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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">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/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">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>assume </b><a NAME="E1:24_1"/>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tex_4.html#K1" title="TEX_4:func.1">MaxADSF</a> <font color="Maroon" title="c2">x</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">C</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font><b> such that </b><br/><a NAME="E3:24_1"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font>
 <b>and </b><br/><a NAME="E4:24_1"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c4">C</font> is <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a>
 <b>and </b><br/><a NAME="E5:24_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font>
 ;<br/><b>thus </b><a NAME="E6:24_1"/>
<font color="Maroon" title="c3">A</font> is <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a>
 <b>by </b><i><a class="txt" href="tex_4.html#E3:24_1"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="tex_4.html#E4:24_1"><i><font color="Green" title="E15">A2</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:24"/>
 <a href="tex_4.html#K1" title="TEX_4:func.1">MaxADSF</a> <font color="Maroon" title="c2">x</font> is <a href="tex_4.html#V2" title="TEX_4:attr.2">anti-discrete-set-family</a>
 <b>by </b><i><a class="ref" href="tex_4.html#D5" target="_self" title="TEX_4:def.5">Def5</a></i>;<br/>


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