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<b>assume </b><a NAME="E1:36"/>
not  <a href="modal_1.html#K4" target="_self">MP-conectives</a>  <a href="subset_1.html#R1">misses</a>  <a href="modal_1.html#K3" target="_self">MP-variables</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:36"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K8">{</a><span class="default">0,1,2</span><a href="domain_1.html#K8">}</a></span>,<a href="numbers.html#K5">NAT</a> </span><a href="mcart_1.html#K12">:]</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default">3</span><a href="domain_1.html#K6">}</a></span>,<a href="numbers.html#K5">NAT</a> </span><a href="mcart_1.html#K12">:]</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:36"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">0,1,2</span><a href="domain_1.html#K8">}</a></span> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  &amp; <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">x1</font>,<font color="Maroon">x2</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E6:36"/>
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T128">ZFMISC_1:128</a></i>;<br/>
<b>hence </b><a NAME="E7:36"/>
contradiction
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>


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