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<b>let </b><font color="Maroon" title="c1">T</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a>;<br/>

<b>assume </b><a NAME="E1:22_1_1"/>
<font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c2">W</font> = <font color="Maroon" title="c1">T</font> as  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a> ;<br/>
<a NAME="E3:22_1_1"/><i><font color="Green" title="E11">A1</font></i>: 
the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="tdlat_3.html#D2" title="TDLAT_3:def.2">TDLAT_3:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">N</font> being  <a href="yellow_9.html#NV1" title="YELLOW_9:NV.1">correct</a> <a href="waybel19.html#V2" title="WAYBEL19:attr.2">Lawson</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c2">W</font>;<br/>
<a NAME="E5:22_1_1"/>
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">T</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">N</font> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4" title="YELLOW_9:def.4">YELLOW_9:def 4</a></i>;<br/>
<b>then </b>the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">T</font> = 
the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c3">N</font>
<b>by </b><i><a class="txt" href="waybel30.html#E3:22_1_1"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="tdlat_3.html#D2" title="TDLAT_3:def.2">TDLAT_3:def 2</a></i>
<br/>.= 
 <a href="waybel19.html#K2" title="WAYBEL19:func.2">lambda</a> <font color="Maroon" title="c1">T</font>
<b>by </b><i><a class="ref" href="waybel19.html#D4" title="WAYBEL19:def.4">WAYBEL19:def 4</a></i>
<br/>.= 
 <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="waybel19.html#K1" title="WAYBEL19:func.1">omega</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="waybel19.html#T33" title="WAYBEL19:th.33">WAYBEL19:33</a></i>
;<br/>
<a NAME="E7:22_1_1"/><b>then </b>
 <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel19.html#K1" title="WAYBEL19:func.1">omega</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">T</font></span>)</span></span>)</span> is    <a href="cantor_1.html#M1" title="CANTOR_1:mode.1">Basis</a> of <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T22" title="YELLOW_9:th.22">YELLOW_9:22</a></i>;<br/>
<b>hence </b><a NAME="E8:22_1_1"/>
<span class="p1">(<span class="default"><a href="waybel19.html#K1" title="WAYBEL19:func.1">omega</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">T</font></span>)</span> is    <a href="cantor_1.html#M2" title="CANTOR_1:mode.2">prebasis</a> of <font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="ref" href="yellow_9.html#T23" title="YELLOW_9:th.23">YELLOW_9:23</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel19.html#D3" title="WAYBEL19:def.3">WAYBEL19:def 3</a><br/>


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