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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">A1</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A2</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<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="E1:9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="prob_1.html#K2">Union</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="setlim_2.html#K1" target="_self">(/\)</a> <font color="Maroon">A2</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:9"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="setlim_2.html#K1" target="_self">(/\)</a> <font color="Maroon">A2</font></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="prob_1.html#T25">PROB_1:25</a></i>;<br/>
<a NAME="E4:9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A2</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:9"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A1</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A2</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:9"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="prob_1.html#K2">Union</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="prob_1.html#K2">Union</a> <font color="Maroon">A2</font> )
 
<b>by </b><i><a class="ref" href="prob_1.html#T25">PROB_1:25</a></i>;<br/>
<b>hence </b><a NAME="E7:9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">A1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2">Union</a> <font color="Maroon">A2</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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