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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#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:24_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="tex_4.html#K1" target="_self">MaxADSF</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:24_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:24_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="tex_4.html#V1" target="_self">anti-discrete</a>
 <b>and </b><br/><a NAME="E5:24_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><b>thus </b><a NAME="E6:24_1"/>
<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="txt" href="tex_4.html#E3:24_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="tex_4.html#E4:24_1"><i><font color="Green">E15</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:24"/>
 <a href="tex_4.html#K1" target="_self">MaxADSF</a> <font color="Maroon">c<sub>2</sub></font> is <a href="tex_4.html#V2" target="_self">anti-discrete-set-family</a>
 <b>by </b><i><a class="ref" href="tex_4.html#D5" target="_self">Def5</a></i>;<br/>


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