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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM2">D_Lattice</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<a NAME="E1:20"/><i><font color="Green">E18</font></i>: 
<span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">F</font> where <font color="Olive">F</font> is    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">L</font> : ( <font color="Olive">F</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K7" target="_self">F_primeSet</a> <font color="Maroon">L</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> ) </span>}</span> 
 
<b>by </b><i/>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:20_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 ;<br/><b>then consider </b><font color="Maroon">F</font> being    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:20_1"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> &amp; <font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K7" target="_self">F_primeSet</a> <font color="Maroon">L</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 <b>by </b><i><a class="txt" href="openlatt.html#E3:20_1"><i><font color="Green">E19</font></i></a></i>;<br/><a NAME="E4:20_1"/>
( <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> &amp; <font color="Maroon">F</font> is <a href="filter_0.html#V2">prime</a> )
 <b>by </b><i><a class="ref" href="openlatt.html#T2" target="_self">Th2</a>, </i>;<br/><b>hence </b><a NAME="E5:20_1"/>
 ex <font color="Olive">F</font> being   <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Olive">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> &amp; <font color="Olive">F</font> is <a href="filter_0.html#V2">prime</a> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> )
 <b>by </b><i><a class="ref" href="openlatt.html#T2" target="_self">Th2</a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">F</font> being    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">L</font><b> such that </b><a NAME="E3:20"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> &amp; <font color="Maroon">F</font> is <a href="filter_0.html#V2">prime</a> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 ;<br/>

<a NAME="E4:20"/>
<font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K7" target="_self">F_primeSet</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="openlatt.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E5:20"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="openlatt.html#T2" target="_self">Th2</a></i>;<br/>


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