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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">R</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</font>;<br/><b>let </b><font color="Maroon">S</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:69"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">R</font> is <a href="tops_1.html#V1" target="_self">dense</a>
 <b>and </b><br/><a NAME="E2:69"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">R</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font>
 ;<br/>

<a NAME="E3:69"/><i><font color="Green">E36</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">GX</font>
 
<b>by </b><i>, <a class="ref" href="tops_1.html#T40" target="_self">Th40</a></i>;<br/>
<a NAME="E4:69"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">GX</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">S</font>
 
<b>by </b><i>, <a class="ref" href="tops_1.html#T43" target="_self">Th43</a>, <a class="ref" href="pre_topc.html#T49">PRE_TOPC:49</a></i>;<br/>
<a NAME="E5:69"/><b>then </b>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">GX</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E6:69"/>
<font color="Maroon">S</font> is <a href="tops_1.html#V1" target="_self">dense</a>
 <b>by </b><i><a class="ref" href="tops_1.html#T40" target="_self">Th40</a></i>;<br/>


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