<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">P</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="lattice4.html#M2">ClosedSubset</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:107"/><i><font color="Green">E14</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Olive">a</font> <a href="lattices.html#R3">[=</a> <font color="Olive">c</font> holds <br/><font color="Olive">a</font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">c</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Olive">c</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D12">LATTICES:def 12</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">P</font></span>)</span>, <font color="Maroon">b'</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">P</font></span>)</span>, <font color="Maroon">c'</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">P</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D12">LATTICES:def 12</a><br/>

<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a'</font>, <font color="Maroon">b</font> = <font color="Maroon">b'</font>, <font color="Maroon">c</font> = <font color="Maroon">c'</font>, <font color="Maroon">bc</font> = <font color="Maroon">b'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c'</font>, <font color="Maroon">ab</font> = <font color="Maroon">a'</font> <a href="lattices.html#K3">"\/"</a> <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/>
<b>assume </b><a NAME="E3:107"/>
<font color="Maroon">a'</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c'</font>
 ;<br/>

<a NAME="E4:107"/><b>then </b><i><font color="Green">E15</font></i>: 
<font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c</font>
 
<b>by </b><i/>;<br/>
<b>thus </b><font color="Maroon">a'</font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">b'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c'</font></span>)</span> = 
<font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">bc</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">ab</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a'</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b'</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c'</font>
<b>by </b><i/>
;<br/>


</div>
