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

<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel11.html#V4">Scott</a> <a href="waybel_9.html#NM1">TopLattice</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:50"/><i><font color="Green">E36</font></i>: 
 <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span> is <a href="waybel_8.html#V2">algebraic</a>
 <b>and </b><br/><a NAME="E2:50"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">V</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span>  ex <font color="Olive">X</font> being  <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span> st <br/>( <font color="Olive">V</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">X</font> &amp; ( for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">X</font> holds <br/><font color="Olive">x</font> is <a href="waybel_6.html#V6">co-prime</a> ) )
 ;<br/>

<b>set </b><font color="Maroon">IPt</font> =  <a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>;<br/>
<b>set </b><font color="Maroon">IPs</font> =  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span>;<br/>
<a NAME="E3:50"/><i><font color="Green">E38</font></i>: 
 <a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:50"/><i><font color="Green">E40</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/>
<a NAME="E5:50"/><i><font color="Green">E41</font></i>: 
 <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:50"/><i><font color="Green">E42</font></i>: 
 <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span> is <a href="waybel_8.html#V1">satisfying_axiom_K</a>
 
<b>by </b><i>, <a class="ref" href="waybel_8.html#D4">WAYBEL_8:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">ips</font> =  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span> as  <a href="waybel_8.html#V2">algebraic</a> <a href="waybel_0.html#NM8">LATTICE</a> <b>by </b><i>, </i>;<br/>
<a NAME="E8:50"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">ips</font> is <a href="waybel_3.html#V3">continuous</a>
 
;<br/>
<a NAME="E9:50"/>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  ex <font color="Olive">X</font> being   <a href="yellow_8.html#M1">Basis</a> of <font color="Olive">x</font> st <br/>for <font color="Olive">Y</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>  st <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Olive">X</font> holds <br/>( <font color="Olive">Y</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">Y</font> is <a href="waybel_0.html#V2">filtered</a> )
 
<b>by </b><i>, <a class="ref" href="waybel14.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E10:50"/><b>then </b>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Olive">V</font></span>)</span> where <font color="Olive">V</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> : ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">V</font> &amp; <font color="Olive">V</font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font> ) </span>}</span> ,<font color="Maroon">L</font>
 
<b>by </b><i><a class="txt" href="waybel14.html#E2:50"><i><font color="Green">E37</font></i></a>, </i>;<br/>
<a NAME="E11:50"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">L</font> is <a href="waybel_3.html#V3">continuous</a>
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">B</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">k</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">L</font></span>)</span> </span>}</span> ;<br/>
<a NAME="E12:50"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">k</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">L</font></span>)</span> </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:50_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">k</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">L</font></span>)</span> </span>}</span> 
 ;<br/>

<a NAME="E2:50_1"/><b>then </b>
 ex <font color="Olive">k</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">L</font></span>)</span> )
 
;<br/>
<b>hence </b><a NAME="E3:50_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">B</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">k</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">L</font></span>)</span> </span>}</span>  as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">L</font> ;<br/>
<b>reconsider </b><font color="Maroon">B</font> = <font color="Maroon">B</font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E15:50"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:50_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/>

<b>then consider </b><font color="Maroon">k</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:50_2"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">L</font></span>)</span> )
 ;<br/>
<a NAME="E4:50_2"/>
<font color="Maroon">k</font> is <a href="waybel_3.html#V1">compact</a>
 
<b>by </b><i><a class="txt" href="waybel14.html#E4:50"><i><font color="Green">E40</font></i></a>, <a class="ref" href="waybel_8.html#D1">WAYBEL_8:def 1</a></i>;<br/>
<a NAME="E5:50_2"/><b>then </b>
 <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">k</font> is <a href="waybel_6.html#V1">Open</a>
 
