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<b>let </b><font color="Maroon">H</font> be  non <a href="realset2.html#V3">trivial</a> <a href="lattice2.html#NM2">H_Lattice</a>;<br/>

<b>assume </b><a NAME="E1:48"/><i><font color="Green">E18</font></i>: 
<span class="p1">(<span class="default"><a href="openlatt.html#K16" target="_self">StoneH</a> <font color="Maroon">H</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">H</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K16" target="_self">StoneH</a> <font color="Maroon">H</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">H</font></span>)</span>;<br/>
<b>consider </b><font color="Maroon">F</font> being    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">H</font><b> such that </b><br/><a NAME="E4:48"/><i><font color="Green">E19</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">H</font> &amp; <font color="Maroon">F</font> is <a href="filter_0.html#V2">prime</a> &amp;  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">H</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 <b>by </b><i>, <a class="txt" href="openlatt.html#E1:48"><i><font color="Green">E18</font></i></a></i>;<br/>
<b>thus </b><a NAME="E5:48"/>
contradiction
 <b>by </b><i>, <a class="ref" href="filter_0.html#T32">FILTER_0:32</a></i>;<br/>


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