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

<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">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>, <font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/>



<a NAME="E1:22"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a>  <a href="margrel1.html#K3" target="_self">relations_on</a> <font color="Maroon">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<a NAME="E1:22_1"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">y</font></span><a href="finseq_1.html#K12">*&gt;</a></span> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>
 
;<br/>
<a NAME="E2:22_1"/><b>then </b>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D9">FINSEQ_1:def 9</a></i>;<br/>
<a NAME="E3:22_1"/><b>then </b>
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> <a href="finseq_1.html#K13">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E4:22_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font> <a href="finseq_1.html#K13">*</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E5:22_1"/>
for <font color="Olive">a1</font>, <font color="Olive">a2</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>  st <font color="Olive">a1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Olive">a2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span> holds <br/> <a href="finseq_1.html#K3">len</a> <font color="Olive">a1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">a2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>, <font color="Maroon">a2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/>

<b>assume </b><a NAME="E1:22_1_1"/>
( <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span> )
 ;<br/>

<a NAME="E2:22_1_1"/><b>then </b>
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:22_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">a2</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:22_1"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a>  <a href="margrel1.html#K3" target="_self">relations_on</a> <font color="Maroon">D</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:22"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span> is    <a href="subset_1.html#M1">Element</a> of  <a href="margrel1.html#K3" target="_self">relations_on</a> <font color="Maroon">D</font>
 ;<br/>


</div>
