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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>2</sub></font>, <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="rearran1.html#NM1">RearrangmentGen</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><a NAME="E1:26"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1">total</a> &amp;  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="rfinseq.html#K2">MIM</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E2:26"/><i><font color="Green">E24</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p5">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:26"/><i><font color="Green">E25</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="rfunct_3.html#K1">min</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="rearran1.html#E1:26"><i><font color="Green">E23</font></i></a>, <a class="ref" href="rearran1.html#T12" target="_self">Th12</a>, <a class="ref" href="rfinseq.html#D3">RFINSEQ:def 3</a>, <a class="ref" href="rfunct_3.html#D6">RFUNCT_3:def 6</a>, <a class="ref" href="rfunct_3.html#D7">RFUNCT_3:def 7</a>, <a class="ref" href="rfunct_3.html#D8">RFUNCT_3:def 8</a></i>;<br/>
<b>thus </b><a NAME="E4:26"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 1 implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="rfinseq.html#K2">MIM</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></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">E26</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 1
 ;<br/>

<a NAME="E2:26_1"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></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">c<sub>10</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:26_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:26_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E3:26_1_1"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E4:26_1_1"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E5:26_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="rearran1.html#E1:26_1_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="rearran1.html#E2:26_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="rearran1.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E6:26_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E1:26_1"><i><font color="Green">E26</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">c<sub>10</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:26_1_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:26_1_2"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:26_1_2"/><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="rfunct_1.html#K5">chi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="rfunct_3.html#D6">RFUNCT_3:def 6</a></i>;<br/><a NAME="E4:26_1_2"/><i><font color="Green">E31</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26_1_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E5:26_1_2"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E2:26_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green">E28</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> as   <a href="real_1.html#NM1">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">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></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">E33</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></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#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="ref" href="rfinseq.html#D3">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#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="rearran1.html#E3:26_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="rfunct_3.html#D7">RFUNCT_3:def 7</a></i>;<br/><a NAME="E4:26_1_2_1_1_1"/><b>then </b><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="rfunct_3.html#D8">RFUNCT_3:def 8</a></i>;<br/> <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T77">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#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E4:26_1_2_1_1_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K4">*</a> 1
<b>by </b><i><a class="txt" href="rearran1.html#E5:26_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="rfunct_1.html#T79">RFUNCT_1:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2_1_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="rfinseq.html#D3">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">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:26_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E4:26_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E3:26_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:26_1_2_1_1_2"/><b>then </b><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="txt" href="rearran1.html#E4:26_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> as   <a href="real_1.html#NM1">Real</a> ;<br/><a NAME="E6:26_1_2_1_1_2"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E4:26_1_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="rearran1.html#E4:26_1_2_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="rfinseq.html#D3">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#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="rearran1.html#E3:26_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="rfunct_3.html#D7">RFUNCT_3:def 7</a></i>;<br/><a NAME="E8:26_1_2_1_1_2"/><b>then </b><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="rfunct_3.html#D8">RFUNCT_3:def 8</a></i>;<br/> <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T77">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#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E8:26_1_2_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K4">*</a> 1
<b>by </b><i><a class="txt" href="rearran1.html#E5:26_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="rfunct_1.html#T79">RFUNCT_1:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="rearran1.html#E4:26_1_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="rearran1.html#E4:26_1_2_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="rfinseq.html#D3">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="E8:26_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></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#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="rfinseq.html#K2">MIM</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


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

<b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="rfinseq.html#K2">MIM</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0;<br/>
<b>assume </b><a NAME="E5:26"/><i><font color="Green">E26</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> )
 ;<br/>

