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

<b>let </b><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C</font>;<br/><b>let </b><font color="Maroon" title="c4">F</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c2">D</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c5">A</font> be   <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Maroon" title="c1">C</font>;<br/>









<b>assume </b><a NAME="E1:26"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c4">F</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">D</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c6">fd</font> =  <a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font>;<br/>
<b>set </b><font color="Maroon" title="c7">mf</font> =  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">h</font> =  <a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font>;<br/>
<b>set </b><font color="Maroon" title="c9">fh</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font>;<br/>
<a NAME="E2:26"/><i><font color="Green" title="E24">A2</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p5">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:26"/><i><font color="Green" title="E25">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> &amp;  <a href="rfunct_3.html#K1" title="RFUNCT_3:func.1">min</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="rearran1.html#E1:26"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="rearran1.html#T12" target="_self" title="REARRAN1:th.12">Th12</a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a>, <a class="ref" href="rfunct_3.html#D6" title="RFUNCT_3:def.6">RFUNCT_3:def 6</a>, <a class="ref" href="rfunct_3.html#D7" title="RFUNCT_3:def.7">RFUNCT_3:def 7</a>, <a class="ref" href="rfunct_3.html#D8" title="RFUNCT_3:def.8">RFUNCT_3:def 8</a></i>;<br/>
<b>thus </b><a NAME="E4:26"/>
( <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_1"/><i><font color="Green" title="E26">A4</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 ;<br/>

<a NAME="E2:26_1"/><i><font color="Green" title="E27">A5</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">A</font> holds <br/><font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:26_1_1"/><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c10">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">A</font>
 ;<br/>

<a NAME="E2:26_1_1"/><b>then </b><i><font color="Green" title="E29">A7</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">n</font> &amp; <font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font> )
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E3:26_1_1"/><b>then </b>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E4:26_1_1"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">A</font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E5:26_1_1"/><b>then </b>
<font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">n</font>
 
<b>by </b><i><a class="txt" href="rearran1.html#E1:26_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="rearran1.html#E2:26_1_1"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="rearran1.html#T2" target="_self" title="REARRAN1:th.2">Th2</a></i>;<br/>
<b>hence </b><a NAME="E6:26_1_1"/>
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">n</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E1:26_1"><i><font color="Green" title="E26">A4</font></i></a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:26_1_2"/><i><font color="Green" title="E28">A8</font></i>: 
<font color="Maroon" title="c10">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:26_1_2"/><b>then </b><i><font color="Green" title="E29">A9</font></i>: 
<font color="Maroon" title="c10">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">m1</font> = <font color="Maroon" title="c10">m</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><a NAME="E4:26_1_2"/><i><font color="Green" title="E30">A10</font></i>: 
<span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green" title="E28">A8</font></i></a>, <a class="ref" href="rfunct_3.html#D6" title="RFUNCT_3:def.6">RFUNCT_3:def 6</a></i>;<br/><a NAME="E5:26_1_2"/><i><font color="Green" title="E31">A11</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">m</font> &amp; <font color="Maroon" title="c10">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26_1_2"><i><font color="Green" title="E29">A9</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E6:26_1_2"/><i><font color="Green" title="E32">A12</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E2:26_1"><i><font color="Green" title="E27">A5</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green" title="E28">A8</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c12">r1</font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_1_2_1_1"/>
( <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> or <font color="Maroon" title="c10">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_2_1_1_1"><b>case </b></a><a NAME="E1:26_1_2_1_1_1"/><i><font color="Green" title="E33">A13</font></i>: 
<font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:26_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">r1</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>;<br/><a NAME="E3:26_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">r1</font> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="rearran1.html#E4:26_1_2"><i><font color="Green" title="E30">A10</font></i></a>, <a class="ref" href="rfunct_3.html#D7" title="RFUNCT_3:def.7">RFUNCT_3:def 7</a></i>;<br/><a NAME="E4:26_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E34">A14</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">r1</font> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green" title="E28">A8</font></i></a>, <a class="ref" href="rfunct_3.html#D8" title="RFUNCT_3:def.8">RFUNCT_3:def 8</a></i>;<br/> <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">r1</font> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c1">C</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T77" title="RFUNCT_1:th.77">RFUNCT_1:77</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font> = 
<font color="Maroon" title="c12">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E4:26_1_2_1_1_1"><i><font color="Green" title="E34">A14</font></i></a>, <a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c12">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1
<b>by </b><i><a class="txt" href="rearran1.html#E6:26_1_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="rfunct_1.html#T79" title="RFUNCT_1:th.79">RFUNCT_1:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font>
<b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2_1_1_1"><i><font color="Green" title="E33">A13</font></i></a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_2_1_1_2"><b>case </b></a><a NAME="E1:26_1_2_1_1_2"/>
<font color="Maroon" title="c10">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:26_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c10">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E5:26_1_2"><i><font color="Green" title="E31">A11</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><a NAME="E3:26_1_2_1_1_2"/><b>then </b>
( <font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c10">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:26_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E33">A15</font></i>: 
( <font color="Maroon" title="c10">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 <b>by </b><i><a class="txt" href="rearran1.html#E5:26_1_2"><i><font color="Green" title="E31">A11</font></i></a>, <a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">r2</font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/><a NAME="E6:26_1_2_1_1_2"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c11">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c13">r2</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E5:26_1_2"><i><font color="Green" title="E31">A11</font></i></a>, <a class="txt" href="rearran1.html#E4:26_1_2_1_1_2"><i><font color="Green" title="E33">A15</font></i></a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>;<br/><a NAME="E7:26_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c13">r2</font></span>)</span> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="rearran1.html#E4:26_1_2"><i><font color="Green" title="E30">A10</font></i></a>, <a class="ref" href="rfunct_3.html#D7" title="RFUNCT_3:def.7">RFUNCT_3:def 7</a></i>;<br/><a NAME="E8:26_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E34">A16</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c13">r2</font></span>)</span> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green" title="E28">A8</font></i></a>, <a class="ref" href="rfunct_3.html#D8" title="RFUNCT_3:def.8">RFUNCT_3:def 8</a></i>;<br/> <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c13">r2</font></span>)</span> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c1">C</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T77" title="RFUNCT_1:th.77">RFUNCT_1:77</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c13">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E8:26_1_2_1_1_2"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c13">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1
<b>by </b><i><a class="txt" href="rearran1.html#E6:26_1_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="rfunct_1.html#T79" title="RFUNCT_1:th.79">RFUNCT_1:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c11">m1</font>
<b>by </b><i><a class="txt" href="rearran1.html#E5:26_1_2"><i><font color="Green" title="E31">A11</font></i></a>, <a class="txt" href="rearran1.html#E4:26_1_2_1_1_2"><i><font color="Green" title="E33">A15</font></i></a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E9:26_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">m</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:26_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c10">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>set </b><font color="Maroon" title="c11">fdn</font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font>;<br/>
<b>set </b><font color="Maroon" title="c12">mfn</font> =  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c13">n0</font> = <font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<b>assume </b><a NAME="E5:26"/><i><font color="Green" title="E26">A17</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">n</font> &amp; <font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">n</font></span>)</span> )
 ;<br/>