<b>by </b><i><a class="ref" href="waybel_8.html#T2">WAYBEL_8:2</a></i>;<br/>
<a NAME="E6:50_2"/><b>then </b>
 <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">k</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="waybel11.html#T41">WAYBEL11:41</a></i>;<br/>
<b>hence </b><a NAME="E7:50_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
 <b>by </b><i><a class="txt" href="waybel14.html#E4:50"><i><font color="Green">E40</font></i></a>, <a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">L</font>;<br/><b>set </b><font color="Maroon">Bx</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : (  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> ) </span>}</span> ;<br/><a NAME="E1:50_3"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : (  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> ) </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:50_3_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : (  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> ) </span>}</span> 
 ;<br/>

<a NAME="E2:50_3_1"/><b>then </b>
 ex <font color="Olive">k</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> &amp;  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> )
 
;<br/>
<b>hence </b><a NAME="E3:50_3_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 ;<br/>


</div><b>end;</b></div><b>then reconsider </b><font color="Maroon">Bx</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : (  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> ) </span>}</span>  as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">L</font> ;<br/><b>reconsider </b><font color="Maroon">Bx</font> = <font color="Maroon">Bx</font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">L</font> ;<br/><a NAME="E4:50_3"/>
<font color="Maroon">Bx</font> is    <a href="yellow_8.html#M1">Basis</a> of <font color="Maroon">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:50_3_2"/>
<font color="Maroon">Bx</font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_8.html#D2">YELLOW_8:def 2</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:50_3_2_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Bx</font>
 ;<br/>

<a NAME="E2:50_3_2_1"/><b>then </b>
 ex <font color="Olive">k</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> &amp;  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> )
 
;<br/>
<b>hence </b><a NAME="E3:50_3_2_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
 <b>by </b><i/>;<br/>


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

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_3_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:50_3_2_2_1"/>
( <font color="Maroon">Bx</font> is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">Bx</font> is <a href="xboole_0.html#V1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_3_2_2_1_1"><b>suppose </b></a><a NAME="E1:50_3_2_2_1_1"/>
<font color="Maroon">Bx</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><a NAME="E2:50_3_2_2_1_1"/><b>then </b>
 <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">Bx</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/><b>hence </b><a NAME="E3:50_3_2_2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">Bx</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_3_2_2_1_2"><b>suppose </b></a><a NAME="E1:50_3_2_2_1_2"/><i><font color="Green">E48</font></i>: 
not <font color="Maroon">Bx</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><a NAME="E2:50_3_2_2_1_2"/><b>then </b><i><font color="Green">E49</font></i>: 
 <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">Bx</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K6">meet</a> <font color="Maroon">Bx</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_2_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:50_3_2_2_1_2_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Bx</font>
 ;<br/><a NAME="E2:50_3_2_2_1_2_1"/><b>then </b>
 ex <font color="Olive">k</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> &amp;  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> )
 ;<br/><b>hence </b><a NAME="E3:50_3_2_2_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:50_3_2_2_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">Bx</font>
 <b>by </b><i><a class="txt" href="waybel14.html#E4:50"><i><font color="Green">E40</font></i></a>, <a class="txt" href="waybel14.html#E5:50"><i><font color="Green">E41</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:50_3_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">Bx</font>
 ;<br/>

<b>let </b><font color="Maroon">S</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E4:50_3_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">S</font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E5:50_3_2"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">S'</font> = <font color="Maroon">S</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font></span>)</span> <b>by </b><i>, , <a class="txt" href="waybel14.html#E4:50"><i><font color="Green">E40</font></i></a>, <a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<a NAME="E7:50_3_2"/>
<font color="Maroon">S'</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">S'</font></span>)</span>
 
