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

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:2_1_1_1_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 0 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:2_1_1_1_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:2_1_1_1_1_1"/>
( ( <font color="Maroon">g</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 0 implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">g</font> ) &amp; ( (  not <font color="Maroon">g</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  or  not  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 0 ) implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">D</font> st <br/>( <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> holds <br/><font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> ) ) )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:2_1_1_1_1_2"/><i><font color="Green">E37</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>for <font color="Olive">F</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>  st  <a href="finseq_1.html#K3">len</a> <font color="Olive">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 holds <br/> ex <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">D</font> st <br/>( <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_1.html#K1">.</a> 1 &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">F</font> holds <br/><font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) &amp; <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Olive">F</font></span>)</span> );<br/><a NAME="E2:2_1_1_1_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 ;<br/><a NAME="E3:2_1_1_1_1_2"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_1_1_2_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:2_1_1_1_1_2_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font>]
 ;<br/>

<b>let </b><font color="Maroon">F</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:2_1_1_1_1_2_1"/><i><font color="Green">E41</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E3:2_1_1_1_1_2_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>reconsider </b><font color="Maroon">G</font> = <font color="Maroon">F</font> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font></span>)</span> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font> <b>by </b><i><a class="ref" href="finseq_1.html#T23">FINSEQ_1:23</a></i>;<br/>
<a NAME="E5:2_1_1_1_1_2_1"/><i><font color="Green">E42</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T59">FINSEQ_3:59</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_1_1_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_1_1_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:2_1_1_1_1_2_1_1_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> 0 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_1_1_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:2_1_1_1_1_2_1_1_1_1"/><i><font color="Green">E43</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>set </b><font color="Maroon">f</font> = <a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>;<br/><a NAME="E2:2_1_1_1_1_2_1_1_1_1"/><i><font color="Green">E44</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><a NAME="E3:2_1_1_1_1_2_1_1_1_1"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><a NAME="E4:2_1_1_1_1_2_1_1_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_1_1_2_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:2_1_1_1_1_2_1_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:2_1_1_1_1_2_1_1_1_1_1"/><b>then </b>
 ex <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E3:2_1_1_1_1_2_1_1_1_1_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:2_1_1_1_1_2_1_1_1_1_1"/>
1 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font>
 
<b>by </b><i>, , , <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E5:2_1_1_1_1_2_1_1_1_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font> )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E6:2_1_1_1_1_2_1_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 ;<br/>