<a NAME="E6:26"/><b>then </b><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E7:26"/><i><font color="Green">E28</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E5:26"><i><font color="Green">E26</font></i></a>, <a class="ref" href="finseq_2.html#T69">FINSEQ_2:69</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a>, <a class="ref" href="rfinseq.html#D3">RFINSEQ:def 3</a></i>;<br/>
<a NAME="E8:26"/><i><font color="Green">E29</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<i><font color="Green">E30</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfinseq.html#D3">RFINSEQ:def 3</a></i>
;<br/>
<a NAME="E10:26"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="rearran1.html#E5:26"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E11:26"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></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">c<sub>14</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:26_3"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>14</sub></font> )
 ;<br/>

<a NAME="E2:26_3"/>
<font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="rearran1.html#E6:26"><i><font color="Green">E27</font></i></a>, <a class="txt" href="rearran1.html#E7:26"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E3:26_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="rearran1.html#E1:26_3"><i><font color="Green">E33</font></i></a>, <a class="ref" href="rearran1.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E4:26_3"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E10:26"><i><font color="Green">E31</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E12:26"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> holds <br/> not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></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">c<sub>14</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:26_4"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> )
 ;<br/>

<a NAME="E2:26_4"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="rearran1.html#E5:26"><i><font color="Green">E26</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E3:26_4"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="rearran1.html#E1:26_4"><i><font color="Green">E34</font></i></a>, <a class="ref" href="rearran1.html#T2" target="_self">Th2</a></i>;<br/>
<b>assume </b><a NAME="E4:26_4"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></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">E26</font></i></a>, <a class="txt" href="rearran1.html#E3:26_4"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xboole_0.html#D4">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">c<sub>14</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:26_5"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:26_5"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:26_5"/><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="rfunct_1.html#K5">chi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green">E34</font></i></a>, <a class="ref" href="rfunct_3.html#D6">RFUNCT_3:def 6</a></i>;<br/><a NAME="E4:26_5"/><i><font color="Green">E37</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>14</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26_5"><i><font color="Green">E35</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> as   <a href="real_1.html#NM1">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">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>14</sub></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">E38</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/><div class="add"><a NAME="E2:26_5_1_1_1"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E12:26"><i><font color="Green">E33</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green">E34</font></i></a></i>;<br/><a NAME="E3:26_5_1_1_1"/><b>then </b><i><font color="Green">E39</font></i>: 
<span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="rfunct_1.html#T80">RFUNCT_1:80</a></i>;<br/><a NAME="E4:26_5_1_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green">E37</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5_1_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E5:26_5_1_1_1"/><b>then </b><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><a NAME="E6:26_5_1_1_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="rearran1.html#E1:26_5_1_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E7:26_5_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E6:26"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E8:26_5_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E9:26_5_1_1_1"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> as   <a href="real_1.html#NM1">Real</a> ;<br/><a NAME="E11:26_5_1_1_1"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green">E37</font></i></a>, <a class="txt" href="rearran1.html#E9:26_5_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="rfinseq.html#D3">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#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green">E34</font></i></a>, <a class="txt" href="rearran1.html#E3:26_5"><i><font color="Green">E36</font></i></a>, <a class="ref" href="rfunct_3.html#D7">RFUNCT_3:def 7</a></i>;<br/><a NAME="E13:26_5_1_1_1"/><b>then </b><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green">E34</font></i></a>, <a class="ref" href="rfunct_3.html#D8">RFUNCT_3:def 8</a></i>;<br/> <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T77">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#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E13:26_5_1_1_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green">E28</font></i></a>, <a class="txt" href="rearran1.html#E8:26"><i><font color="Green">E29</font></i></a>, <a class="txt" href="rearran1.html#E3:26_5_1_1_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5_1_1_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="rearran1.html#E5:26_5_1_1_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="finseq_1.html#D7">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">E38</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/><div class="add"><a NAME="E2:26_5_1_1_2"/><b>then </b><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E3:26_5_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E11:26"><i><font color="Green">E32</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green">E34</font></i></a></i>;<br/><a NAME="E4:26_5_1_1_2"/><b>then </b><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="rfunct_1.html#T79">RFUNCT_1:79</a></i>;<br/><a NAME="E5:26_5_1_1_2"/>
