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<b>let </b><font color="Maroon">T</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E1:29"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> is <a href="tops_2.html#V2" target="_self">closed</a>
 ;<br/>

<b>let </b><font color="Maroon">G</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">A</font>;<br/>

<b>assume </b><a NAME="E2:29"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font>
 ;<br/>

<b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">A</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D2" target="_self">TOPS_2:def 2</a><br/>

<b>assume </b><a NAME="E3:29"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">PP</font> = <font color="Maroon">P</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> <b>by </b><i><a class="ref" href="pre_topc.html#T39">PRE_TOPC:39</a></i>;<br/>
<a NAME="E5:29"/>
<font color="Maroon">PP</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E6:29"/>
<font color="Maroon">P</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i/>;<br/>


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