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<b>let </b><font color="Maroon" title="c1">H</font> be  non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="lattice2.html#NM2" title="LATTICE2:NM.2">H_Lattice</a>;<br/><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="E1:49"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="openlatt.html#K9" title="OPENLATT:func.9">StoneS</a> <font color="Maroon" title="c1">H</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">p'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font><b> such that </b><br/><a NAME="E3:49"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <font color="Maroon" title="c3">p'</font>
 <b>by </b><i><a class="ref" href="openlatt.html#T15" target="_self" title="OPENLATT:th.15">Th15</a></i>;<br/>
<a NAME="E4:49"/><i><font color="Green" title="E35">A2</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">F</font> where <font color="Olive" title="b1">F</font> is    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">H</font> : ( <font color="Olive" title="b1">F</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> &amp; <font color="Maroon" title="c3">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">F</font> ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="openlatt.html#E3:49"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="openlatt.html#D6" target="_self" title="OPENLATT:def.6">Def6</a></i>;<br/>
<a NAME="E5:49"/>
<font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">H</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">y</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="E1:49_1"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">x</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">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="E3:49_1"/><i><font color="Green" title="E36">A3</font></i>: 
( <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> &amp; <font color="Maroon" title="c5">F</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> &amp; <font color="Maroon" title="c3">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font> )
 <b>by </b><i><a class="txt" href="openlatt.html#E4:49"><i><font color="Green" title="E35">A2</font></i></a></i>;<br/>
<b>thus </b><a NAME="E4:49_1"/>
<font color="Maroon" title="c4">y</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#E3:49_1"><i><font color="Green" title="E36">A3</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:49"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">H</font></span>)</span>
 ;<br/>


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