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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">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>, <font color="Maroon">Y</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E1:26"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span> )
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:26_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Y</font>
 ;<br/><a NAME="E2:26_1"/><b>then </b>
for <font color="Olive">V</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>  st <font color="Olive">V</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">V</font> holds <br/><font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">V</font>
 <b>by </b><i>, <a class="ref" href="yellow14.html#T22">YELLOW14:22</a></i>;<br/><b>hence </b><a NAME="E3:26_1"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="yellow14.html#T23">YELLOW14:23</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:26"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Y</font>
 ;<br/>

<b>hence </b><a NAME="E4:26"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="yellow14.html#T21">YELLOW14:21</a></i>;<br/>


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