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<b>let </b><font color="Maroon">L</font> be  <a href="waybel_1.html#V11">Boolean</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="waybel_0.html#NM4">Filter</a> of <font color="Maroon">L</font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:30_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> is <a href="waybel_7.html#V2" target="_self">prime</a>
 ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>set </b><font color="Maroon">b</font> =  <a href="waybel_1.html#K7">'not'</a> <font color="Maroon">a</font>;<br/><a NAME="E2:30_1"/>
<font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7">'not'</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T37">YELLOW_5:37</a></i>;<br/><a NAME="E3:30_1"/><b>then </b>
<font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7">'not'</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="waybel_4.html#T22">WAYBEL_4:22</a></i>;<br/><b>hence </b><a NAME="E4:30_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> or  <a href="waybel_1.html#K7">'not'</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:30"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  holds <br/>( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> or  <a href="waybel_1.html#K7">'not'</a> <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</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_7.html#D2" target="_self">WAYBEL_7:def 2</a><br/>

<b>assume </b><a NAME="E3:30"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; not <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 ;<br/>

<a NAME="E4:30"/><b>then </b>
(  <a href="waybel_1.html#K7">'not'</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp;  <a href="waybel_1.html#K7">'not'</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E5:30"/><b>then </b>
<span class="p1">(<span class="default"><a href="waybel_1.html#K7">'not'</a> <font color="Maroon">a</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7">'not'</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T41">WAYBEL_0:41</a></i>;<br/>
<a NAME="E6:30"/><b>then </b>
 <a href="waybel_1.html#K7">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T39">YELLOW_5:39</a></i>;<br/>
<a NAME="E7:30"/><b>then </b>
<span class="p1">(<span class="default"><a href="waybel_1.html#K7">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#T41">WAYBEL_0:41</a></i>;<br/>
<a NAME="E8:30"/><b>then </b>
(  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">a</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a>  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T44">YELLOW_0:44</a>, <a class="ref" href="yellow_5.html#T37">YELLOW_5:37</a></i>;<br/>
<b>hence </b><a NAME="E9:30"/>
contradiction
 <b>by </b><i>, <a class="ref" href="waybel_0.html#D20">WAYBEL_0:def 20</a></i>;<br/>


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