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<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" target="_self">MaxADSet</a> <font color="Maroon">A</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:58_1_1_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font> <b>by </b><i/>;<br/><a NAME="E5:58_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">b</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font> : <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> 
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">D</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:58_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 <b>and </b><br/><a NAME="E8:58_1_1_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">b</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font> : <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/><b>consider </b><font color="Maroon">b</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font><b> such that </b><br/><a NAME="E10:58_1_1_1"/>
<font color="Maroon">D</font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">b</font>
 <b>and </b><br/><a NAME="E11:58_1_1_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E12:58_1_1_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:58_1_1"/>
 <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">A</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>


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