<b>by </b><i>, <a class="txt" href="waybel14.html#E1:50"><i><font color="Green">E36</font></i></a>, <a class="ref" href="waybel_8.html#D3">WAYBEL_8:def 3</a></i>;<br/>
<a NAME="E8:50_3_2"/><b>then </b>
<font color="Maroon">S'</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">S'</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T22">YELLOW_1:22</a></i>;<br/>
<b>then consider </b><font color="Maroon">UA</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E10:50_3_2"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">UA</font> &amp; <font color="Maroon">UA</font> <a href="hidden.html#R2">in</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">S'</font> )
 <b>by </b><i><a class="txt" href="waybel14.html#E5:50"><i><font color="Green">E41</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">UA</font> = <font color="Maroon">UA</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font></span>)</span> <b>by </b><i><a class="txt" href="waybel14.html#E6:50"><i><font color="Green">E42</font></i></a></i>;<br/>
<a NAME="E12:50_3_2"/><i><font color="Green">E118</font></i>: 
( <font color="Maroon">UA</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">S'</font> &amp; <font color="Maroon">UA</font> is <a href="waybel_3.html#V1">compact</a> )
 
<b>by </b><i><a class="txt" href="waybel14.html#E6:50"><i><font color="Green">E42</font></i></a>, <a class="ref" href="waybel_8.html#T4">WAYBEL_8:4</a></i>;<br/>
<b>consider </b><font color="Maroon">F</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span><b> such that </b><br/><a NAME="E14:50_3_2"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">UA</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">F</font>
 <b>and </b><br/><a NAME="E15:50_3_2"/><i><font color="Green">E120</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> holds <br/><font color="Olive">x</font> is <a href="waybel_6.html#V6">co-prime</a>
 <b>by </b><i>, </i>;<br/>
<a NAME="E16:50_3_2"/><i><font color="Green">E121</font></i>: 
<font color="Maroon">UA</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">F</font>
 
<b>by </b><i>, <a class="txt" href="waybel14.html#E8:50"><i><font color="Green">E44</font></i></a>, <a class="ref" href="yellow_1.html#T22">YELLOW_1:22</a></i>;<br/>
<a NAME="E17:50_3_2"/>
<font color="Maroon">UA</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
 
<b>by </b><i>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">UA'</font> = <font color="Maroon">UA</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E19:50_3_2"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">UA</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">UA</font>
 
<b>by </b><i>, <a class="ref" href="waybel_3.html#D2">WAYBEL_3:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">F'</font> = <font color="Maroon">F</font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">L</font> <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E21:50_3_2"/>
<font color="Maroon">F'</font> is <a href="tops_2.html#V1">open</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D1">TOPS_2:def 1</a><br/>

<b>assume </b><a NAME="E1:50_3_2_3"/>
<font color="Maroon">P</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F'</font>
 ;<br/>

<b>hence </b><a NAME="E2:50_3_2_3"/>
<font color="Maroon">P</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i>, , <a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">G</font> being  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">F'</font><b> such that </b><br/><a NAME="E23:50_3_2"/><i><font color="Green">E123</font></i>: 
<font color="Maroon">UA</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="txt" href="waybel14.html#E15:50"><i><font color="Green">E46</font></i></a>, , <a class="ref" href="waybel_3.html#T34">WAYBEL_3:34</a></i>;<br/>
<a NAME="E24:50_3_2"/>
 <a href="tarski.html#K3">union</a> <font color="Maroon">G</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T95">ZFMISC_1:95</a></i>;<br/>
<a NAME="E25:50_3_2"/><b>then </b><i><font color="Green">E124</font></i>: 
<font color="Maroon">UA</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">G</font>
 
