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

<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="yellow_0.html#V3" title="YELLOW_0:attr.3">bounded</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:142"/><i><font color="Green" title="E84">A1</font></i>: 
<font color="Maroon" title="c1">L</font> <a href="waybel_1.html#NR13" title="WAYBEL_1:NR.13">is_a_Heyting_algebra</a> 
 <b>and </b><br/><a NAME="E2:142"/><i><font color="Green" title="E85">A2</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds   <a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>

<a NAME="E3:142"/><i><font color="Green" title="E86">A3</font></i>: 
 <a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a>  <a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#T24" title="ORDERS_2:th.24">ORDERS_2:24</a></i>;<br/>
<a NAME="E4:142"/><b>then </b><i><font color="Green" title="E87">A4</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E1:142"><i><font color="Green" title="E84">A1</font></i></a>, <a class="ref" href="waybel_1.html#T85" target="_self" title="WAYBEL_1:th.85">Th85</a></i>;<br/>
 <a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E1:142"><i><font color="Green" title="E84">A1</font></i></a>, <a class="ref" href="waybel_1.html#T81" target="_self" title="WAYBEL_1:th.81">Th81</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <font color="Maroon" title="c2">x</font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E2:142"><i><font color="Green" title="E85">A2</font></i></a></i>
;<br/>
<b>hence </b><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <font color="Maroon" title="c2">x</font></span>)</span> = 
 <a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E2:142"><i><font color="Green" title="E85">A2</font></i></a>, <a class="txt" href="waybel_1.html#E4:142"><i><font color="Green" title="E87">A4</font></i></a></i>
<br/>.= 
 <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">L</font>
<b>by </b><i><a class="txt" href="waybel_1.html#E1:142"><i><font color="Green" title="E84">A1</font></i></a>, <a class="ref" href="waybel_1.html#T83" target="_self" title="WAYBEL_1:th.83">Th83</a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D23" target="_self" title="WAYBEL_1:def.23">WAYBEL_1:def 23</a><br/>

<b>thus </b><a NAME="E7:142"/>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" title="WAYBEL_1:func.7">'not'</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="txt" href="waybel_1.html#E1:142"><i><font color="Green" title="E84">A1</font></i></a>, <a class="txt" href="waybel_1.html#E3:142"><i><font color="Green" title="E86">A3</font></i></a>, <a class="ref" href="waybel_1.html#T85" target="_self" title="WAYBEL_1:th.85">Th85</a></i>;<br/>


</div>
