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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V3">complete</a> <a href="waybel11.html#V4">Scott</a>  <a href="waybel_9.html#L1">TopRelStr</a> , <font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V3">complete</a> <a href="waybel11.html#V4">Scott</a>  <a href="waybel_9.html#L1">TopRelStr</a> ;<br/>

<b>assume </b><a NAME="E1:77"/><i><font color="Green">E32</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S</font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">T</font> #)
 ;<br/>

<b>let </b><font color="Maroon">F</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">G</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E2:77"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> &amp; <font color="Maroon">F</font> is <a href="pre_topc.html#V3">open</a> )
 ;<br/>

<a NAME="E3:77"/><b>then </b>
( <font color="Maroon">F</font> is <a href="waybel_0.html#V13">upper</a> &amp; <font color="Maroon">F</font> is <a href="waybel11.html#V1">inaccessible_by_directed_joins</a> )
 
<b>by </b><i><a class="ref" href="waybel11.html#D4">WAYBEL11:def 4</a></i>;<br/>
<a NAME="E4:77"/><b>then </b>
( <font color="Maroon">G</font> is <a href="waybel_0.html#V13">upper</a> &amp; <font color="Maroon">G</font> is <a href="waybel11.html#V1">inaccessible_by_directed_joins</a> )
 
<b>by </b><i>, , <a class="txt" href="yellow_9.html#E1:77"><i><font color="Green">E32</font></i></a>, <a class="ref" href="waybel_0.html#T25">WAYBEL_0:25</a></i>;<br/>
<b>hence </b><a NAME="E5:77"/>
<font color="Maroon">G</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="waybel11.html#D4">WAYBEL11:def 4</a></i>;<br/>


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