<a NAME="E6:26"/><b>then </b><i><font color="Green" title="E27">A18</font></i>: 
( <font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E7:26"/><i><font color="Green" title="E28">A19</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c10">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">n</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c10">n</font> )
 
<b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E5:26"><i><font color="Green" title="E26">A17</font></i></a>, <a class="ref" href="finseq_2.html#T69" title="FINSEQ_2:th.69">FINSEQ_2:69</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a>, <a class="ref" href="rfinseq.html#D2" title="RFINSEQ:def.2">RFINSEQ:def 2</a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>;<br/>
<a NAME="E8:26"/><i><font color="Green" title="E29">A20</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<i><font color="Green" title="E30">A21</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon" title="c10">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c10">n</font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green" title="E28">A19</font></i></a>, <a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>
;<br/>
<a NAME="E10:26"/><i><font color="Green" title="E31">A22</font></i>: 
( <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; not <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">n</font> )
 
<b>by </b><i><a class="txt" href="rearran1.html#E5:26"><i><font color="Green" title="E26">A17</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E11:26"/><i><font color="Green" title="E32">A23</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> holds <br/><font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:26_3"/><i><font color="Green" title="E33">A24</font></i>: 
( <font color="Maroon" title="c14">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">k</font> )
 ;<br/>

<a NAME="E2:26_3"/>
<font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">A</font>
 
<b>by </b><i><a class="txt" href="rearran1.html#E6:26"><i><font color="Green" title="E27">A18</font></i></a>, <a class="txt" href="rearran1.html#E7:26"><i><font color="Green" title="E28">A19</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E3:26_3"/><b>then </b>
<font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font>
 
<b>by </b><i><a class="txt" href="rearran1.html#E1:26_3"><i><font color="Green" title="E33">A24</font></i></a>, <a class="ref" href="rearran1.html#T2" target="_self" title="REARRAN1:th.2">Th2</a></i>;<br/>
<b>hence </b><a NAME="E4:26_3"/>
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E10:26"><i><font color="Green" title="E31">A22</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E12:26"/><i><font color="Green" title="E33">A25</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">n</font> holds <br/> not <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:26_4"/><i><font color="Green" title="E34">A26</font></i>: 
( <font color="Maroon" title="c14">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c14">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">n</font> )
 ;<br/>