 <a href="square_1.html#K2">max</a> 0,<span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E1:26_5_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseq_2.html#T4">FINSEQ_2:4</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="finseq_2.html#T5">FINSEQ_2:5</a></i>;<br/><a NAME="E7:26_5_1_1_2"/><i><font color="Green">E41</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26_5_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xreal_1.html#T21">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">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> or <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></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">E42</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></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#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="ref" href="rfinseq.html#D3">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#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green">E34</font></i></a>, <a class="txt" href="rearran1.html#E3:26_5"><i><font color="Green">E36</font></i></a>, <a class="ref" href="rfunct_3.html#D7">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">E43</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green">E34</font></i></a>, <a class="ref" href="rfunct_3.html#D8">RFUNCT_3:def 8</a></i>;<br/><a NAME="E5:26_5_1_1_2_1_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green">E28</font></i></a>, <a class="txt" href="rearran1.html#E7:26_5_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5_1_1_2_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><i><font color="Green">E45</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green">E28</font></i></a>, <a class="txt" href="rearran1.html#E9:26"><i><font color="Green">E30</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green">E37</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseq_1.html#T37">FINSEQ_1:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="ref" href="rfinseq.html#T28">RFINSEQ:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E5:26"><i><font color="Green">E26</font></i></a>, <a class="txt" href="rearran1.html#E5:26_5_1_1_2_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5_1_1_2_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="rfinseq.html#D3">RFINSEQ:def 3</a></i>
;<br/> <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T77">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#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> = 
<font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></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">E43</font></i></a>, <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="rearran1.html#E4:26_5_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="rearran1.html#E6:26_5_1_1_2_1_1_1"><i><font color="Green">E45</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">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green">E37</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E3:26_5_1_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">c<sub>14</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>14</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:26_5_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>14</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> as   <a href="real_1.html#NM1">Real</a> ;<br/><a NAME="E6:26_5_1_1_2_1_1_2"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green">E37</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5_1_1_2_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="rfinseq.html#D3">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#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green">E34</font></i></a>, <a class="txt" href="rearran1.html#E3:26_5"><i><font color="Green">E36</font></i></a>, <a class="ref" href="rfunct_3.html#D7">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">E43</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5"><i><font color="Green">E34</font></i></a>, <a class="ref" href="rfunct_3.html#D8">RFUNCT_3:def 8</a></i>;<br/><a NAME="E9:26_5_1_1_2_1_1_2"/>
<font color="Maroon">c<sub>16</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green">E28</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green">E37</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E10:26_5_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E7:26_5_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><i><font color="Green">E45</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E7:26"><i><font color="Green">E28</font></i></a>, <a class="txt" href="rearran1.html#E9:26"><i><font color="Green">E30</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green">E37</font></i></a>, <a class="txt" href="rearran1.html#E1:26_5_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseq_1.html#T37">FINSEQ_1:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="ref" href="rfinseq.html#T28">RFINSEQ:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E5:26"><i><font color="Green">E26</font></i></a>, <a class="txt" href="rearran1.html#E10:26_5_1_1_2_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>17</sub></font>
<b>by </b><i><a class="txt" href="rearran1.html#E4:26_5"><i><font color="Green">E37</font></i></a>, <a class="txt" href="rearran1.html#E4:26_5_1_1_2_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="rfinseq.html#D3">RFINSEQ:def 3</a></i>
;<br/> <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="rearran1.html#K1" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T77">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#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_1.html#K5">chi</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></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">E43</font></i></a>, <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="rearran1.html#E4:26_5_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="rearran1.html#E11:26_5_1_1_2_1_1_2"><i><font color="Green">E45</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#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E7:26_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></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#K2">MIM</a> <span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K17">(#)</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfunct_3.html#K18">#</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseqop.html#K4">|-&gt;</a> 0</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E3:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rearran1.html#E9:26"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


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