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

<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#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>thus </b><a NAME="E1:82"/>
(  not  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> ) or ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:82_1"/><i><font color="Green">E53</font></i>: 
 <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:82_1_1_1"/>
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> ) or ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="tex_4.html#E1:82_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="tex_4.html#T55" target="_self">Th55</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1_1"><b>suppose </b></a><a NAME="E1:82_1_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/><div class="add"><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="E3:82_1_1_1_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E4:82_1_1_1_1"/><i><font color="Green">E55</font></i>: 
 <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E5:82_1_1_1_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1_1_1_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K3">`</a> ;<br/><b>thus </b><a NAME="E1:82_1_1_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="txt" href="tex_4.html#E3:82_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="tops_1.html#T30">TOPS_1:30</a></i>;<br/><b>thus </b><a NAME="E2:82_1_1_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="tex_4.html#E4:82_1_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="subset_1.html#T44">SUBSET_1:44</a></i>;<br/><b>thus </b><a NAME="E3:82_1_1_1_1_1"/>
 <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="tex_4.html#E5:82_1_1_1_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:82_1_1_1_1"/>
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> ) or ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1_2"><b>suppose </b></a><a NAME="E1:82_1_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/><div class="add"><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="E3:82_1_1_1_2"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E4:82_1_1_1_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E5:82_1_1_1_2"/><i><font color="Green">E56</font></i>: 
 <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1_1_1_2_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K3">`</a> ;<br/><b>thus </b><a NAME="E1:82_1_1_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="txt" href="tex_4.html#E3:82_1_1_1_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="tops_1.html#T30">TOPS_1:30</a></i>;<br/><b>thus </b><a NAME="E2:82_1_1_1_2_1"/>
 <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="tex_4.html#E4:82_1_1_1_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><b>thus </b><a NAME="E3:82_1_1_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="tex_4.html#E5:82_1_1_1_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="subset_1.html#T44">SUBSET_1:44</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:82_1_1_1_2"/>
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> ) or ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:82"/><i><font color="Green">E53</font></i>: 
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> ) or ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/>

<b>assume </b><a NAME="E3:82"/>
 <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#R2">meets</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E4:82"/><b>then </b><i><font color="Green">E54</font></i>: 
 <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="tex_4.html#T24" target="_self">Th24</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:82_2_1"/>
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> ) or ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="tex_4.html#E2:82"><i><font color="Green">E53</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_2_1_1"><b>suppose </b></a><a NAME="E1:82_2_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/><div class="add"><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="E3:82_2_1_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>and </b><br/><a NAME="E4:82_2_1_1"/><i><font color="Green">E55</font></i>: 
 <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E5:82_2_1_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E6:82_2_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="tex_4.html#E5:82_2_1_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><b>hence </b><a NAME="E7:82_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_4.html#E4:82"><i><font color="Green">E54</font></i></a>, <a class="txt" href="tex_4.html#E4:82_2_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_2_1_2"><b>suppose </b></a><a NAME="E1:82_2_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/><div class="add"><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="E3:82_2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>and </b><br/><a NAME="E4:82_2_1_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E5:82_2_1_2"/><i><font color="Green">E56</font></i>: 
 <a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E6:82_2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K4" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="tex_4.html#E4:82_2_1_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><b>hence </b><a NAME="E7:82_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_4.html#E4:82"><i><font color="Green">E54</font></i></a>, <a class="txt" href="tex_4.html#E5:82_2_1_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:82"/>
contradiction
 ;<br/>


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