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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> 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="E1:17"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="connsp_1.html#V2">connected</a>
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E3:17"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T48">PRE_TOPC:48</a></i>;<br/>
<a NAME="E4:17"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i><a class="txt" href="connsp_3.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="ref" href="connsp_1.html#T20">CONNSP_1:20</a></i>;<br/>
<b>hence </b><a NAME="E5:17"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="connsp_3.html#K1" target="_self">skl</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="connsp_3.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="connsp_3.html#E2:17"><i><font color="Green">E15</font></i></a>, <a class="txt" href="connsp_3.html#E3:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="connsp_3.html#T13" target="_self">Th13</a></i>;<br/>


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