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<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/>



<a NAME="E1:27"/>
<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> <a href="yellow_7.html#NK1" target="_self">opp</a>  <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #)
 
<b>by </b><i><a class="ref" href="lattice3.html#T8">LATTICE3:8</a></i>;<br/>
<a NAME="E2:27"/><b>then </b>
( <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 <font color="Maroon">c<sub>1</sub></font> iff <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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="waybel_7.html#T19" target="_self">Th19</a></i>;<br/>
<b>hence </b><a NAME="E3:27"/>
( <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 <font color="Maroon">c<sub>1</sub></font> iff <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 <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="waybel_7.html#T20" target="_self">Th20</a></i>;<br/>


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