<a NAME="E2:26_4"/>
<font color="Maroon" title="c10">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">A</font>
 
<b>by </b><i><a class="txt" href="rearran1.html#E5:26"><i><font color="Green" title="E26">A17</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E3:26_4"/><b>then </b><i><font color="Green" title="E35">A27</font></i>: 
<font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">n</font>
 
<b>by </b><i><a class="txt" href="rearran1.html#E1:26_4"><i><font color="Green" title="E34">A26</font></i></a>, <a class="ref" href="rearran1.html#T2" target="_self" title="REARRAN1:th.2">Th2</a></i>;<br/>
<b>assume </b><a NAME="E4:26_4"/>
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font>
 ;<br/>

<b>hence </b><a NAME="E5:26_4"/>
contradiction
 <b>by </b><i><a class="txt" href="rearran1.html#E5:26"><i><font color="Green" title="E26">A17</font></i></a>, <a class="txt" href="rearran1.html#E3:26_4"><i><font color="Green" title="E35">A27</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c14">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:26_5"/><i><font color="Green" title="E34">A28</font></i>: 
<font color="Maroon" title="c14">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:26_5"/><b>then </b><i><font color="Green" title="E35">A29</font></i>: 
<font color="Maroon" title="c14">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c15">m1</font> = <font color="Maroon" title="c14">m</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><a NAME="E4:26_5"/><i><font color="Green" title="E36">A30</font></i>: 
<span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green" title="E34">A28</font></i></a>, <a class="ref" href="rfunct_3.html#D6" title="RFUNCT_3:def.6">RFUNCT_3:def 6</a></i>;<br/><a NAME="E5:26_5"/><i><font color="Green" title="E37">A31</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">m</font> &amp; <font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26_5"><i><font color="Green" title="E35">A29</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c16">r1</font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_5_1_1"/>
( <font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">n</font> or <font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c14">m</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_5_1_1_1"><b>case </b></a><a NAME="E1:26_5_1_1_1"/><i><font color="Green" title="E38">A32</font></i>: 
<font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">n</font>
 ;<br/><div class="add"><a NAME="E2:26_5_1_1_1"/><b>then </b>
not <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E12:26"><i><font color="Green" title="E33">A25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green" title="E34">A28</font></i></a></i>;<br/><a NAME="E3:26_5_1_1_1"/><b>then </b><i><font color="Green" title="E39">A33</font></i>: 
<span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="rfunct_1.html#T80" title="RFUNCT_1:th.80">RFUNCT_1:80</a></i>;<br/><a NAME="E4:26_5_1_1_1"/><i><font color="Green" title="E40">A34</font></i>: 
<font color="Maroon" title="c14">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c10">n</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E5:26_5"><i><font color="Green" title="E37">A31</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5_1_1_1"><i><font color="Green" title="E38">A32</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E5:26_5_1_1_1"/><b>then </b><i><font color="Green" title="E41">A35</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/><a NAME="E6:26_5_1_1_1"/>
<font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="rearran1.html#E1:26_5_1_1_1"><i><font color="Green" title="E38">A32</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E7:26_5_1_1_1"/><b>then </b>
<font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E6:26"><i><font color="Green" title="E27">A18</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E8:26_5_1_1_1"/><b>then </b>
<font color="Maroon" title="c14">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E9:26_5_1_1_1"/><b>then </b><i><font color="Green" title="E42">A36</font></i>: 
<font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1
 <b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c17">r2</font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/><a NAME="E11:26_5_1_1_1"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c15">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c17">r2</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E5:26_5"><i><font color="Green" title="E37">A31</font></i></a>, <a class="txt" href="rearran1.html#E9:26_5_1_1_1"><i><font color="Green" title="E42">A36</font></i></a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>;<br/><a NAME="E12:26_5_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c17">r2</font></span>)</span> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green" title="E34">A28</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green" title="E36">A30</font></i></a>, <a class="ref" href="rfunct_3.html#D7" title="RFUNCT_3:def.7">RFUNCT_3:def 7</a></i>;<br/><a NAME="E13:26_5_1_1_1"/><b>then </b><i><font color="Green" title="E43">A37</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c17">r2</font></span>)</span> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green" title="E34">A28</font></i></a>, <a class="ref" href="rfunct_3.html#D8" title="RFUNCT_3:def.8">RFUNCT_3:def 8</a></i>;<br/> <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c17">r2</font></span>)</span> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c1">C</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T77" title="RFUNCT_1:th.77">RFUNCT_1:77</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c17">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E13:26_5_1_1_1"><i><font color="Green" title="E43">A37</font></i></a>, <a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font>
