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<b>thus </b><a NAME="E1:22_1_1"/>
( <font color="Maroon">T</font> is <a href="waybel11.html#V4" target="_self">Scott</a> implies for <font color="Olive">S</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> holds <br/> ( <font color="Olive">S</font> is <a href="pre_topc.html#V3">open</a> iff <font color="Olive">S</font> is <a href="waybel_0.html#V13">upper</a> ) )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E2:22_1_1"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">S</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> holds <br/> ( <font color="Olive">S</font> is <a href="pre_topc.html#V3">open</a> iff <font color="Olive">S</font> is <a href="waybel_0.html#V13">upper</a> )
 ;<br/>

<b>let </b><font color="Maroon">S</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel11.html#D4" target="_self">WAYBEL11:def 4</a><br/>

<b>thus </b><a NAME="E3:22_1_1"/>
( <font color="Maroon">S</font> is <a href="pre_topc.html#V3">open</a> iff ( <font color="Maroon">S</font> is <a href="waybel11.html#V1" target="_self">inaccessible_by_directed_joins</a> &amp; <font color="Maroon">S</font> is <a href="waybel_0.html#V13">upper</a> ) )
 <b>by </b><i/>;<br/>


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