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

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:58_1_1_1"/>
not  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><b>then consider </b><font color="Maroon" title="c3">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:58_1_1_1"/><i><font color="Green" title="E38">A1</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c4">a</font> = <font color="Maroon" title="c3">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font> <b>by </b><i><a class="txt" href="tex_4.html#E3:58_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c5">D</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:58_1_1_1"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font>
 <b>and </b><br/><a NAME="E7:58_1_1_1"/><i><font color="Green" title="E39">A2</font></i>: 
<font color="Maroon" title="c5">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font> : <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="tex_4.html#E3:58_1_1_1"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/><b>consider </b><font color="Maroon" title="c6">b</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font><b> such that </b><br/><a NAME="E9:58_1_1_1"/>
<font color="Maroon" title="c5">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c6">b</font>
 <b>and </b><br/><a NAME="E10:58_1_1_1"/><i><font color="Green" title="E40">A3</font></i>: 
<font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="tex_4.html#E7:58_1_1_1"><i><font color="Green" title="E39">A2</font></i></a></i>;<br/><b>thus </b><a NAME="E11:58_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_4.html#E10:58_1_1_1"><i><font color="Green" title="E40">A3</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:58_1_1"/>
 <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c2">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/>


</div>