<b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green" title="E28">A19</font></i></a>, <a class="txt" href="rearran1.html#E8:26"><i><font color="Green" title="E29">A20</font></i></a>, <a class="txt" href="rearran1.html#E3:26_5_1_1_1"><i><font color="Green" title="E39">A33</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5_1_1_1"><i><font color="Green" title="E40">A34</font></i></a>, <a class="txt" href="rearran1.html#E5:26_5_1_1_1"><i><font color="Green" title="E41">A35</font></i></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_5_1_1_2"><b>case </b></a><a NAME="E1:26_5_1_1_2"/><i><font color="Green" title="E38">A38</font></i>: 
<font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c14">m</font>
 ;<br/><div class="add"><a NAME="E2:26_5_1_1_2"/><b>then </b><i><font color="Green" title="E39">A39</font></i>: 
( <font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">m</font> &amp; <font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">m</font> )
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E3:26_5_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E11:26"><i><font color="Green" title="E32">A23</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green" title="E34">A28</font></i></a></i>;<br/><a NAME="E4:26_5_1_1_2"/><b>then </b><i><font color="Green" title="E40">A40</font></i>: 
<span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="ref" href="rfunct_1.html#T79" title="RFUNCT_1:th.79">RFUNCT_1:79</a></i>;<br/><a NAME="E5:26_5_1_1_2"/>
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c14">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c10">n</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E1:26_5_1_1_2"><i><font color="Green" title="E38">A38</font></i></a>, <a class="ref" href="finseq_2.html#T4" title="FINSEQ_2:th.4">FINSEQ_2:4</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c17">mn</font> = <font color="Maroon" title="c14">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c10">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T5" title="FINSEQ_2:th.5">FINSEQ_2:5</a></i>;<br/><a NAME="E7:26_5_1_1_2"/><i><font color="Green" title="E41">A41</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c17">mn</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26_5_1_1_2"><i><font color="Green" title="E39">A39</font></i></a>, <a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_5_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_5_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_5_1_1_2_1_1"/>
( <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> or <font color="Maroon" title="c14">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_5_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:26_5_1_1_2_1_1_1"/><i><font color="Green" title="E42">A42</font></i>: 
<font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:26_5_1_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">r1</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>;<br/><a NAME="E3:26_5_1_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">r1</font> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green" title="E34">A28</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green" title="E36">A30</font></i></a>, <a class="ref" href="rfunct_3.html#D7" title="RFUNCT_3:def.7">RFUNCT_3:def 7</a></i>;<br/><a NAME="E4:26_5_1_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E43">A43</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">r1</font> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green" title="E34">A28</font></i></a>, <a class="ref" href="rfunct_3.html#D8" title="RFUNCT_3:def.8">RFUNCT_3:def 8</a></i>;<br/><a NAME="E5:26_5_1_1_2_1_1_1"/><i><font color="Green" title="E44">A44</font></i>: 
<font color="Maroon" title="c17">mn</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green" title="E28">A19</font></i></a>, <a class="txt" href="rearran1.html#E7:26_5_1_1_2"><i><font color="Green" title="E41">A41</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5_1_1_2_1_1_1"><i><font color="Green" title="E42">A42</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><i><font color="Green" title="E45">A45</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> = 
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c10">n</font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green" title="E28">A19</font></i></a>, <a class="txt" href="rearran1.html#E9:26"><i><font color="Green" title="E30">A21</font></i></a>, <a class="txt" href="rearran1.html#E5:26_5"><i><font color="Green" title="E37">A31</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5_1_1_2"><i><font color="Green" title="E38">A38</font></i></a>, <a class="ref" href="finseq_1.html#T37" title="FINSEQ_1:th.37">FINSEQ_1:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c17">mn</font>
<b>by </b><i><a class="ref" href="rfinseq.html#T28" title="RFINSEQ:th.28">RFINSEQ:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">mn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">n</font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E5:26"><i><font color="Green" title="E26">A17</font></i></a>, <a class="txt" href="rearran1.html#E5:26_5_1_1_2_1_1_1"><i><font color="Green" title="E44">A44</font></i></a>, <a class="ref" href="rfinseq.html#D2" title="RFINSEQ:def.2">RFINSEQ:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c16">r1</font>
<b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5_1_1_2_1_1_1"><i><font color="Green" title="E42">A42</font></i></a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>
;<br/> <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">r1</font> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c1">C</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T77" title="RFUNCT_1:th.77">RFUNCT_1:77</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> = 
<font color="Maroon" title="c16">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E4:26_5_1_1_2_1_1_1"><i><font color="Green" title="E43">A43</font></i></a>, <a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font>
