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<b>let </b><font color="Maroon">L</font> be  <a href="waybel_1.html#V2">distributive</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">L</font>;<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/>





<b>assume </b><a NAME="E1:39"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">I</font> <a href="subset_1.html#R1">misses</a> <font color="Maroon">F</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">F'</font> = <font color="Maroon">I</font> as   <a href="waybel_0.html#NM4">Filter</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span> <b>by </b><i><a class="ref" href="yellow_7.html#T26">YELLOW_7:26</a>, <a class="ref" href="yellow_7.html#T28">YELLOW_7:28</a></i>;<br/>
<b>reconsider </b><font color="Maroon">I'</font> = <font color="Maroon">F</font> as   <a href="waybel_0.html#NM3">Ideal</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span> <b>by </b><i><a class="ref" href="yellow_7.html#T27">YELLOW_7:27</a>, <a class="ref" href="yellow_7.html#T29">YELLOW_7:29</a></i>;<br/>
<b>consider </b><font color="Maroon">P'</font> being   <a href="waybel_0.html#NM3">Ideal</a> of <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span><b> such that </b><br/><a NAME="E5:39"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">P'</font> is <a href="waybel_7.html#V1" target="_self">prime</a> &amp; <font color="Maroon">I'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P'</font> &amp; <font color="Maroon">P'</font> <a href="subset_1.html#R1">misses</a> <font color="Maroon">F'</font> )
 <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">P</font> = <font color="Maroon">P'</font> as   <a href="waybel_0.html#NM4">Filter</a> of <font color="Maroon">L</font> <b>by </b><i><a class="ref" href="yellow_7.html#T27">YELLOW_7:27</a>, <a class="ref" href="yellow_7.html#T29">YELLOW_7:29</a></i>;<br/>
<b>take </b>
<font color="Maroon">P</font>
;<br/>

<b>thus </b><a NAME="E7:39"/>
( <font color="Maroon">P</font> is <a href="waybel_7.html#V2" target="_self">prime</a> &amp; <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> &amp; <font color="Maroon">I</font> <a href="subset_1.html#R1">misses</a> <font color="Maroon">P</font> )
 <b>by </b><i>, </i>;<br/>


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