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





<b>assume </b><a NAME="E1:33"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">V</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:33"/><i><font color="Green">E37</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 <span class="p1">(<span class="default"><a href="yellow_6.html#K14">ConvergenceSpace</a> <span class="p2">(<span class="default"><a href="waybel11.html#K2">Scott-Convergence</a> <font color="Maroon">L</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel11.html#D12">WAYBEL11:def 12</a></i>;<br/>
<a NAME="E3:33"/><i><font color="Green">E38</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="E4:33"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">X</font> is <a href="waybel_0.html#V13">upper</a>
 
<b>by </b><i>, , <a class="ref" href="waybel11.html#T31">WAYBEL11:31</a></i>;<br/>
<a NAME="E5:33"/><i><font color="Green">E41</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font> #) <a href="hidden.html#R1">=</a>  <a href="yellow_6.html#K14">ConvergenceSpace</a> <span class="p1">(<span class="default"><a href="waybel11.html#K2">Scott-Convergence</a> <font color="Maroon">L</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel11.html#T32">WAYBEL11:32</a></i>;<br/>
<a NAME="E6:33"/><i><font color="Green">E42</font></i>: 
(  <a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font> is <a href="lattice3.html#V1">with_suprema</a> &amp;  <a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font> is <a href="lattice3.html#V2">with_infima</a> &amp;  <a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">L</font> is <a href="orders_2.html#V4">antisymmetric</a> )
 
;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:33_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">V</font> is <a href="waybel_6.html#V6">co-prime</a>
 ;<br/><b>thus </b><a NAME="E2:33_1"/>
<font color="Maroon">X</font> is <a href="waybel_0.html#V2">filtered</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">w</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D2">WAYBEL_0:def 2</a><br/>

<b>assume </b><a NAME="E1:33_1_1"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 ;<br/>

<a NAME="E2:33_1_1"/>
( <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">w</font></span>)</span> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V3">open</a> &amp; <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">v</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>then reconsider </b><font color="Maroon">mdw</font> = <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">w</font></span>)</span> <a href="subset_1.html#K3">`</a> , <font color="Maroon">mdv</font> = <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">v</font></span>)</span> <a href="subset_1.html#K3">`</a>  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> <b>by </b><i>, , , <a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<a NAME="E4:33_1_1"/>
( <font color="Maroon">v</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">v</font> &amp; <font color="Maroon">w</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">w</font> )
 
;<br/>
<a NAME="E5:33_1_1"/><b>then </b>
( <font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">v</font> &amp; <font color="Maroon">w</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">w</font> )
 
<b>by </b><i><a class="ref" href="waybel_0.html#T17">WAYBEL_0:17</a></i>;<br/>
<a NAME="E6:33_1_1"/><b>then </b>
( not <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">v</font></span>)</span> <a href="subset_1.html#K3">`</a>  &amp; not <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">w</font></span>)</span> <a href="subset_1.html#K3">`</a>  )
 
<b>by </b><i>, , <a class="ref" href="yellow_6.html#T10">YELLOW_6:10</a></i>;<br/>
<a NAME="E7:33_1_1"/><b>then </b>
( not <font color="Maroon">V</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">mdv</font> &amp; not <font color="Maroon">V</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">mdw</font> )
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E8:33_1_1"/><b>then </b>
not <font color="Maroon">V</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">mdv</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">mdw</font>
 
<b>by </b><i>, , , <a class="ref" href="waybel14.html#T1" target="_self">Th1</a>, </i>;<br/>
<a NAME="E9:33_1_1"/><b>then </b><i><font color="Green">E46</font></i>: 
not <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">mdv</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">mdw</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E10:33_1_1"/>
<font color="Maroon">mdv</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">mdw</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">mdv</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">mdw</font>
 
<b>by </b><i>, , , <a class="ref" href="yellow_1.html#T6">YELLOW_1:6</a></i>;<br/>
<a NAME="E11:33_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
not <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">mdv</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">mdw</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<font color="Maroon">mdv</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">mdw</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">v</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">w</font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
<b>by </b><i><a class="ref" href="xboole_1.html#T54">XBOOLE_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
<b>by </b><i/>
;<br/>
<a NAME="E13:33_1_1"/><b>then </b>
<font color="Maroon">X</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i>, , <a class="ref" href="subset_1.html#T44">SUBSET_1:44</a></i>;<br/>
<a NAME="E14:33_1_1"/><b>then </b>
<font color="Maroon">X</font> <a href="subset_1.html#K9">/\</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> <span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>then consider </b><font color="Maroon">zz</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E16:33_1_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">zz</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E17:33_1_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">zz</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">zz</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5">downarrow</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">zz</font> = <font color="Maroon">zz</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i/>;<br/>
<a NAME="E19:33_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">zz</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#T17">WAYBEL_0:17</a></i>;<br/>
<b>take </b><font color="Maroon">z</font> = <font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font>;<br/>

<b>thus </b><a NAME="E20:33_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, , <a class="txt" href="waybel14.html#E1:33"><i><font color="Green">E36</font></i></a>, <a class="ref" href="waybel_0.html#D20">WAYBEL_0:def 20</a></i>;<br/>

