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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  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:97"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V4" target="_self">maximal_discrete</a>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V1">strict</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:97"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T10">TSEP_1:10</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E4:97"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="tex_2.html#V5" target="_self">maximal_discrete</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="tex_2.html#E1:97"><i><font color="Green">E42</font></i></a>, <a class="txt" href="tex_2.html#E3:97"><i><font color="Green">E43</font></i></a>, <a class="ref" href="tex_2.html#T51" target="_self">Th51</a></i>;<br/>


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