<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">L1</font> be  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/><b>let </b><font color="Maroon" title="c2">B1</font> be  <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>;<br/>



<b>thus </b><a NAME="E1:20"/>
(  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">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> implies <font color="Maroon" title="c2">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">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>
 ;<br/>

<a NAME="E2:20_1"/><b>then </b><i><font color="Green" title="E15">A1</font></i>: 
 <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="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">L1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B1</font>
 
<b>by </b><i><a class="ref" href="waybel31.html#T5" target="_self" title="WAYBEL31:th.5">Th5</a></i>;<br/>
<a NAME="E3:20_1"/><i><font color="Green" title="E16">A2</font></i>: 
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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B1</font>
 
<b>by </b><i><a class="ref" href="waybel23.html#T72" title="WAYBEL23:th.72">WAYBEL23:72</a></i>;<br/>
<a NAME="E4:20_1"/><b>then </b>
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> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T13" title="FINSET_1:th.13">FINSET_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1"/>
<font color="Maroon" title="c2">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 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="waybel31.html#E2:20_1"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="waybel31.html#E3:20_1"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="triang_1.html#T3" title="TRIANG_1:th.3">TRIANG_1:3</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:20"/>
<font color="Maroon" title="c2">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 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>
 ;<br/>

<b>hence </b><a NAME="E3:20"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">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#T5" target="_self" title="WAYBEL31:th.5">Th5</a></i>;<br/>


</div>
