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<b>let </b><font color="Maroon">T</font> be    <a href="pre_topc.html#L1" target="_self">TopStruct</a> ;<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/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:44_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/><b>assume </b><a NAME="E2:44_1"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K4" target="_self">Cl</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E3:44_1"/><b>then </b>
 ex <font color="Olive">C</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">C</font> is <a href="pre_topc.html#V4" target="_self">closed</a> &amp; <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Olive">C</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">C</font> )
 <b>by </b><i><a class="txt" href="pre_topc.html#E1:44_1"><i><font color="Green">E19</font></i></a>, </i>;<br/><b>hence </b><a NAME="E4:44_1"/>
contradiction
 <b>by </b><i><a class="txt" href="pre_topc.html#E1:44_1"><i><font color="Green">E19</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:44"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4" target="_self">Cl</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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