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<b>let </b><font color="Maroon">T</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">M</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">T</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="E1:36"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="tops_2.html#K1" target="_self">|</a> <font color="Maroon">M</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">A</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:36"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E4:36"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> <a href="tops_2.html#K1" target="_self">|</a> <font color="Maroon">M</font>
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">Q</font> = <font color="Maroon">A</font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">M</font></span>)</span> <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">R</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E7:36"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">R</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 <b>and </b><br/><a NAME="E8:36"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">R</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Q</font>
 <b>by </b><i>, </i>;<br/>
<a NAME="E9:36"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> &amp; <font color="Maroon">R</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 
<b>by </b><i>, , , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E10:36"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K5">union</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>


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