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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:26_1"/>
<font color="Maroon">c<sub>2</sub></font> is  <a href="waybel_7.html#V1" target="_self">prime</a> <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  <a href="waybel_7.html#V1" target="_self">prime</a> <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</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/><a NAME="E4:26_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="waybel_7.html#V2" target="_self">prime</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</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>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_7.html#D2" target="_self">WAYBEL_7:def 2</a><br/>

<a NAME="E1:26_1_1"/>
(  <a href="lattice3.html#K9">~</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="lattice3.html#K9">~</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lattice3.html#K9">~</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="lattice3.html#K9">~</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="lattice3.html#D7">LATTICE3:def 7</a>, <a class="ref" href="yellow_7.html#T22">YELLOW_7:22</a></i>;<br/>
<b>hence </b><a NAME="E2:26_1_1"/>
(  not <font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="waybel_7.html#D1" target="_self">Def1</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:26_1"/>
<font color="Maroon">c<sub>2</sub></font> is  <a href="waybel_7.html#V2" target="_self">prime</a> <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>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:26"/>
<font color="Maroon">c<sub>2</sub></font> is  <a href="waybel_7.html#V2" target="_self">prime</a> <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>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  <a href="waybel_7.html#V2" target="_self">prime</a> <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> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">c<sub>1</sub></font> <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/>
<a NAME="E5:26"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="waybel_7.html#V1" target="_self">prime</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_7.html#D1" target="_self">WAYBEL_7:def 1</a><br/>

<a NAME="E1:26_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K8">~</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K8">~</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K8">~</a> </span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K8">~</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="lattice3.html#D6">LATTICE3:def 6</a>, <a class="ref" href="yellow_7.html#T21">YELLOW_7:21</a></i>;<br/>
<b>hence </b><a NAME="E2:26_2"/>
(  not <font color="Maroon">c<sub>5</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="waybel_7.html#D2" target="_self">Def2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:26"/>
<font color="Maroon">c<sub>2</sub></font> is  <a href="waybel_7.html#V1" target="_self">prime</a> <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div>
