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<b>let </b><font color="Maroon">T</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">O</font> be  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>





<a NAME="E1:14"/>
( <font color="Maroon">O</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A</font> implies <font color="Maroon">O</font> <a href="xboole_0.html#R1">misses</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_1"/>
<font color="Maroon">O</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:14_1"/><b>then </b>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">O</font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E3:14_1"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">O</font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="tops_1.html#T31">TOPS_1:31</a></i>;<br/>
<b>hence </b><a NAME="E4:14_1"/>
<font color="Maroon">O</font> <a href="xboole_0.html#R1">misses</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:14"/>
( <font color="Maroon">O</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> implies <font color="Maroon">O</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> )
 ;<br/>


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