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<b>let </b><font color="Maroon">GX</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">T</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</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="E1:25"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1" target="_self">Int</a> <font color="Maroon">T</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">x''</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">GX</font> <b>by </b><i><a class="ref" href="tops_1.html#T22" target="_self">Th22</a></i>;<br/>
<a NAME="E3:25"/><i><font color="Green">E24</font></i>: 
not <font color="Maroon">GX</font> is <a href="struct_0.html#V3">empty</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T22" target="_self">Th22</a>, <a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>
<a NAME="E4:25"/>
<font color="Maroon">T</font> <a href="subset_1.html#K3">`</a>  <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="subset_1.html#K3">`</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T48">PRE_TOPC:48</a></i>;<br/>
<a NAME="E5:25"/><b>then </b>
not <font color="Maroon">x''</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="tops_1.html#T22" target="_self">Th22</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>hence </b><a NAME="E6:25"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="tops_1.html#T26" target="_self">Th26</a>, </i>;<br/>


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