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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L1</font></span>)</span></span>)</span></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">S</font> being   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c1">L1</font>;<br/>
<a NAME="E2:43"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
 <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">S</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">S</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> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#D4" title="YELLOW_9:def.4">YELLOW_9:def 4</a></span>;<br/>
<a NAME="E3:43"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
 <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#T51" title="YELLOW_9:th.51">YELLOW_9:51</a></span>;<br/>
<a NAME="E4:43"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
 <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel31.html#T29" target="_self" title="WAYBEL31:th.29">Th29</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:43_1_1"/>
(  not <font color="Maroon" title="c1">L1</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  or <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="43_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:43_1_1_1"/>
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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L1</font></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:43_1_1_1"/><span class="kw">then </span>
not <font color="Maroon" title="c2">S</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E26">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:43_1_1_1"/>
 <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L1</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="waybel31.html#T8" target="_self" title="WAYBEL31:th.8">Th8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:43_1_1_2"/><span class="lab"><font color="Green" title="E29">A4</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L1</font></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:43_1_1_2"/><span class="lab"><font color="Green" title="E30">A5</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</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> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L1</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="waybel31.html#T9" target="_self" title="WAYBEL31:th.9">Th9</a></span>;<br/><a NAME="E3:43_1_1_2"/><span class="lab"><font color="Green" title="E31">A6</font></span>: 
<font color="Maroon" title="c2">S</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="#E1:43_1_1_2"><span class="lab"><font color="Green" title="E29">A4</font></span></a></span>;<br/><a NAME="E4:43_1_1_2"/><span class="kw">then </span>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel31.html#T10" target="_self" title="WAYBEL31:th.10">Th10</a></span>;<br/><span class="kw">hence </span><a NAME="E5:43_1_1_2"/>
 <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L1</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="txt" href="#E3:43_1_1_2"><span class="lab"><font color="Green" title="E31">A6</font></span></a>, <a class="txt" href="#E2:43_1_1_2"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="ref" href="waybel31.html#T11" target="_self" title="WAYBEL31:th.11">Th11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:43"/>
 <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <font color="Maroon" title="c1">L1</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel31.html#K1" title="WAYBEL31:func.1">CLweight</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L1</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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