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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">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>;<br/>



<b>thus </b><a NAME="E1:54"/>
( <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">B</font> implies  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">B</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:54_1"/>
( <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">B</font> )
 ;<br/>

<a NAME="E2:54_1"/><b>then </b>
(  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">A</font> &amp;  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">B</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:54_1"/>
 <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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


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