<b>thus </b><a NAME="E21:33_1_1"/>
( <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">v</font> &amp; <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">w</font> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>


</div><b>end;</b></div><b>thus </b><a NAME="E3:33_1"/>
<font color="Maroon">X</font> is <a href="waybel_0.html#V13">upper</a>
 <b>by </b><i>, , , <a class="ref" href="waybel11.html#T31">WAYBEL11:31</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E8:33"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">X</font> is <a href="waybel_0.html#V2">filtered</a> &amp; <font color="Maroon">X</font> is <a href="waybel_0.html#V13">upper</a> )
 ;<br/>

<b>assume </b><a NAME="E9:33"/>
not <font color="Maroon">V</font> is <a href="waybel_6.html#V6">co-prime</a>
 ;<br/>

<b>then consider </b><font color="Maroon">Xx</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>, <font color="Maroon">Y</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><b> such that </b><br/><a NAME="E11:33"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">V</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">Xx</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">Y</font> &amp; not <font color="Maroon">V</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">Xx</font> &amp; not <font color="Maroon">V</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">Y</font> )
 <b>by </b><i>, , , </i>;<br/>
<a NAME="E12:33"/>
( <font color="Maroon">Xx</font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">Xx'</font> = <font color="Maroon">Xx</font>, <font color="Maroon">Y'</font> = <font color="Maroon">Y</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E14:33"/><i><font color="Green">E118</font></i>: 
( <font color="Maroon">Xx'</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">Y'</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="E15:33"/><b>then </b>
<font color="Maroon">Xx'</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y'</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T37">TOPS_1:37</a></i>;<br/>
<a NAME="E16:33"/><b>then </b>
<font color="Maroon">Xx</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">L</font>
 
<b>by </b><i>, , <a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<a NAME="E17:33"/><b>then </b>
<font color="Maroon">Xx</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Xx</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T8">YELLOW_1:8</a></i>;<br/>
<a NAME="E18:33"/><b>then </b><i><font color="Green">E119</font></i>: 
<font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Xx</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E19:33"/><i><font color="Green">E120</font></i>: 
( not <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Xx</font> &amp; not <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</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">v</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E21:33"/><i><font color="Green">E121</font></i>: 
( <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; not <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Xx</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon">w</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E23:33"/><i><font color="Green">E122</font></i>: 
( <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; not <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 <b>by </b><i>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E24:33"/><i><font color="Green">E123</font></i>: 
( <font color="Maroon">Xx'</font> is <a href="waybel_0.html#V13">upper</a> &amp; <font color="Maroon">Y'</font> is <a href="waybel_0.html#V13">upper</a> )
 
<b>by </b><i>, <a class="ref" href="waybel11.html#D4">WAYBEL11:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">v</font> = <font color="Maroon">v</font>, <font color="Maroon">w</font> = <font color="Maroon">w</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i>, , <a class="txt" href="waybel14.html#E1:33"><i><font color="Green">E36</font></i></a></i>;<br/>
<div><i><font color="Green">E124</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="33_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_2"/><i><font color="Green">E125</font></i>: 
<font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Xx'</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y'</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:33_2_1"/>
( <font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Xx'</font> or <font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y'</font> )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_2_1_1"><b>suppose </b></a><a NAME="E1:33_2_1_1"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Xx'</font>
 ;<br/><div class="add"><a NAME="E2:33_2_1_1"/>
<font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">v</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><b>hence </b><a NAME="E3:33_2_1_1"/>
contradiction
 <b>by </b><i>, <a class="txt" href="waybel14.html#E2:33"><i><font color="Green">E37</font></i></a>, <a class="txt" href="waybel14.html#E4:33"><i><font color="Green">E40</font></i></a>, <a class="ref" href="waybel_0.html#D20">WAYBEL_0:def 20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_2_1_2"><b>suppose </b></a><a NAME="E1:33_2_1_2"/><i><font color="Green">E127</font></i>: 
<font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y'</font>
 ;<br/><div class="add"><a NAME="E2:33_2_1_2"/>
<font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">w</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><b>hence </b><a NAME="E3:33_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="waybel14.html#E1:33"><i><font color="Green">E36</font></i></a>, <a class="txt" href="waybel14.html#E2:33"><i><font color="Green">E37</font></i></a>, <a class="txt" href="waybel14.html#E4:33"><i><font color="Green">E40</font></i></a>, <a class="ref" href="waybel_0.html#D20">WAYBEL_0:def 20</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E27:33"/>
<font color="Maroon">v</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i>, <a class="ref" href="waybel14.html#T1" target="_self">Th1</a>, , <a class="txt" href="waybel14.html#E1:33"><i><font color="Green">E36</font></i></a>, <a class="ref" href="waybel_0.html#T41">WAYBEL_0:41</a></i>;<br/>
<b>hence </b><a NAME="E28:33"/>
contradiction
 <b>by </b><i>, , <a class="txt" href="waybel14.html#E3:33"><i><font color="Green">E38</font></i></a></i>;<br/>


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