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<b>let </b><font color="Maroon">X1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X3</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X4</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X5</font> be    <a href="hidden.html#M1">set</a> ;<br/>









<b>assume </b><a NAME="E1:20"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">X1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">X2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">X3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">X4</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">X5</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<a NAME="E2:20"/><b>then </b><i><font color="Green">E45</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">X2</font>,<font color="Maroon">X3</font>,<font color="Maroon">X4</font></span><a href="zfmisc_1.html#K4">:]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="mcart_1.html#T55">MCART_1:55</a></i>;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="mcart_2.html#K2" target="_self">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">X2</font>,<font color="Maroon">X3</font>,<font color="Maroon">X4</font>,<font color="Maroon">X5</font></span><a href="mcart_2.html#K2" target="_self">:]</a></span>;<br/>

<b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K4">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">X2</font>,<font color="Maroon">X3</font>,<font color="Maroon">X4</font></span><a href="zfmisc_1.html#K4">:]</a></span>,<font color="Maroon">X5</font></span><a href="zfmisc_1.html#K2">:]</a></span> ;<br/>
<b>consider </b><font color="Maroon">x1234</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">X2</font>,<font color="Maroon">X3</font>,<font color="Maroon">X4</font></span><a href="zfmisc_1.html#K4">:]</a></span>, <font color="Maroon">xx5</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X5</font><b> such that </b><br/><a NAME="E5:20"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">x'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1234</font>,<font color="Maroon">xx5</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i>, , </i>;<br/>
<b>consider </b><font color="Maroon">xx1</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X1</font>, <font color="Maroon">xx2</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X2</font>, <font color="Maroon">xx3</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X3</font>, <font color="Maroon">xx4</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X4</font><b> such that </b><br/><a NAME="E7:20"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">x1234</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Maroon">xx1</font>,<font color="Maroon">xx2</font>,<font color="Maroon">xx3</font>,<font color="Maroon">xx4</font></span><a href="mcart_1.html#K4">]</a></span>
 <b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">xx1</font>
;<br/>

<b>take </b>
<font color="Maroon">xx2</font>
;<br/>

<b>take </b>
<font color="Maroon">xx3</font>
;<br/>

<b>take </b>
<font color="Maroon">xx4</font>
;<br/>

<b>take </b>
<font color="Maroon">xx5</font>
;<br/>

<b>thus </b><a NAME="E8:20"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_2.html#K1" target="_self">[</a><span class="default"><font color="Maroon">xx1</font>,<font color="Maroon">xx2</font>,<font color="Maroon">xx3</font>,<font color="Maroon">xx4</font>,<font color="Maroon">xx5</font></span><a href="mcart_2.html#K1" target="_self">]</a></span>
 <b>by </b><i>, </i>;<br/>


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