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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">x</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="lopclset.html#K1" target="_self">OpenClosedSet</a> <font color="Maroon">T</font>;<br/>



<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> ;<br/>
<a NAME="E2:9"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">y</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:9"/>
<font color="Maroon">y</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i/>;<br/>
<a NAME="E4:9"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">x</font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T29">TOPS_1:29</a></i>;<br/>
<a NAME="E5:9"/>
<font color="Maroon">x</font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i>, <a class="ref" href="tops_1.html#T30">TOPS_1:30</a></i>;<br/>
<b>hence </b><a NAME="E6:9"/>
<font color="Maroon">x</font> <a href="subset_1.html#K3">`</a>  is    <a href="subset_1.html#M2">Element</a> of  <a href="lopclset.html#K1" target="_self">OpenClosedSet</a> <font color="Maroon">T</font>
 <b>by </b><i>, </i>;<br/>


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