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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><a NAME="E1:78"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="pre_topc.html#V3">open</a> )
 ;<br/>

<b>assume </b><a NAME="E2:78"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V3" target="_self">discrete</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="tex_2.html#V3" target="_self">discrete</a> )
 ;<br/>

<a NAME="E3:78"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">b<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Olive">b<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Olive">b<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="ref" href="tops_1.html#T37">TOPS_1:37</a>, <a class="ref" href="tops_1.html#T38">TOPS_1:38</a></i>;<br/>
<b>hence </b><a NAME="E4:78"/>
<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="tex_2.html#V3" target="_self">discrete</a>
 <b>by </b><i><a class="txt" href="tex_2.html#E1:78"><i><font color="Green">E30</font></i></a>, <a class="txt" href="tex_2.html#E2:78"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tex_2.html#T30" target="_self">Th30</a></i>;<br/>


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