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<b>let </b><font color="Maroon">GX</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</font>;<br/>



<b>assume </b><a NAME="E1:42"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">C</font> is <a href="connsp_1.html#V2" target="_self">connected</a>
 ;<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><a NAME="E2:42"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">S</font> <a href="connsp_1.html#R3" target="_self">is_a_component_of</a> <font color="Maroon">GX</font>
 ;<br/>

<b>assume </b><a NAME="E3:42"/>
<font color="Maroon">C</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">S</font>
 ;<br/>

<a NAME="E4:42"/><b>then </b><i><font color="Green">E25</font></i>: 
not <font color="Maroon">C</font>,<font color="Maroon">S</font> <a href="connsp_1.html#R1" target="_self">are_separated</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E5:42"/>
<font color="Maroon">S</font> is <a href="connsp_1.html#V2" target="_self">connected</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:42"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">S</font> is <a href="connsp_1.html#V2" target="_self">connected</a>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T6" target="_self">Th6</a>, , </i>;<br/>
<a NAME="E7:42"/>
<font color="Maroon">S</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E8:42"/><b>then </b>
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">S</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E9:42"/>
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>


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