.html#K3">Rev</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span>;<br/>
<a NAME="E1:163"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6">.reverse()</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="glib_001.html#T22">GLIB_001:22</a></i>;<br/>
<a NAME="E2:163"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6">.reverse()</a> </span>)</span> <a href="glib_001.html#K15">.length()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="glib_001.html#K15">.length()</a> 
 
<b>by </b><i><a class="ref" href="glib_001.html#T114">GLIB_001:114</a></i>;<br/>
<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">W</font> <a href="glib_001.html#K6">.reverse()</a> </span>)</span> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span> = 
<font color="Maroon">W</font> <a href="glib_001.html#K15">.length()</a> 
<b>by </b><i><a class="ref" href="glib_001.html#D18">GLIB_001:def 18</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span>
<b>by </b><i><a class="ref" href="glib_001.html#D18">GLIB_001:def 18</a></i>
;<br/>
<a NAME="E4:163"/><b>then </b><i><font color="Green">E30</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">W</font> <a href="glib_001.html#K6">.reverse()</a> </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">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:163"/><i><font color="Green">E32</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <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">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E6:163"/><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">W</font> <a href="glib_001.html#K6">.reverse()</a> </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">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="163_2"><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="E1:163_2"/><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">W</font> <a href="glib_001.html#K6">.reverse()</a> </span>)</span> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span> )
 ;<br/><b>then </b><i><font color="Green">E55</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6">.reverse()</a> </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">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6">.reverse()</a> </span>)</span> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="glib_001.html#T85">GLIB_001:85</a></i>
;<br/><a NAME="E3:163_2"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span>
 <b>by </b><i>, , <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E4:163_2"/><b>then </b><i><font color="Green">E56</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6">.reverse()</a> </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> <a href="hidden.html#R1">=</a> <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">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_5.html#T61">FINSEQ_5:61</a></i>;<br/><b>set </b><font color="Maroon">rn</font> = <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">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1;<br/><b>reconsider </b><font color="Maroon">rn</font> = <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">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</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="txt" href="glib_003.html#E5:163"><i><font color="Green">E32</font></i></a>, , <a class="ref" href="finseq_5.html#T1">FINSEQ_5:1</a></i>;<br/><a NAME="E6:163_2"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="glib_003.html#E5:163"><i><font color="Green">E32</font></i></a>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E7:163_2"/><b>then </b>
<font color="Maroon">rn</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_5.html#T2">FINSEQ_5:2</a></i>;<br/><a NAME="E8:163_2"/><b>then </b><i><font color="Green">E57</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">rn</font> &amp; <font color="Maroon">rn</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">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E9:163_2"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span>
 <b>by </b><i>, <a class="txt" href="glib_003.html#E5:163"><i><font color="Green">E32</font></i></a>, , <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">rn</font>
<b>by </b><i><a class="ref" href="finseq_5.html#T61">FINSEQ_5:61</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K12">.edgeSeq()</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">rn</font></span>)</span>
<b>by </b><i>, </i>
;<br/><b>hence </b><a NAME="E11:163_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6">.reverse()</a> </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> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:163"/>
<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K6">.reverse()</a> </span>)</span> <a href="glib_003.html#K8" target="_self">.weightSeq()</a>  <a href="hidden.html#R1">=</a>  <a href="finseq_5.html#K3">Rev</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_003.html#K8" target="_self">.weightSeq()</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


</div>
