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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>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:29_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" target="_self">Der</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E2:29_1"/><b>then </b><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="topgen_1.html#K2" target="_self">Der</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:29_1"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="topgen_1.html#R1" target="_self">is_an_accumulation_point_of</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="topgen_1.html#T18" target="_self">Th18</a></i>;<br/><b>hence </b><a NAME="E4:29_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="topgen_1.html#R2" target="_self">is_isolated_in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="topgen_1.html#E2:29_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="topgen_1.html#D4" target="_self">Def4</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:29"/>
<font color="Maroon">c<sub>3</sub></font> <a href="topgen_1.html#R2" target="_self">is_isolated_in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:29"/><b>then </b><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="topgen_1.html#R1" target="_self">is_an_accumulation_point_of</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="topgen_1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E4:29"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="topgen_1.html#K2" target="_self">Der</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="topgen_1.html#T18" target="_self">Th18</a></i>;<br/>
<b>hence </b><a NAME="E5:29"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" target="_self">Der</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="topgen_1.html#E3:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>


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