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

<b>let </b><font color="Maroon" title="c1">z</font>, <font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font>, <font color="Maroon" title="c5">D</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>









<b>assume </b><a NAME="E1:8"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c5">D</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span>
 ;<br/>

<a NAME="E2:8"/><b>then </b>
( not <font color="Maroon" title="c2">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c3">B</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c4">C</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c5">D</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T55" title="MCART_1:th.55">MCART_1:55</a></i>;<br/>
<a NAME="E3:8"/><b>then </b>
 ex <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">A</font> ex <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">B</font> ex <font color="Olive" title="b3">c</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">C</font> ex <font color="Olive" title="b4">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">D</font> st <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 
<b>by </b><i><a class="txt" href="recdef_2.html#E1:8"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="domain_1.html#T31" title="DOMAIN_1:th.31">DOMAIN_1:31</a></i>;<br/>
<b>hence </b><a NAME="E4:8"/>
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K4" title="RECDEF_2:func.4">`1_4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K5" title="RECDEF_2:func.5">`2_4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K6" title="RECDEF_2:func.6">`3_4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K7" title="RECDEF_2:func.7">`4_4</a> </span>)</span></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="recdef_2.html#T4" target="_self" title="RECDEF_2:th.4">Th4</a></i>;<br/>


</div>
