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

<b>let </b><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">b</font> be    <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> ;<br/><b>let </b><font color="Maroon" title="c3">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E8">A1</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ;<br/>

<a NAME="E2:12"/><b>then </b>
<font color="Maroon" title="c2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="afinsq_1.html#T18" title="AFINSQ_1:th.18">AFINSQ_1:18</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">c'</font> being   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>, <font color="Maroon" title="c5">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:12"/><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c'</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><font color="Maroon" title="c5">x</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</a></span>
 <b>by </b><i><a class="ref" href="afinsq_1.html#T44" title="AFINSQ_1:th.44">AFINSQ_1:44</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">c</font> = <font color="Maroon" title="c4">c'</font> as    <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a>  <b>by </b><i><a class="txt" href="flang_1.html#E4:12"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="flang_1.html#T5" target="_self" title="FLANG_1:th.5">Th5</a></i>;<br/>
<i><font color="Green" title="E10">A3</font></i>: <font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 = 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><font color="Maroon" title="c5">x</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="flang_1.html#E1:12"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="flang_1.html#E4:12"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<b>by </b><i><a class="ref" href="afinsq_1.html#T37" title="AFINSQ_1:th.37">AFINSQ_1:37</a></i>
;<br/>
<a NAME="E7:12"/>
<span class="p1"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><font color="Maroon" title="c5">x</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</a></span> is    <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> 
 
<b>by </b><i><a class="txt" href="flang_1.html#E4:12"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="flang_1.html#T5" target="_self" title="FLANG_1:th.5">Th5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">e</font> = <font color="Maroon" title="c5">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">E</font> <b>by </b><i><a class="ref" href="flang_1.html#T6" target="_self" title="FLANG_1:th.6">Th6</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">c</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c7">e</font>
;<br/>

<b>thus </b><a NAME="E9:12"/>
(  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c6">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">n</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><font color="Maroon" title="c7">e</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</a></span> )
 <b>by </b><i><a class="txt" href="flang_1.html#E4:12"><i><font color="Green" title="E9">A2</font></i></a>, <a class="txt" href="flang_1.html#E6:12"><i><font color="Green" title="E10">A3</font></i></a></i>;<br/>


</div>
