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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">B</font> be    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E1:11"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">V</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<a NAME="E2:11"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">V</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <font color="Olive">G</font> where <font color="Olive">G</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> : ( <font color="Olive">G</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Olive">G</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="yellow_8.html#T18">YELLOW_8:18</a></i>;<br/>
<b>consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:11"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">Y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:11"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">G</font> where <font color="Olive">G</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> : ( <font color="Olive">G</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Olive">G</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> ) </span>}</span>  )
 <b>by </b><i>, , <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">Z</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E8:11"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E9:11"/>
 ex <font color="Olive">W</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">W</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Olive">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> &amp; <font color="Olive">W</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, </i>;<br/>


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