<?xml version="1.0"?>
<div class="add">

<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">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="E1:81"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" target="_self">bool</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" target="_self">bool</a> <span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">A</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:81"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1" target="_self">bool</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">B</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1" target="_self">bool</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:81"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">B</font> or <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">A</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:81"/>
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">A</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">z</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="E1:81_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:81_1"/><b>then </b>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">B</font> or <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">A</font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T6" target="_self">Th6</a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:81_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:81"/><b>then </b>
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">B</font>
 
;<br/>
<b>hence </b><a NAME="E6:81"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1" target="_self">bool</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">B</font></span>)</span>
 <b>by </b><i/>;<br/>


</div>
