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<span class="kw">let </span><font color="Maroon" title="c1">N</font> be   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="waybel19.html#V2" title="WAYBEL19:attr.2">Lawson</a>  <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="waybel19.html#K2" title="WAYBEL19:func.2">lambda</a> <font color="Maroon" title="c1">N</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">Z</font> = <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">W</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span> where <font color="Olive" title="b1">W</font>, <font color="Olive" title="b2">F</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">N</font> : ( <font color="Olive" title="b1">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Olive" title="b2">F</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) </span> } </span> ;<br/>
<a NAME="E1:18"/>
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">W</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span> where <font color="Olive" title="b1">W</font>, <font color="Olive" title="b2">F</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">N</font> : ( <font color="Olive" title="b1">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Olive" title="b2">F</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) </span> } </span>  is   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <font color="Maroon" title="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel19.html#T32" onmouseover="rs('waybel19/T32')" onmouseout="rh()">WAYBEL19:32</a></span>;<br/>
<a NAME="E2:18"/><span class="kw">then </span>
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">W</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span> where <font color="Olive" title="b1">W</font>, <font color="Olive" title="b2">F</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">N</font> : ( <font color="Olive" title="b1">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Olive" title="b2">F</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#T64" onmouseover="rs('tops_2/T64')" onmouseout="rh()">TOPS_2:64</a></span>;<br/>
<a NAME="E3:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">W</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span> where <font color="Olive" title="b1">W</font>, <font color="Olive" title="b2">F</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">N</font> : ( <font color="Olive" title="b1">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Olive" title="b2">F</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="waybel19.html#K2" title="WAYBEL19:func.2">lambda</a> <font color="Maroon" title="c1">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel30.html#T9" target="_self" onmouseover="rs('waybel30/T9')" onmouseout="rh()">Th9</a></span>;<br/>
<a NAME="E4:18"/>
 <a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">W</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Olive" title="b2">F</font></span>)</span></span>)</span> where <font color="Olive" title="b1">W</font>, <font color="Olive" title="b2">F</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">N</font> : ( <font color="Olive" title="b1">W</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Olive" title="b2">F</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel30.html#T8" target="_self" onmouseover="rs('waybel30/T8')" onmouseout="rh()">Th8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:18"/>
 <a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="waybel19.html#K2" title="WAYBEL19:func.2">lambda</a> <font color="Maroon" title="c1">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E10">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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