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<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font>;<br/>



<b>assume </b><a NAME="E1:38"/>
<span class="p1">(<span class="default"><a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c3">y</font></span>)</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> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a><br/>

<b>then consider </b><font color="Maroon" title="c4">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:38"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c3">y</font></span>)</span>
 <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="c5">a</font> = <font color="Maroon" title="c4">a</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#E3:38"><i><font color="Green" title="E26">A1</font></i></a></i>;<br/>
<a NAME="E5:38"/>
( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c3">y</font> )
 
<b>by </b><i><a class="txt" href="tex_4.html#E3:38"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:38"/><b>then </b>
(  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c5">a</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="c2">x</font> &amp;  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c5">a</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="c3">y</font> )
 
<b>by </b><i><a class="ref" href="tex_4.html#T23" target="_self" title="TEX_4:th.23">Th23</a></i>;<br/>
<b>hence </b><a NAME="E7:38"/>
 <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c2">x</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="c3">y</font>
 ;<br/>


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