<b>by </b><i><a class="txt" href="waybel14.html#E15:50"><i><font color="Green">E46</font></i></a>, , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<b>reconsider </b><font color="Maroon">G</font> = <font color="Maroon">G</font> as  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">L</font> <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>consider </b><font color="Maroon">Gg</font> being  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E28:50_3_2"/><i><font color="Green">E125</font></i>: 
<font color="Maroon">Gg</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font>
 <b>and </b><br/><a NAME="E29:50_3_2"/><i><font color="Green">E126</font></i>: 
 <a href="setfam_1.html#K5">union</a> <font color="Maroon">Gg</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K5">union</a> <font color="Maroon">G</font>
 <b>and </b><br/><a NAME="E30:50_3_2"/><i><font color="Green">E127</font></i>: 
for <font color="Olive">g</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>  st <font color="Olive">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Gg</font> holds <br/> not <font color="Olive">g</font> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><font color="Maroon">Gg</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">g</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">U1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E32:50_3_2"/><i><font color="Green">E144</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1</font> &amp; <font color="Maroon">U1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Gg</font> )
 <b>by </b><i><a class="txt" href="waybel14.html#E6:50"><i><font color="Green">E42</font></i></a>, , <a class="txt" href="waybel14.html#E4:50_3_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E33:50_3_2"/><i><font color="Green">E145</font></i>: 
<font color="Maroon">Gg</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E34:50_3_2"/><b>then </b>
<font color="Maroon">U1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="txt" href="waybel14.html#E10:50_3_2"><i><font color="Green">E53</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">U1</font> = <font color="Maroon">U1</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span> ;<br/>
<a NAME="E36:50_3_2"/>
<font color="Maroon">U1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
 
<b>by </b><i>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">U1'</font> = <font color="Maroon">U1</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E38:50_3_2"/>
<font color="Maroon">U1</font> is <a href="waybel_6.html#V6">co-prime</a>
 
<b>by </b><i><a class="txt" href="waybel14.html#E11:50"><i><font color="Green">E45</font></i></a>, <a class="txt" href="waybel14.html#E10:50_3_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="waybel14.html#E2"><i><font color="Green">Lemma54</font></i></a></i>;<br/>
<a NAME="E39:50_3_2"/><b>then </b><i><font color="Green">E146</font></i>: 
( <font color="Maroon">U1'</font> is <a href="waybel_0.html#V2">filtered</a> &amp; <font color="Maroon">U1'</font> is <a href="waybel_0.html#V13">upper</a> )
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">k</font> =  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:50_3_2_4"/><i><font color="Green">E147</font></i>: 
not  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font>
 ;<br/><b>set </b><font color="Maroon">D</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Olive">u</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> where <font color="Olive">u</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font> </span>}</span> ;<br/><b>consider </b><font color="Maroon">u</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:50_3_2_4"/><i><font color="Green">E148</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font>
 <b>by </b><i><a class="txt" href="waybel14.html#E10:50_3_2"><i><font color="Green">E53</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">u</font> = <font color="Maroon">u</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i><a class="ref" href="waybel14.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E5:50_3_2_4"/><i><font color="Green">E149</font></i>: 
<span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">u</font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Olive">u</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> where <font color="Olive">u</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="waybel14.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E6:50_3_2_4"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Olive">u</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> where <font color="Olive">u</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font> </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">d</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:50_3_2_4_1"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Olive">u</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> where <font color="Olive">u</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">u</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:50_3_2_4_1"/><i><font color="Green">E150</font></i>: 
( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">u</font></span>)</span> <a href="subset_1.html#K3">`</a>  &amp; <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font> )
 ;<br/>
<a NAME="E4:50_3_2_4_1"/>
<span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">u</font></span>)</span> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="waybel11.html#T12">WAYBEL11:12</a></i>;<br/>
<b>hence </b><a NAME="E5:50_3_2_4_1"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
 <b>by </b><i>, <a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>


