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<b>let </b><font color="Maroon">R</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">T</font> be  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V1" target="_self">lower</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">S</font> be  <a href="pre_topc.html#V2">correct</a> <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">M</font> be    <a href="yellow_9.html#M3">Refinement</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/>







<a NAME="E1:49"/><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">R</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R</font> #) &amp;  <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">R</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R</font> #) )
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<a NAME="E2:49"/>
(  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S</font> &amp;  <a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> )
 
<b>by </b><i>, <a class="ref" href="yellow_9.html#T51">YELLOW_9:51</a></i>;<br/>
<a NAME="E3:49"/><b>then </b><i><font color="Green">E34</font></i>: 
( <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">R</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">R</font></span>)</span> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">M</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> )
 
<b>by </b><i>, <a class="ref" href="yellow_9.html#D6">YELLOW_9:def 6</a></i>;<br/>
<a NAME="E4:49"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="cantor_1.html#K2">FinMeetCl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">R</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">R</font></span>)</span></span>)</span> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T23">YELLOW_9:23</a></i>;<br/>
<b>thus </b> <a href="waybel19.html#K2" target="_self">lambda</a> <font color="Maroon">R</font> = 
 <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">R</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">R</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">M</font>
<b>by </b><i>, <a class="txt" href="waybel19.html#E3:49"><i><font color="Green">E34</font></i></a>, <a class="ref" href="yellow_9.html#T22">YELLOW_9:22</a></i>
;<br/>


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