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

<b>let </b><font color="Maroon">A</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">o</font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> <font color="Maroon">A</font></span>)</span>;<br/>



<a NAME="E1:58"/>
the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default">1 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default">3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:58"/><b>then </b>
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default">1 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> or <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default">3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:58"/><b>then </b>
( ( <font color="Maroon">o</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">o</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R2">in</a> 1 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font> ) or ( <font color="Maroon">o</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">o</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R2">in</a> 3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font> ) )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/>
<b>hence </b><a NAME="E4:58"/>
( ( <font color="Maroon">o</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">o</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">o</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 2 &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">o</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="hidden.html#R1">=</a> 3 ) )
 <b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div>
