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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>consider </b><font color="Maroon">T</font> being  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V2">Lawson</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">L</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">L</font>;<br/>
<b>consider </b><font color="Maroon">LL</font> being  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V1">lower</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">L</font>;<br/>
<b>consider </b><font color="Maroon">LI</font> being  <a href="waybel33.html#V1" target="_self">lim-inf</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">L</font>;<br/>
<a NAME="E5:38"/><i><font color="Green">E46</font></i>: 
 <a href="waybel19.html#K2">lambda</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="waybel19.html#D4">WAYBEL19:def 4</a></i>;<br/>
<a NAME="E6:38"/><i><font color="Green">E47</font></i>: 
 <a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T51">YELLOW_9:51</a></i>;<br/>
<a NAME="E7:38"/><i><font color="Green">E52</font></i>: 
 <a href="waybel19.html#K1">omega</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">LL</font>
 
<b>by </b><i><a class="ref" href="waybel19.html#D2">WAYBEL19:def 2</a></i>;<br/>
<a NAME="E8:38"/><i><font color="Green">E53</font></i>: 
 <a href="waybel28.html#K4">xi</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">LI</font>
 
<b>by </b><i/>;<br/>
<a NAME="E9:38"/><i><font color="Green">E54</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> #) &amp;  <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">L</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> #) &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">LL</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">LL</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> #) &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">LI</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">LI</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/>
<a NAME="E10:38"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">T</font> is    <a href="yellow_9.html#M3">Refinement</a> of <font color="Maroon">S</font>,<font color="Maroon">LL</font>
 
<b>by </b><i><a class="ref" href="waybel19.html#T29">WAYBEL19:29</a></i>;<br/>
<a NAME="E11:38"/>
( the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S</font> <a href="tarski.html#R1">c=</a>  <a href="waybel28.html#K4">xi</a> <font color="Maroon">L</font> &amp; the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">LL</font> <a href="tarski.html#R1">c=</a>  <a href="waybel28.html#K4">xi</a> <font color="Maroon">L</font> )
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E12:38"/><b>then </b>
( <font color="Maroon">LI</font> is    <a href="yellow_9.html#M2">TopExtension</a> of <font color="Maroon">S</font> &amp; <font color="Maroon">LI</font> is    <a href="yellow_9.html#M2">TopExtension</a> of <font color="Maroon">LL</font> )
 
<b>by </b><i>, , <a class="ref" href="yellow_9.html#D5">YELLOW_9:def 5</a></i>;<br/>
<a NAME="E13:38"/><b>then </b>
<font color="Maroon">LI</font> is    <a href="yellow_9.html#M2">TopExtension</a> of <font color="Maroon">T</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E14:38"/>
 <a href="waybel19.html#K2">lambda</a> <font color="Maroon">L</font> <a href="tarski.html#R1">c=</a>  <a href="waybel28.html#K4">xi</a> <font color="Maroon">L</font>
 <b>by </b><i>, , <a class="ref" href="yellow_9.html#D5">YELLOW_9:def 5</a></i>;<br/>


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