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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">C</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">D</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="enumset1.html#K2">}</a></span>
 ;<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="E3:2_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 <b>and </b><br/><a NAME="E4:2_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/><a NAME="E5:2_1"/>
( <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> )
 <b>by </b><i>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/><b>hence </b><a NAME="E6:2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><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> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">D</font>
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<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="E2:2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><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> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">D</font>
 ;<br/>

<a NAME="E3:2"/><b>then </b><i><font color="Green">E50</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:2"/>
( <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="enumset1.html#K2">}</a></span> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="enumset1.html#K2">}</a></span> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="enumset1.html#K2">}</a></span> &amp; <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="enumset1.html#K2">}</a></span> )
 
<b>by </b><i><a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>


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