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

<b>assume </b><a NAME="E1:53"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">B</font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:53"/>
for <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> holds <br/><font color="Olive">Y</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E3:53"/><b>then </b>
 <a href="tarski.html#K3">union</a> <font color="Maroon">B</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T98">ZFMISC_1:98</a></i>;<br/>
<a NAME="E4:53"/><b>then </b><i><font color="Green">E18</font></i>: 
<span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E5:53"/>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/>
<a NAME="E6:53"/><b>then </b>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <font color="Maroon">A</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T96">ZFMISC_1:96</a></i>;<br/>
<a NAME="E7:53"/><b>then </b><i><font color="Green">E19</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<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">X</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E8:53"/>
<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">X</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>hence </b><a NAME="E9:53"/>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">A</font>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


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