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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="waybel19.html#V2">Lawson</a> <a href="waybel_9.html#NM1">TopLattice</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a> ) </span>}</span> ;<br/>
<a NAME="E1:18"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a> ) </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="waybel19.html#T32">WAYBEL19:32</a></i>;<br/>
<a NAME="E2:18"/><b>then </b>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a> ) </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="cantor_1.html#D2">CANTOR_1:def 2</a></i>;<br/>
<a NAME="E3:18"/><b>then </b><i><font color="Green">E10</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a> ) </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="waybel19.html#K2">lambda</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="waybel30.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E4:18"/>
 <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel30.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E5:18"/>
 <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel19.html#K2">lambda</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="waybel30.html#E3:18"><i><font color="Green">E10</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


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