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<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:40"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">A</font> is <a href="waybel_0.html#V13">upper</a>
 ;<br/>

<b>assume </b><a NAME="E2:40"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="waybel28.html#K4" target="_self">xi</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E3:40"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">A</font> is <a href="waybel11.html#V3">property(S)</a>
 
<b>by </b><i><a class="txt" href="waybel28.html#E1:40"><i><font color="Green">E25</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">T</font> being  <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">L</font>;<br/>
<a NAME="E5:40"/><i><font color="Green">E29</font></i>: 
 <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> #) <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">L</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">A'</font> = <font color="Maroon">A</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> ;<br/>
<b>reconsider </b><font color="Maroon">A'</font> = <font color="Maroon">A'</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> ;<br/>
<a NAME="E8:40"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">A'</font> is <a href="waybel11.html#V3">property(S)</a>
 
<b>by </b><i><a class="txt" href="waybel28.html#E5:40"><i><font color="Green">E29</font></i></a>, <a class="txt" href="waybel28.html#E8:40"><i><font color="Green">E30</font></i></a>, <a class="ref" href="yellow12.html#T19">YELLOW12:19</a></i>;<br/>
<a NAME="E9:40"/>
<font color="Maroon">A'</font> is <a href="waybel_0.html#V13">upper</a>
 
<b>by </b><i><a class="txt" href="waybel28.html#E3:40"><i><font color="Green">E28</font></i></a>, <a class="txt" href="waybel28.html#E8:40"><i><font color="Green">E30</font></i></a>, <a class="ref" href="waybel_0.html#T25">WAYBEL_0:25</a></i>;<br/>
<a NAME="E10:40"/><b>then </b>
<font color="Maroon">A'</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i>, <a class="ref" href="waybel11.html#T15">WAYBEL11:15</a></i>;<br/>
<a NAME="E11:40"/><b>then </b>
<font color="Maroon">A'</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<b>hence </b><a NAME="E12:40"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="yellow_9.html#T51">YELLOW_9:51</a></i>;<br/>


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