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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">I</font> be    <a href="filter_2.html#M2" target="_self">Ideal</a> of <font color="Maroon">L</font>;<br/>



<b>given </b><font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><a NAME="E1:106"/><i><font color="Green">E14</font></i>: 
for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds <br/> ( <font color="Maroon">c</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Olive">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D13">LATTICES:def 13</a><br/>

<b>consider </b><font color="Maroon">b'</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">I</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">b</font> = <font color="Maroon">b'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i/>;<br/>
<a NAME="E4:106"/>
( <font color="Maroon">H<sub>1</sub></font>( <a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">I</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">I</font> &amp; <font color="Maroon">c</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 
<b>by </b><i>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">c'</font> = <font color="Maroon">c</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">I</font></span>)</span> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">c'</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D13">LATTICES:def 13</a><br/>

<b>let </b><font color="Maroon">a'</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">I</font></span>)</span>;<br/>

<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i/>;<br/>
<b>thus </b><font color="Maroon">c'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a'</font> = 
<font color="Maroon">c</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">c'</font>
<b>by </b><i/>
;<br/>

<b>hence </b><a NAME="E8:106"/>
<font color="Maroon">a'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c'</font>
 ;<br/>


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