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

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="comput_1.html#K16" target="_self">(1,2)-&gt;(1,?,2)</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D4" target="_self">COMPUT_1:def 4</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:155_1_1"/><i><font color="Green">E102</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="comput_1.html#K16" target="_self">(1,2)-&gt;(1,?,2)</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E2:155_1_1"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="comput_1.html#K16" target="_self">(1,2)-&gt;(1,?,2)</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<a NAME="E3:155_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span>,<span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_6.html#T62">FUNCT_6:62</a></i>;<br/>
<b>then </b> <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span>,<span class="p3">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span> = 
<span class="p1">(<span class="default">3 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comput_1.html#T40" target="_self">Th40</a></i>
<br/>.= 
<span class="p1">(<span class="default">3 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default">3 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> </span>)</span>
<b>by </b><i><a class="ref" href="comput_1.html#T40" target="_self">Th40</a></i>
<br/>.= 
3 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 

;<br/>
<a NAME="E5:155_1_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p4">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span>,<span class="p4">(<span class="default">3 <a href="comput_1.html#K8" target="_self">proj</a> 3</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span> <a href="tarski.html#R1">c=</a> 3 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T44">RELAT_1:44</a></i>;<br/>
<a NAME="E6:155_1_1"/><b>then </b>
( 3 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp; 3 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="comput_1.html#E1:155_1_1"><i><font color="Green">E102</font></i></a>, <a class="txt" href="comput_1.html#E2:155_1_1"><i><font color="Green">E103</font></i></a>, <a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<b>hence </b><a NAME="E7:155_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>


</div>
