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<b>let </b><font color="Maroon">c<sub>2</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="E1:35_1_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<a NAME="E2:35_1_1"/><b>then </b><i><font color="Green">E18</font></i>: 
for <font color="Olive">b<sub>1</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> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a>
 
;<br/>
<a NAME="E3:35_1_1"/>
for <font color="Olive">b<sub>1</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> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E1:35_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:35_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="tops_2.html#V1">open</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="tops_2.html#V2">closed</a> )
 <b>by </b><i><a class="txt" href="topgen_4.html#E2:35_1_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="tops_2.html#D2">TOPS_2:def 2</a>, <a class="ref" href="tops_2.html#D1">TOPS_2:def 1</a></i>;<br/>


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