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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Z</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<a NAME="E1:54"/>
<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Z</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:54"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Z</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E3:54"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Z</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:54"/><b>then </b>
<font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Z</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E5:54"/>
<font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Z</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Y</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T28" target="_self">Th28</a>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E6:54"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Y</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font></span>)</span>
 ;<br/>

<a NAME="E7:54"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E8:54"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E9:54"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Z</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E10:54"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Z</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>


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