</div><b>end;</b></div><b>then reconsider </b><font color="Maroon">f</font> = <a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span> as   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">D</font> <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/><b>take </b><font color="Maroon">d</font> = <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> 1;<br/><b>take </b><font color="Maroon">f</font> = <font color="Maroon">f</font>;<br/><b>thus </b><a NAME="E6:2_1_1_1_1_2_1_1_1_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E7:2_1_1_1_1_2_1_1_1_1"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><b>thus </b><a NAME="E8:2_1_1_1_1_2_1_1_1_1"/>
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_1_1_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:2_1_1_1_1_2_1_1_1_2"/><i><font color="Green">E47</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>, <font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">D</font><b> such that </b><br/><a NAME="E3:2_1_1_1_1_2_1_1_1_2"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 1
 <b>and </b><br/><a NAME="E4:2_1_1_1_1_2_1_1_1_2"/><i><font color="Green">E49</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> holds <br/><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:2_1_1_1_1_2_1_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E6:2_1_1_1_1_2_1_1_1_2"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E7:2_1_1_1_1_2_1_1_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E8:2_1_1_1_1_2_1_1_1_2"/><b>then </b>
( <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>then reconsider </b><font color="Maroon">t</font> = <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> ;<br/><b>reconsider </b><font color="Maroon">j</font> =  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> = <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a<sub>1</sub></font>;<br/><b>consider </b><font color="Maroon">h</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">D</font><b> such that </b><br/><a NAME="E12:2_1_1_1_1_2_1_1_1_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">d</font>,<font color="Maroon">t</font>
 <b>and </b><br/><a NAME="E13:2_1_1_1_1_2_1_1_1_2"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">j</font> holds <br/><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">n</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S6">FUNCT_2:sch 6</a>();<br/></i><b>take </b><font color="Maroon">a</font> = <font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">j</font>;<br/><b>take </b><font color="Maroon">h</font> = <font color="Maroon">h</font>;<br/><a NAME="E14:2_1_1_1_1_2_1_1_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i>, <a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><a NAME="E15:2_1_1_1_1_2_1_1_1_2"/><b>then </b><i><font color="Green">E56</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E16:2_1_1_1_1_2_1_1_1_2"/>
1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">j</font>
 <b>by </b><i>, , <a class="ref" href="finseq_3.html#T59">FINSEQ_3:59</a></i>;<br/><b>hence </b><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> 1 = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/><br/><b>thus </b><a NAME="E18:2_1_1_1_1_2_1_1_1_2"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_1_1_2_1_1_1_2_2"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:2_1_1_1_1_2_1_1_1_2_2"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_1_1_2_1_1_1_2_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_1_1_2_1_1_1_2_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:2_1_1_1_1_2_1_1_1_2_2_1_1"/>
( <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> or <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_1_1_2_1_1_1_2_2_1_1_1"><b>suppose </b></a><a NAME="E1:2_1_1_1_1_2_1_1_1_2_2_1_1_1"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font>
 ;<br/><div class="add"><a NAME="E2:2_1_1_1_1_2_1_1_1_2_2_1_1_1"/><b>then </b><i><font color="Green">E59</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:2_1_1_1_1_2_1_1_1_2_2_1_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:2_1_1_1_1_2_1_1_1_2_2_1_1_1"/>
<font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, , , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_1_1_2_1_1_1_2_2_1_1_2"><b>suppose </b></a><a NAME="E1:2_1_1_1_1_2_1_1_1_2_2_1_1_2"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_1_1_2_1_1_1_2_2_1_1_2_1"><b>now </b></a><div class="add"><a NAME="E1:2_1_1_1_1_2_1_1_1_2_2_1_1_2_1"/>
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E2:2_1_1_1_1_2_1_1_1_2_2_1_1_2_1"/><b>then </b><i><font color="Green">E61</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E3:2_1_1_1_1_2_1_1_1_2_2_1_1_2_1"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font>
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:2_1_1_1_1_2_1_1_1_2_2_1_1_2_1"/><i><font color="Green">E63</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E5:2_1_1_1_1_2_1_1_1_2_2_1_1_2_1"/>
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font>
 <b>by </b><i>, , , <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E6:2_1_1_1_1_2_1_1_1_2_2_1_1_2_1"/><b>then </b><i><font color="Green">E64</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>thus </b><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, </i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:2_1_1_1_1_2_1_1_1_2_2_1_1_2"/>
<font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:2_1_1_1_1_2_1_1_1_2_2"/>
<font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/>


</div><b>end;</b></div><b>thus </b><a NAME="E19:2_1_1_1_1_2_1_1_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:2_1_1_1_1_2_1"/>
 ex <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">D</font> st <br/>( <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> holds <br/><font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) &amp; <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> )
 ;<br/>


</div><b>end;</b></div><a NAME="E4:2_1_1_1_1_2"/>
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>]
 <b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(, );<br/></i><b>hence </b><a NAME="E5:2_1_1_1_1_2"/>
( ( <font color="Maroon">g</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 0 implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">g</font> ) &amp; ( (  not <font color="Maroon">g</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  or  not  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 0 ) implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">D</font> st <br/>( <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> holds <br/><font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> ) ) )
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:2_1_1"/>
( ( <font color="Maroon">g</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 0 implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">g</font> ) &amp; ( (  not <font color="Maroon">g</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  or  not  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 0 ) implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">D</font> st <br/>( <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> holds <br/><font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> ) ) )
 ;<br/>


</div>
