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

<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">p1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">p2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:20"/><i><font color="Green">E49</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E2:20"/><i><font color="Green">E52</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">q1</font> = <font color="Maroon">p1</font>, <font color="Maroon">q2</font> = <font color="Maroon">p2</font> as    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">M</font> = <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">q1</font>,<font color="Maroon">q2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T15">FINSEQ_2:15</a></i>;<br/>
<b>reconsider </b><font color="Maroon">M</font> = <font color="Maroon">M</font> as   <a href="matrix_1.html#NM1">Matrix</a> of <font color="Maroon">D</font> <b>by </b><i>, , </i>;<br/>
<a NAME="E6:20"/>
<font color="Maroon">M</font> is    <a href="matrix_1.html#M1" target="_self">Matrix</a> of 2,<font color="Maroon">n</font>,<font color="Maroon">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:20_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> 2
 <b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="matrix_1.html#D3" target="_self">MATRIX_1:def 3</a><br/>

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

<b>assume </b><a NAME="E2:20_1"/>
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font>
 ;<br/>

<a NAME="E3:20_1"/><b>then </b>
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">p1</font>,<font color="Maroon">p2</font></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T147">FINSEQ_2:147</a></i>;<br/>
<b>hence </b><a NAME="E4:20_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:20"/>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">p1</font>,<font color="Maroon">p2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> is    <a href="matrix_1.html#M1" target="_self">Matrix</a> of 2,<font color="Maroon">n</font>,<font color="Maroon">D</font>
 ;<br/>


</div>
