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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">M</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<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>assume </b><a NAME="E1:39"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> is <a href="tops_2.html#V1" target="_self">open</a>
 ;<br/>

<b>let </b><font color="Maroon">Q</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">M</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D1" target="_self">TOPS_2:def 1</a><br/>

<b>assume </b><a NAME="E2:39"/>
<font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> <a href="tops_2.html#K1" target="_self">|</a> <font color="Maroon">M</font>
 ;<br/>

<b>then consider </b><font color="Maroon">R</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E4:39"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">R</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 <b>and </b><br/><a NAME="E5:39"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">R</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Q</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">R</font> = <font color="Maroon">R</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> ;<br/>
<a NAME="E7:39"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">R</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E8:39"/>
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>;<br/>
<b>hence </b><a NAME="E9:39"/>
<font color="Maroon">Q</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i>, </i>;<br/>


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