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<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>;<br/><b>let </b><font color="Maroon" title="c3">x</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font>;<br/>





<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E30">A1</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 ;<br/>

<b>assume </b><a NAME="E2:44"/>
<font color="Maroon" title="c2">A</font> is <a href="tex_4.html#V3" title="TEX_4:attr.3">maximal_anti-discrete</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font><b> such that </b><br/><a NAME="E4:44"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <b>and </b><br/><a NAME="E5:44"/><i><font color="Green" title="E31">A2</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="ref" href="tex_4.html#D9" target="_self" title="TEX_4:def.9">Def9</a></i>;<br/>
<b>thus </b><a NAME="E6:44"/>
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E1:44"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="tex_4.html#E5:44"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="tex_4.html#T23" target="_self" title="TEX_4:th.23">Th23</a></i>;<br/>


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