<b>by </b><i><a class="txt" href="rearran1.html#E4:26_5_1_1_2"><i><font color="Green" title="E40">A40</font></i></a>, <a class="txt" href="rearran1.html#E6:26_5_1_1_2_1_1_1"><i><font color="Green" title="E45">A45</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_5_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:26_5_1_1_2_1_1_2"/>
<font color="Maroon" title="c14">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:26_5_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E5:26_5"><i><font color="Green" title="E37">A31</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><a NAME="E3:26_5_1_1_2_1_1_2"/><b>then </b>
( <font color="Maroon" title="c14">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:26_5_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E42">A46</font></i>: 
( <font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a>, <a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c18">r2</font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/><a NAME="E6:26_5_1_1_2_1_1_2"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c15">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">r2</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E5:26_5"><i><font color="Green" title="E37">A31</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5_1_1_2_1_1_2"><i><font color="Green" title="E42">A46</font></i></a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>;<br/><a NAME="E7:26_5_1_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">r2</font></span>)</span> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green" title="E34">A28</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green" title="E36">A30</font></i></a>, <a class="ref" href="rfunct_3.html#D7" title="RFUNCT_3:def.7">RFUNCT_3:def 7</a></i>;<br/><a NAME="E8:26_5_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E43">A47</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">r2</font></span>)</span> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green" title="E34">A28</font></i></a>, <a class="ref" href="rfunct_3.html#D8" title="RFUNCT_3:def.8">RFUNCT_3:def 8</a></i>;<br/><a NAME="E9:26_5_1_1_2_1_1_2"/>
<font color="Maroon" title="c17">mn</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green" title="E28">A19</font></i></a>, <a class="txt" href="rearran1.html#E5:26_5"><i><font color="Green" title="E37">A31</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E10:26_5_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E44">A48</font></i>: 
<font color="Maroon" title="c17">mn</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E7:26_5_1_1_2"><i><font color="Green" title="E41">A41</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><i><font color="Green" title="E45">A49</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> = 
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c10">n</font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green" title="E28">A19</font></i></a>, <a class="txt" href="rearran1.html#E9:26"><i><font color="Green" title="E30">A21</font></i></a>, <a class="txt" href="rearran1.html#E5:26_5"><i><font color="Green" title="E37">A31</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5_1_1_2"><i><font color="Green" title="E38">A38</font></i></a>, <a class="ref" href="finseq_1.html#T37" title="FINSEQ_1:th.37">FINSEQ_1:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c17">mn</font>
<b>by </b><i><a class="ref" href="rfinseq.html#T28" title="RFINSEQ:th.28">RFINSEQ:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">mn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">n</font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E5:26"><i><font color="Green" title="E26">A17</font></i></a>, <a class="txt" href="rearran1.html#E10:26_5_1_1_2_1_1_2"><i><font color="Green" title="E44">A48</font></i></a>, <a class="ref" href="rfinseq.html#D2" title="RFINSEQ:def.2">RFINSEQ:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">r2</font>
<b>by </b><i><a class="txt" href="rearran1.html#E5:26_5"><i><font color="Green" title="E37">A31</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5_1_1_2_1_1_2"><i><font color="Green" title="E42">A46</font></i></a>, <a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a></i>
;<br/> <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">r2</font></span>)</span> <a href="rearran1.html#K1" title="REARRAN1:func.1">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c1">C</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T77" title="RFUNCT_1:th.77">RFUNCT_1:77</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">r1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c18">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">m</font></span>)</span>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E8:26_5_1_1_2_1_1_2"><i><font color="Green" title="E43">A47</font></i></a>, <a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font>
<b>by </b><i><a class="txt" href="rearran1.html#E4:26_5_1_1_2"><i><font color="Green" title="E40">A40</font></i></a>, <a class="txt" href="rearran1.html#E11:26_5_1_1_2_1_1_2"><i><font color="Green" title="E45">A49</font></i></a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E9:26_5_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:26_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">m</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E14:26"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="rfunct_3.html#K17" title="RFUNCT_3:func.17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">#</a> <font color="Maroon" title="c3">c</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">FinS</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c2">D</font></span>)</span> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Maroon" title="c10">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="rearran1.html#E9:26"><i><font color="Green" title="E30">A21</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>


</div>
