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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>



<b>set </b><font color="Maroon">F</font> = <span class="p1">{<span class="default"> <font color="Olive">G</font> where <font color="Olive">G</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> : ( <font color="Olive">G</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Olive">G</font> ) </span>}</span> ;<br/>
<b>assume </b><a NAME="E1:84"/>
<font color="Maroon">P</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<a NAME="E2:84"/><b>then </b>
<font color="Maroon">P</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">G</font> where <font color="Olive">G</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> : ( <font color="Olive">G</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Olive">G</font> ) </span>}</span> 
 
;<br/>
<a NAME="E3:84"/><b>then </b><i><font color="Green">E13</font></i>: 
 <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <font color="Olive">G</font> where <font color="Olive">G</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> : ( <font color="Olive">G</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Olive">G</font> ) </span>}</span>  <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#T4">SETFAM_1:4</a></i>;<br/>
<a NAME="E4:84"/>
 <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <font color="Olive">G</font> where <font color="Olive">G</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> : ( <font color="Olive">G</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Olive">G</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="tex_4.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E5:84"/><b>then </b>
(  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">P</font> )
 
<b>by </b><i><a class="ref" href="tex_4.html#D5" target="_self">Def5</a>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E6:84"/>
 <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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