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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:5"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="connsp_1.html#V2">connected</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="connsp_1.html#V2">connected</a> )
 <b>and </b><br/><a NAME="E2:5"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E3:5"/>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="connsp_1.html#R1">are_separated</a> 
 
<b>by </b><i><a class="txt" href="jordan1.html#E2:5"><i><font color="Green">E8</font></i></a>, <a class="ref" href="connsp_1.html#T2">CONNSP_1:2</a></i>;<br/>
<b>hence </b><a NAME="E4:5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="jordan1.html#E1:5"><i><font color="Green">E7</font></i></a>, <a class="ref" href="connsp_1.html#T18">CONNSP_1:18</a></i>;<br/>


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