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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#NM3">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:9"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="nagata_1.html#V1" target="_self">discrete</a>
 ;<br/>

<a NAME="E2:9"/>
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/>
<b>hence </b><a NAME="E3:9"/>
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>3</sub></font> is <a href="nagata_1.html#V1" target="_self">discrete</a>
 <b>by </b><i><a class="txt" href="nagata_1.html#E1:9"><i><font color="Green">E6</font></i></a>, <a class="ref" href="nagata_1.html#T2" target="_self">Th2</a></i>;<br/>


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