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<b>let </b><font color="Maroon" title="c1">L1</font> be  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="waybel_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">T</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="c1">L1</font> holds   <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Olive" title="b1">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font></span><br/><b>let </b><font color="Maroon" title="c2">T</font> be  <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="c1">L1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font></span><br/>



<a NAME="E1:29"/><i><font color="Green" title="E21">A1</font></i>: 
 <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="c2">T</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">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="c1">L1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L1</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>consider </b><font color="Maroon" title="c3">B1</font> being  <a href="waybel23.html#V6" title="WAYBEL23:attr.6">with_bottom</a>  <a href="waybel23.html#M1" title="WAYBEL23:mode.1">CLbasis</a> of <font color="Maroon" title="c1">L1</font><b> such that </b><br/><a NAME="E3:29"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font>
 <b>by </b><i><a class="ref" href="waybel31.html#T4" target="_self" title="WAYBEL31:th.4">Th4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1_1"/>
( <font color="Maroon" title="c1">L1</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> or  not <font color="Maroon" title="c1">L1</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1"><b>suppose </b></a><a NAME="E1:29_1_1_1"/><i><font color="Green" title="E23">A3</font></i>: 
<font color="Maroon" title="c1">L1</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font></span><br/><div class="add"><a NAME="E2:29_1_1_1"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ;<br/><a NAME="E3:29_1_1_1"/><b>then </b><i><font color="Green" title="E24">A4</font></i>: 
<font color="Maroon" title="c2">T</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E21">A1</font></i></a></i>;<br/><font color="Maroon" title="c3">B1</font> = 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">L1</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:29"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="#E1:29_1_1_1"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="waybel31.html#T16" target="_self" title="WAYBEL31:th.16">Th16</a></i>
<br/>.= 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>
<b>by </b><i><a class="txt" href="#E1:29_1_1_1"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="yellow15.html#T27" title="YELLOW15:th.27">YELLOW15:27</a></i>
;<br/><b>hence </b><a NAME="E5:29_1_1_1"/>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font>
 <b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="#E3:29"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="#E3:29_1_1_1"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="waybel31.html#T10" target="_self" title="WAYBEL31:th.10">Th10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_2"><b>suppose </b></a><a NAME="E1:29_1_1_2"/><i><font color="Green" title="E23">A5</font></i>: 
not <font color="Maroon" title="c1">L1</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c4">WU</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel31.html#K2" title="WAYBEL31:func.2">Way_Up</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">A</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font>, <font color="Olive" title="b2">A</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L1</font> : ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B1</font> &amp; <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B1</font> ) </span>}</span> ;<br/><a NAME="E2:29_1_1_2"/><i><font color="Green" title="E24">A6</font></i>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel31.html#K2" title="WAYBEL31:func.2">Way_Up</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">A</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font>, <font color="Olive" title="b2">A</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L1</font> : ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B1</font> &amp; <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B1</font> ) </span>}</span>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font>
 <b>by </b><i><a class="txt" href="#E3:29"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="#E1:29_1_1_2"><i><font color="Green" title="E23">A5</font></i></a>, <a class="ref" href="waybel31.html#T24" target="_self" title="WAYBEL31:th.24">Th24</a></i>;<br/><a NAME="E3:29_1_1_2"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel31.html#K2" title="WAYBEL31:func.2">Way_Up</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">A</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font>, <font color="Olive" title="b2">A</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L1</font> : ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B1</font> &amp; <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B1</font> ) </span>}</span>  is    <a href="cantor_1.html#M1" title="CANTOR_1:mode.1">Basis</a> of <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="waybel31.html#T26" target="_self" title="WAYBEL31:th.26">Th26</a></i>;<br/><a NAME="E4:29_1_1_2"/><b>then </b>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel31.html#K2" title="WAYBEL31:func.2">Way_Up</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">A</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font>, <font color="Olive" title="b2">A</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L1</font> : ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B1</font> &amp; <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B1</font> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="waybel23.html#T74" title="WAYBEL23:th.74">WAYBEL23:74</a></i>;<br/><b>hence </b><a NAME="E5:29_1_1_2"/>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font>
 <b>by </b><i><a class="txt" href="#E2:29_1_1_2"><i><font color="Green" title="E24">A6</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:29"/>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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