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<b>let </b><font color="Maroon">IT1</font> be   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">IT2</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:100_1_2"/><i><font color="Green">E32</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">IT1</font> <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> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">IT1</font> holds <br/><font color="Maroon">IT1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">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> <font color="Olive">n</font></span>)</span> ) )
 <b>and </b><br/><a NAME="E2:100_1_2"/><i><font color="Green">E51</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">IT2</font> <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> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">IT2</font> holds <br/><font color="Maroon">IT2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">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> <font color="Olive">n</font></span>)</span> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="100_1_2_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="E1:100_1_2_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> <font color="Maroon">IT1</font> )
 ;<br/><b>hence </b><font color="Maroon">IT1</font> <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"><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">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">IT2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
<b>by </b><i>, , </i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:100_1_2"/>
<font color="Maroon">IT1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT2</font>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


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