</div><b>end;</b></div><b>then reconsider </b><font color="Maroon">D</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Olive">u</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> where <font color="Olive">u</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font> </span>}</span>  as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font></span>)</span> <b>by </b><i><a class="ref" href="waybel14.html#T3" target="_self">Th3</a>, <a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><a NAME="E8:50_3_2_4"/><i><font color="Green">E151</font></i>: 
<font color="Maroon">D</font> is <a href="waybel_0.html#V1">directed</a>
 <b>by </b><i>, , </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:50_3_2_4_2"/>
not <font color="Maroon">UA</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">D</font>
 ;<br/><b>then consider </b><font color="Maroon">l</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:50_3_2_4_2"/><i><font color="Green">E152</font></i>: 
( <font color="Maroon">l</font> <a href="hidden.html#R2">in</a> <font color="Maroon">UA'</font> &amp; not <font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">D</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon">l</font> = <font color="Maroon">l</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">Uk</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:50_3_2_4_2"/><i><font color="Green">E153</font></i>: 
( <font color="Maroon">l</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Uk</font> &amp; <font color="Maroon">Uk</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Gg</font> )
 <b>by </b><i>, <a class="txt" href="waybel14.html#E4:50_3_2"><i><font color="Green">E51</font></i></a>, , <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/><a NAME="E7:50_3_2_4_2"/><i><font color="Green">E206</font></i>: 
<font color="Maroon">Gg</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E8:50_3_2_4_2"/><b>then </b>
<font color="Maroon">Uk</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 <b>by </b><i/>;<br/><b>then reconsider </b><font color="Maroon">Uk</font> = <font color="Maroon">Uk</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span> ;<br/><a NAME="E10:50_3_2_4_2"/>
<font color="Maroon">Uk</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font>
 <b>by </b><i>, </i>;<br/><b>then reconsider </b><font color="Maroon">Uk'</font> = <font color="Maroon">Uk</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> ;<br/><a NAME="E12:50_3_2_4_2"/>
<font color="Maroon">Uk</font> is <a href="waybel_6.html#V6">co-prime</a>
 <b>by </b><i><a class="txt" href="waybel14.html#E11:50"><i><font color="Green">E45</font></i></a>, , </i>;<br/><a NAME="E13:50_3_2_4_2"/><b>then </b><i><font color="Green">E208</font></i>: 
( <font color="Maroon">Uk'</font> is <a href="waybel_0.html#V2">filtered</a> &amp; <font color="Maroon">Uk'</font> is <a href="waybel_0.html#V13">upper</a> )
 <b>by </b><i/>;<br/><a NAME="E14:50_3_2_4_2"/><i><font color="Green">E209</font></i>: 
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">U1'</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T33">YELLOW_0:33</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_4_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:50_3_2_4_2_1"/>
not <font color="Maroon">l</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">U1'</font>
 ;<br/><b>then consider </b><font color="Maroon">m</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:50_3_2_4_2_1"/><i><font color="Green">E211</font></i>: 
( <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font> &amp; not <font color="Maroon">l</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">m</font> )
 <b>by </b><i><a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/><a NAME="E4:50_3_2_4_2_1"/>
<span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">m</font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="waybel14.html#T7" target="_self">Th7</a></i>;<br/><a NAME="E5:50_3_2_4_2_1"/><b>then </b>
not <font color="Maroon">l</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">m</font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/><a NAME="E6:50_3_2_4_2_1"/><b>then </b>
<font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="yellow_6.html#T10">YELLOW_6:10</a></i>;<br/><b>hence </b><a NAME="E7:50_3_2_4_2_1"/>
contradiction
 <b>by </b><i><a class="ref" href="waybel14.html#T7" target="_self">Th7</a>, <a class="ref" href="waybel_0.html#T17">WAYBEL_0:17</a></i>;<br/></div><b>end;</b></div><a NAME="E16:50_3_2_4_2"/><b>then </b>
<font color="Maroon">l</font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T33">YELLOW_0:33</a></i>;<br/><a NAME="E17:50_3_2_4_2"/><b>then </b><i><font color="Green">E212</font></i>: 
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Uk'</font>
 <b>by </b><i>, <a class="ref" href="waybel14.html#T5" target="_self">Th5</a>, <a class="ref" href="waybel_0.html#D20">WAYBEL_0:def 20</a></i>;<br/><a NAME="E18:50_3_2_4_2"/><i><font color="Green">E213</font></i>: 
<font color="Maroon">U1'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Uk</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_4_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:50_3_2_4_2_2"/><i><font color="Green">E214</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">u</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E3:50_3_2_4_2_2"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="waybel14.html#T10" target="_self">Th10</a>, <a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/>
<b>hence </b><a NAME="E4:50_3_2_4_2_2"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Uk</font>
 <b>by </b><i><a class="ref" href="waybel14.html#T5" target="_self">Th5</a>, <a class="ref" href="waybel14.html#T7" target="_self">Th7</a>, <a class="ref" href="waybel_0.html#D20">WAYBEL_0:def 20</a></i>;<br/>


