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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="waybel_0.html#NM4">Filter</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:39"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#R1">misses</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="waybel_0.html#NM4">Filter</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></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">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="waybel_0.html#NM3">Ideal</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></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">c<sub>6</sub></font> being   <a href="waybel_0.html#NM3">Ideal</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></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">E25</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> is <a href="waybel_7.html#V1" target="_self">prime</a> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="subset_1.html#R1">misses</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="waybel_7.html#E1:39"><i><font color="Green">E24</font></i></a>, <a class="ref" href="waybel_7.html#T27" target="_self">Th27</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="waybel_0.html#NM4">Filter</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>7</sub></font>
;<br/>

<b>thus </b><a NAME="E7:39"/>
( <font color="Maroon">c<sub>7</sub></font> is <a href="waybel_7.html#V2" target="_self">prime</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#R1">misses</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="waybel_7.html#E5:39"><i><font color="Green">E25</font></i></a>, <a class="ref" href="waybel_7.html#T21" target="_self">Th21</a></i>;<br/>


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