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<b>let </b><font color="Maroon">Y</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">F</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">Y</font>;<br/>



<b>assume </b><a NAME="E1:21"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">F</font> is <a href="tex_4.html#V2" target="_self">anti-discrete-set-family</a>
 ;<br/>

<div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_1"/>
(  <a href="setfam_1.html#K6">meet</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or  <a href="setfam_1.html#K6">meet</a> <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_1_1"><b>suppose </b></a><a NAME="E1:21_1_1_1"/>
 <a href="setfam_1.html#K6">meet</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:21_1_1_1"/>
 <a href="setfam_1.html#K6">meet</a> <font color="Maroon">F</font> is <a href="tex_4.html#V1" target="_self">anti-discrete</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_1_2"><b>suppose </b></a><a NAME="E1:21_1_1_2"/>
 <a href="setfam_1.html#K6">meet</a> <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:21_1_1_2"/><b>then </b>
(  <a href="setfam_1.html#K6">meet</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K5">union</a> <font color="Maroon">F</font> &amp;  <a href="setfam_1.html#K5">union</a> <font color="Maroon">F</font> is <a href="tex_4.html#V1" target="_self">anti-discrete</a> )
 <b>by </b><i><a class="txt" href="tex_4.html#E1:21"><i><font color="Green">E13</font></i></a>, , <a class="ref" href="setfam_1.html#T3">SETFAM_1:3</a></i>;<br/><b>hence </b><a NAME="E3:21_1_1_2"/>
 <a href="setfam_1.html#K6">meet</a> <font color="Maroon">F</font> is <a href="tex_4.html#V1" target="_self">anti-discrete</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>


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