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<b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">B</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:3"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="zfmisc_1.html#K3">:]</a></span>
 ;<br/>

<a NAME="E2:3"/><b>then </b><i><font color="Green">E40</font></i>: 
( not <font color="Maroon">A</font> is <a href="xboole_0.html#V1">empty</a> &amp; not <font color="Maroon">B</font> is <a href="xboole_0.html#V1">empty</a> &amp; not <font color="Maroon">C</font> is <a href="xboole_0.html#V1">empty</a> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T35">MCART_1:35</a></i>;<br/>
<b>then consider </b><font color="Maroon">a</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>, <font color="Maroon">b</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">B</font>, <font color="Maroon">c</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E4:3"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K3">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="mcart_1.html#K3">]</a></span>
 <b>by </b><i>, <a class="ref" href="domain_1.html#T15">DOMAIN_1:15</a></i>;<br/>
<a NAME="E5:3"/>
( <font color="Maroon">z</font> <a href="recdef_2.html#K1" target="_self">`1_3</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">z</font> <a href="recdef_2.html#K2" target="_self">`2_3</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">z</font> <a href="recdef_2.html#K3" target="_self">`3_3</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E6:3"/>
( <font color="Maroon">z</font> <a href="recdef_2.html#K1" target="_self">`1_3</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">z</font> <a href="recdef_2.html#K2" target="_self">`2_3</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">z</font> <a href="recdef_2.html#K3" target="_self">`3_3</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 <b>by </b><i/>;<br/>


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