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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> is   <a href="waybel_7.html#V2" title="WAYBEL_7:attr.2">prime</a>  <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <font color="Maroon" title="c1">L</font> iff <font color="Olive" title="b1">x</font> is   <a href="waybel_7.html#V1" title="WAYBEL_7:attr.1">prime</a>  <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> is   <a href="waybel_7.html#V2" title="WAYBEL_7:attr.2">prime</a>  <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <font color="Maroon" title="c1">L</font> iff <font color="Maroon" title="c2">x</font> is   <a href="waybel_7.html#V1" title="WAYBEL_7:attr.1">prime</a>  <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span> )</span><br/>



<a NAME="E1:25"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L</font> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#T8" title="LATTICE3:th.8">LATTICE3:8</a></span>;<br/>
<a NAME="E2:25"/><span class="kw">then </span>
( <font color="Maroon" title="c2">x</font> is   <a href="waybel_7.html#V2" title="WAYBEL_7:attr.2">prime</a>  <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <font color="Maroon" title="c1">L</font> iff <font color="Maroon" title="c2">x</font> is   <a href="waybel_7.html#V2" title="WAYBEL_7:attr.2">prime</a>  <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_7.html#T15" target="_self" title="WAYBEL_7:th.15">Th19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:25"/>
( <font color="Maroon" title="c2">x</font> is   <a href="waybel_7.html#V2" title="WAYBEL_7:attr.2">prime</a>  <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <font color="Maroon" title="c1">L</font> iff <font color="Maroon" title="c2">x</font> is   <a href="waybel_7.html#V1" title="WAYBEL_7:attr.1">prime</a>  <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_7.html#T16" target="_self" title="WAYBEL_7:th.16">Th20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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