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<b>let </b><font color="Maroon">T</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_3.html#V3">continuous</a> <a href="waybel19.html#V2" target="_self">Lawson</a> <a href="waybel_9.html#NM1">TopLattice</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>;<br/>



<b>consider </b><font color="Maroon">S</font> being  <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">T</font>;<br/>
<a NAME="E2:58"/><i><font color="Green">E30</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> #)
 
<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">v</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> ;<br/>
<a NAME="E4:58"/>
(  <a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">v</font> is <a href="pre_topc.html#V3">open</a> &amp;  <a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">x</font> &amp; <font color="Maroon">T</font> is    <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="waybel19.html#T1" target="_self">Th1</a>, <a class="ref" href="waybel11.html#T36">WAYBEL11:36</a>, <a class="ref" href="yellow12.html#T13">YELLOW12:13</a>, <a class="ref" href="yellow_9.html#T45">YELLOW_9:45</a></i>;<br/>
<b>hence </b><a NAME="E5:58"/>
 <a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">x</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i/>;<br/>

<b>hence </b><a NAME="E6:58"/>
<span class="p1">(<span class="default"><a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">x</font></span>)</span> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="ref" href="tops_1.html#T30">TOPS_1:30</a></i>;<br/>


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