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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_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">  for <font color="Olive" title="b1">F</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">L</font> iff ( <font color="Olive" title="b1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> &amp; <font color="Olive" title="b1">F</font> is  <a href="filter_0.html#V2" title="FILTER_0:attr.2">prime</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c1">L</font>; <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"> ( <font color="Maroon" title="c2">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">L</font> iff ( <font color="Maroon" title="c2">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> &amp; <font color="Maroon" title="c2">F</font> is  <a href="filter_0.html#V2" title="FILTER_0:attr.2">prime</a>  ) )</span><br/>



<a NAME="E1:17"/>
( <font color="Maroon" title="c2">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">L</font> iff  ex <font color="Olive" title="b1">F0</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Olive" title="b1">F0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Olive" title="b1">F0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> &amp; <font color="Olive" title="b1">F0</font> is  <a href="filter_0.html#V2" title="FILTER_0:attr.2">prime</a>  ) )
 
;<br/>
<span class="kw">hence </span><a NAME="E2:17"/>
( <font color="Maroon" title="c2">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">L</font> iff ( <font color="Maroon" title="c2">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> &amp; <font color="Maroon" title="c2">F</font> is  <a href="filter_0.html#V2" title="FILTER_0:attr.2">prime</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"> verum</span><br/>


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