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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">L</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> is  <a href="filter_2.html#V2" title="FILTER_2:attr.2">prime</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">F</font> = <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">L</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span>;<br/>
<a NAME="E1:7"/>
 for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b2">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">L</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> iff ( <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">L</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> or <font color="Olive" title="b2">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">L</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> ) )
 
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<span class="kw">hence </span><a NAME="E2:7"/>
<span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">L</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> is  <a href="filter_2.html#V2" title="FILTER_2:attr.2">prime</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#D10" onmouseover="rs('filter_2/D10')" onmouseout="rh()">FILTER_2:def 10</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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