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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="yellow_0.html#V3">bounded</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:142"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="waybel_1.html#NR13" target="_self">is_a_Heyting_algebra</a> 
 <b>and </b><br/><a NAME="E2:142"/><i><font color="Green">E87</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds  <a href="waybel_1.html#K7" target="_self">'not'</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" target="_self">'not'</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E3:142"/><i><font color="Green">E88</font></i>: 
 <a href="waybel_1.html#K7" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a>  <a href="waybel_1.html#K7" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="orders_2.html#T24">ORDERS_2:24</a></i>;<br/>
<a NAME="E4:142"/><b>then </b><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E1:142"><i><font color="Green">E86</font></i></a>, <a class="ref" href="waybel_1.html#T85" target="_self">Th85</a></i>;<br/>
 <a href="waybel_1.html#K7" target="_self">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K7" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="waybel_1.html#K7" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" target="_self">'not'</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K7" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E1:142"><i><font color="Green">E86</font></i></a>, <a class="ref" href="waybel_1.html#T87" target="_self">Th87</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E2:142"><i><font color="Green">E87</font></i></a></i>
;<br/>
<b>hence </b><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="waybel_1.html#K7" target="_self">'not'</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E2:142"><i><font color="Green">E87</font></i></a>, <a class="txt" href="waybel_1.html#E4:142"><i><font color="Green">E89</font></i></a></i>
<br/>.= 
 <a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="waybel_1.html#E1:142"><i><font color="Green">E86</font></i></a>, <a class="ref" href="waybel_1.html#T83" target="_self">Th83</a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D23" target="_self">WAYBEL_1:def 23</a><br/>

<b>thus </b><a NAME="E7:142"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K11">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K7" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="waybel_1.html#E1:142"><i><font color="Green">E86</font></i></a>, <a class="txt" href="waybel_1.html#E3:142"><i><font color="Green">E88</font></i></a>, <a class="ref" href="waybel_1.html#T85" target="_self">Th85</a></i>;<br/>


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