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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="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:75"/><i><font color="Green">E50</font></i>: 
 <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:75"/><b>then </b><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="tex_4.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E3:75"/>
 <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> is <a href="tex_4.html#V3" target="_self">maximal_anti-discrete</a>
 
<b>by </b><i><a class="ref" href="tex_4.html#T22" target="_self">Th22</a></i>;<br/>
<a NAME="E4:75"/><b>then </b>
 <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> is <a href="tex_4.html#V1" target="_self">anti-discrete</a>
 
<b>by </b><i><a class="ref" href="tex_4.html#D7" target="_self">Def7</a></i>;<br/>
<b>hence </b><a NAME="E5:75"/>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="tex_4.html#E1:75"><i><font color="Green">E50</font></i></a>, <a class="txt" href="tex_4.html#E2:75"><i><font color="Green">E51</font></i></a>, <a class="ref" href="tex_4.html#D14" target="_self">Def14</a></i>;<br/>


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