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<b>let </b><font color="Maroon" title="c1">H</font> be  non <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a> <a href="lattice2.html#NM2" title="LATTICE2:NM.2">H_Lattice</a>;<br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:47_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K16" title="OPENLATT:func.16">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">H</font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c3">F</font> being    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">H</font><b> such that </b><br/><a NAME="E3:47_1"/><i><font color="Green" title="E39">A1</font></i>: 
( <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c3">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">H</font> &amp; <font color="Maroon" title="c3">F</font> is <a href="filter_0.html#V2" title="FILTER_0:attr.2">prime</a> &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> )
 <b>by </b><i><a class="ref" href="openlatt.html#T14" target="_self" title="OPENLATT:th.14">Th14</a></i>;<br/><b>thus </b><a NAME="E4:47_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="openlatt.html#E3:47_1"><i><font color="Green" title="E39">A1</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:47"/><i><font color="Green" title="E39">A2</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">H</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">F</font> being    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">H</font><b> such that </b><br/><a NAME="E4:47"/><i><font color="Green" title="E40">A3</font></i>: 
( <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c3">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">H</font> &amp; <font color="Maroon" title="c3">F</font> is <a href="filter_0.html#V2" title="FILTER_0:attr.2">prime</a> )
 <b>by </b><i><a class="txt" href="openlatt.html#E2:47"><i><font color="Green" title="E39">A2</font></i></a></i>;<br/>
<a NAME="E5:47"/>
 <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="ref" href="filter_0.html#T12" title="FILTER_0:th.12">FILTER_0:12</a></i>;<br/>
<b>hence </b><a NAME="E6:47"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K16" title="OPENLATT:func.16">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="openlatt.html#E4:47"><i><font color="Green" title="E40">A3</font></i></a>, <a class="ref" href="openlatt.html#T14" target="_self" title="OPENLATT:th.14">Th14</a></i>;<br/>


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