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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>thus </b><a NAME="E1:77"/>
(  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#R1">misses</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> implies  <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#NR2" target="_self">&lt;&gt;</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="ref" href="tex_4.html#T51" target="_self">Th51</a></i>;<br/>

<b>assume </b><a NAME="E2:77"/><i><font color="Green">E51</font></i>: 
 <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#NR2" target="_self">&lt;&gt;</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>
 ;<br/>

<b>assume </b><a NAME="E3:77"/>
 <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#R2">meets</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E4:77"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="tex_4.html#T24" target="_self">Th24</a></i>;<br/>
<b>hence </b><a NAME="E5:77"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_4.html#E2:77"><i><font color="Green">E51</font></i></a>, <a class="ref" href="tex_4.html#T51" target="_self">Th51</a></i>;<br/>


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