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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="armstrng.html#NM3">Dependency</a> of <font color="Maroon">X</font>, <font color="Maroon">q</font> be   <a href="armstrng.html#NM3">Dependency</a> of <font color="Maroon">X</font>;<br/>



<b>assume </b><a NAME="E1:37"/>
( <font color="Maroon">p</font> <a href="armstrng.html#NR6" target="_self">&lt;=</a> <font color="Maroon">q</font> &amp; <font color="Maroon">q</font> <a href="armstrng.html#NR6" target="_self">&lt;=</a> <font color="Maroon">p</font> )
 ;<br/>

<a NAME="E2:37"/><b>then </b>
( <font color="Maroon">p</font> <a href="mcart_1.html#K1">`1</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">q</font> <a href="mcart_1.html#K1">`1</a>  &amp; <font color="Maroon">q</font> <a href="mcart_1.html#K2">`2</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">p</font> <a href="mcart_1.html#K2">`2</a>  &amp; <font color="Maroon">q</font> <a href="mcart_1.html#K1">`1</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">p</font> <a href="mcart_1.html#K1">`1</a>  &amp; <font color="Maroon">p</font> <a href="mcart_1.html#K2">`2</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">q</font> <a href="mcart_1.html#K2">`2</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:37"/><b>then </b><i><font color="Green">E33</font></i>: 
( <font color="Maroon">p</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="mcart_1.html#K1">`1</a>  &amp; <font color="Maroon">p</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="mcart_1.html#K2">`2</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E4:37"/>
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T24">MCART_1:24</a></i>;<br/>
<b>hence </b><a NAME="E5:37"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font>
 <b>by </b><i/>;<br/>


</div>
