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<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>assume </b><a NAME="E1:86"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">X</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B</font>
 ;<br/>

<b>assume </b><a NAME="E2:86"/>
 <a href="tarski.html#K3">union</a> <font color="Maroon">A</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">B</font>
 ;<br/>

<b>then consider </b><font color="Maroon">z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:86"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <font color="Maroon">A</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/>
<a NAME="E5:86"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">A</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T10" target="_self">Th10</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<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="E7:86"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>and </b><br/><a NAME="E8:86"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E9:86"/>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font> &amp; <font color="Maroon">X</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B</font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T9" target="_self">Th9</a>, <a class="ref" href="zfmisc_1.html#T12" target="_self">Th12</a>, <a class="txt" href="zfmisc_1.html#E21"><i><font color="Green">Lemma42</font></i></a>, <a class="txt" href="zfmisc_1.html#E23"><i><font color="Green">Lemma43</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E10:86"/>
contradiction
 <b>by </b><i><a class="ref" href="xboole_0.html#T4">XBOOLE_0:4</a></i>;<br/>


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