<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:9"/><i><font color="Green">E30</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font>
 <b>and </b><br/><a NAME="E2:9"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font>
 ;<br/>

<b>set </b><font color="Maroon">mp</font> = <font color="Maroon">m</font>,<font color="Maroon">m</font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">p</font>;<br/>
<a NAME="E3:9"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">m</font>,<font color="Maroon">m</font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E4:9"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">m</font>,<font color="Maroon">m</font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon">m</font>,<font color="Maroon">m</font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">p</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 0</span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font>

;<br/>
<b>hence </b><a NAME="E6:9"/>
<font color="Maroon">m</font>,<font color="Maroon">m</font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">p</font> <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"><font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>


</div>
