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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_9.html#NM1">TopLattice</a>;<br/>

<b>assume </b><a NAME="E1:22_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="realset2.html#V3">trivial</a> <a href="lattice3.html#V3">complete</a> <a href="waybel_9.html#NM1">TopLattice</a> ;<br/>
<a NAME="E3:22_1_1"/><i><font color="Green">E11</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="tdlat_3.html#D2">TDLAT_3:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font>;<br/>
<a NAME="E5:22_1_1"/>
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>3</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>3</sub></font> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>then </b>the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> = 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="waybel30.html#E3:22_1_1"><i><font color="Green">E11</font></i></a>, <a class="ref" href="tdlat_3.html#D2">TDLAT_3:def 2</a></i>
<br/>.= 
 <a href="waybel19.html#K2">lambda</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="waybel19.html#D4">WAYBEL19:def 4</a></i>
<br/>.= 
 <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">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="waybel19.html#K1">omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="waybel19.html#T33">WAYBEL19:33</a></i>
;<br/>
<a NAME="E7:22_1_1"/><b>then </b>
 <a href="cantor_1.html#K2">FinMeetCl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel19.html#K1">omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T22">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">omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="yellow_9.html#T23">YELLOW_9:23</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel19.html#D3">WAYBEL19:def 3</a><br/>


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