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<b>let </b><font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font>, <font color="Maroon">y</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font>;<br/>



<b>assume </b><a NAME="E1:38"/>
<span class="p1">(<span class="default"><a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">x</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a><br/>

<b>then consider </b><font color="Maroon">a</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:38"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">x</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">y</font></span>)</span>
 <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">a</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font> <b>by </b><i><a class="ref" href="tex_4.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E5:38"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">y</font> )
 
<b>by </b><i><a class="ref" href="tex_4.html#T2" target="_self">Th2</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:38"/><b>then </b>
(  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">x</font> &amp;  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">y</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:38"/>
 <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K2" target="_self">MaxADSet</a> <font color="Maroon">y</font>
 ;<br/>


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