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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><a NAME="E1:88"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="card_4.html#V1">countable</a>
 ;<br/>

<b>assume </b><a NAME="E2:88"/>
<font color="Maroon">c<sub>2</sub></font> <a href="topgen_4.html#K4" target="_self">^0</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:88"/><i><font color="Green">E49</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> <a href="topgen_4.html#K4" target="_self">^0</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="topgen_4.html#E4:88"><i><font color="Green">E49</font></i></a></i>;<br/>
<a NAME="E6:88"/>
<font color="Maroon">c<sub>4</sub></font> <a href="topgen_4.html#R1" target="_self">is_a_condensation_point_of</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E4:88"><i><font color="Green">E49</font></i></a>, <a class="ref" href="topgen_4.html#D10" target="_self">Def10</a></i>;<br/>
<b>hence </b><a NAME="E7:88"/>
contradiction
 <b>by </b><i><a class="txt" href="topgen_4.html#E1:88"><i><font color="Green">E48</font></i></a>, <a class="ref" href="topgen_4.html#T58" target="_self">Th58</a></i>;<br/>


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