<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font> holds   <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="tex_4.html#K1" title="TEX_4:func.1">MaxADSF</a> <font color="Olive" title="b1">x</font></span>)</span> is <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="tex_4.html#K1" title="TEX_4:func.1">MaxADSF</a> <font color="Maroon" title="c2">x</font></span>)</span> is <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a></span><br/>



<a NAME="E1:27"/>
( <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <span class="p1">(<span class="default"><a href="tex_4.html#K1" title="TEX_4:func.1">MaxADSF</a> <font color="Maroon" title="c2">x</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="tex_4.html#T13" target="_self" title="TEX_4:th.13">Th13</a></i>;<br/>
<b>hence </b><a NAME="E2:27"/>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="tex_4.html#K1" title="TEX_4:func.1">MaxADSF</a> <font color="Maroon" title="c2">x</font></span>)</span> is <a href="tex_4.html#V1" title="TEX_4:attr.1">anti-discrete</a>
 <b>by </b><i><a class="ref" href="tex_4.html#T10" target="_self" title="TEX_4:th.10">Th10</a>, <a class="ref" href="tex_4.html#T12" target="_self" title="TEX_4:th.12">Th12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
