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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">G</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:93"/><i><font color="Green" title="E49">A1</font></i>: 
<font color="Maroon" title="c2">F</font> is <a href="topgen_4.html#V1" title="TOPGEN_4:attr.1">all-open-containing</a>
 <b>and </b><br/><a NAME="E2:93"/><i><font color="Green" title="E50">A2</font></i>: 
<font color="Maroon" title="c2">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">G</font>
 ;<br/>

<a NAME="E3:93"/>
for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> holds <br/><font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">G</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="93_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>;<br/>

<b>assume </b><a NAME="E1:93_1"/>
<font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 ;<br/>

<a NAME="E2:93_1"/><b>then </b>
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E1:93"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="topgen_4.html#D2" target="_self" title="TOPGEN_4:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E3:93_1"/>
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">G</font>
 <b>by </b><i><a class="txt" href="topgen_4.html#E2:93"><i><font color="Green" title="E50">A2</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:93"/>
<font color="Maroon" title="c3">G</font> is <a href="topgen_4.html#V1" title="TOPGEN_4:attr.1">all-open-containing</a>
 <b>by </b><i><a class="ref" href="topgen_4.html#D2" target="_self" title="TOPGEN_4:def.2">Def2</a></i>;<br/>


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