</div><b>end;</b></div><a NAME="E19:50_3_2_4_2"/>
<font color="Maroon">U1'</font> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><font color="Maroon">Gg</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">U1'</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_4_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:50_3_2_4_2_3"/><i><font color="Green">E215</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font>
 ;<br/>

<a NAME="E2:50_3_2_4_2_3"/>
<font color="Maroon">Uk</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Gg</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">U1'</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, , <a class="ref" href="waybel14.html#T7" target="_self">Th7</a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>
<b>hence </b><a NAME="E3:50_3_2_4_2_3"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><font color="Maroon">Gg</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">U1'</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="waybel14.html#T9" target="_self">Th9</a>, <a class="ref" href="waybel14.html#T10" target="_self">Th10</a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E20:50_3_2_4_2"/>
contradiction
 <b>by </b><i><a class="txt" href="waybel14.html#E5:50_3_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="waybel14.html#E10:50_3_2"><i><font color="Green">E53</font></i></a></i>;<br/></div><b>end;</b></div><a NAME="E10:50_3_2_4"/><b>then </b>
<font color="Maroon">UA</font> <a href="tarski.html#R1">c=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T22">YELLOW_1:22</a></i>;<br/><a NAME="E11:50_3_2_4"/><b>then </b>
<font color="Maroon">UA</font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>then consider </b><font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font></span>)</span><b> such that </b><br/><a NAME="E13:50_3_2_4"/><i><font color="Green">E216</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 <b>and </b><br/><a NAME="E14:50_3_2_4"/><i><font color="Green">E217</font></i>: 
<font color="Maroon">UA</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">d</font>
 <b>by </b><i>, , <a class="ref" href="waybel_3.html#D1">WAYBEL_3:def 1</a></i>;<br/><b>consider </b><font color="Maroon">u</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E16:50_3_2_4"/><i><font color="Green">E218</font></i>: 
( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">u</font></span>)</span> <a href="subset_1.html#K3">`</a>  &amp; <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font> )
 <b>by </b><i/>;<br/><a NAME="E17:50_3_2_4"/>
<font color="Maroon">U1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">UA</font>
 <b>by </b><i><a class="txt" href="waybel14.html#E15:50"><i><font color="Green">E46</font></i></a>, <a class="txt" href="waybel14.html#E10:50_3_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="waybel14.html#E2"><i><font color="Green">Lemma54</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/><a NAME="E18:50_3_2_4"/><b>then </b><i><font color="Green">E219</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">UA</font>
 <b>by </b><i/>;<br/><a NAME="E19:50_3_2_4"/>
<font color="Maroon">UA</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E20:50_3_2_4"/><b>then </b><i><font color="Green">E220</font></i>: 
not <font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">u</font>
 <b>by </b><i>, <a class="ref" href="waybel14.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_6.html#T10">YELLOW_6:10</a></i>;<br/><a NAME="E21:50_3_2_4"/>
<font color="Maroon">u</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">u</font>
 ;<br/><b>hence </b><a NAME="E22:50_3_2_4"/>
contradiction
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T17">WAYBEL_0:17</a></i>;<br/></div><b>end;</b></div>
<a NAME="E41:50_3_2"/><b>then </b><i><font color="Green">E221</font></i>: 
 <a href="waybel_0.html#K6">uparrow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">U1'</font>
 
<b>by </b><i>, <a class="ref" href="waybel11.html#T42">WAYBEL11:42</a></i>;<br/>
<a NAME="E42:50_3_2"/><i><font color="Green">E222</font></i>: 
<font color="Maroon">U1'</font> <a href="tarski.html#R1">c=</a>  <a href="waybel_0.html#K6">uparrow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_2_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:50_3_2_5"/><i><font color="Green">E223</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1'</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E3:50_3_2_5"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">U1'</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T33">YELLOW_0:33</a></i>;<br/>
<a NAME="E4:50_3_2_5"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x'</font>
 
<b>by </b><i><a class="ref" href="waybel14.html#T3" target="_self">Th3</a>, <a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/>
<b>hence </b><a NAME="E5:50_3_2_5"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_0.html#T18">WAYBEL_0:18</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E43:50_3_2"/><b>then </b><i><font color="Green">E224</font></i>: 
<font color="Maroon">U1'</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K6">uparrow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E44:50_3_2"/>
<font color="Maroon">U1'</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i>, , <a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<a NAME="E45:50_3_2"/><b>then </b>
<font color="Maroon">U1'</font> is <a href="waybel_6.html#V1">Open</a>
 
<b>by </b><i><a class="txt" href="waybel14.html#E3:50"><i><font color="Green">E38</font></i></a>, , <a class="ref" href="waybel11.html#T46">WAYBEL11:46</a></i>;<br/>
<a NAME="E46:50_3_2"/><b>then </b><i><font color="Green">E225</font></i>: 
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font> is <a href="waybel_3.html#V1">compact</a>
 
<b>by </b><i><a class="ref" href="waybel14.html#T3" target="_self">Th3</a>, <a class="ref" href="waybel_8.html#T2">WAYBEL_8:2</a></i>;<br/>
<b>take </b><font color="Maroon">V</font> =  <a href="waybel_0.html#K6">uparrow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font></span>)</span>;<br/>

<a NAME="E47:50_3_2"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">L</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="waybel_8.html#D1">WAYBEL_8:def 1</a></i>;<br/>
<a NAME="E48:50_3_2"/><b>then </b>
 <a href="waybel_0.html#K6">uparrow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">U1'</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 
;<br/>
<b>hence </b><a NAME="E49:50_3_2"/>
<font color="Maroon">V</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Bx</font>
 <b>by </b><i><a class="txt" href="waybel14.html#E10:50_3_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="waybel14.html#T2" target="_self">Th2</a></i>;<br/>

<a NAME="E50:50_3_2"/><i><font color="Green">E226</font></i>: 
<font color="Maroon">UA</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font>
 
<b>by </b><i>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E51:50_3_2"/>
<font color="Maroon">U1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">UA</font>
 
<b>by </b><i>, <a class="txt" href="waybel14.html#E4:50_3_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="waybel14.html#E10:50_3_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<b>hence </b><a NAME="E52:50_3_2"/>
<font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="waybel14.html#T3" target="_self">Th3</a>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


</div><b>end;</b></div><b>then reconsider </b><font color="Maroon">Bx</font> = <font color="Maroon">Bx</font> as    <a href="yellow_8.html#M1">Basis</a> of <font color="Maroon">x</font> ;<br/><b>take </b><font color="Maroon">Bx</font> = <font color="Maroon">Bx</font>;<br/><b>thus </b><a NAME="E6:50_3"/>
<font color="Maroon">Bx</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:50_3_3"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Bx</font>
 ;<br/>

<a NAME="E2:50_3_3"/><b>then </b>
 ex <font color="Olive">k</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> &amp;  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Olive">k</font> )
 
;<br/>
<b>hence </b><a NAME="E3:50_3_3"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">B</font> = <font color="Maroon">B</font> as    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">L</font> <b>by </b><i>, <a class="ref" href="yellow_8.html#T23">YELLOW_8:23</a></i>;<br/>
<b>take </b>
<font color="Maroon">B</font>
;<br/>

<b>thus </b><a NAME="E18:50"/>
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">x</font></span>)</span> where <font color="Olive">x</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">L</font></span>)</span> </span>}</span> 
 ;<br/>


</div>
