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<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="E1:140"/><i><font color="Green" title="E82">A1</font></i>: 
<font color="Maroon" title="c1">L</font> is <a href="waybel_1.html#V2" title="WAYBEL_1:attr.2">distributive</a>
 <b>and </b><br/><a NAME="E2:140"/><i><font color="Green" title="E83">A2</font></i>: 
<font color="Maroon" title="c1">L</font> is <a href="waybel_1.html#V10" title="WAYBEL_1:attr.10">complemented</a>
 ;<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/>

<b>consider </b><font color="Maroon" title="c3">x'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E4:140"/><i><font color="Green" title="E84">A3</font></i>: 
<font color="Maroon" title="c3">x'</font> <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="txt" href="waybel_1.html#E2:140"><i><font color="Green" title="E83">A2</font></i></a>, <a class="ref" href="waybel_1.html#D24" target="_self" title="WAYBEL_1:def.24">Def24</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">x'</font>
;<br/>

<b>let </b><font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">x'</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">x'</font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E1:140"><i><font color="Green" title="E82">A1</font></i></a>, <a class="ref" href="waybel_1.html#D3" target="_self" title="WAYBEL_1:def.3">Def3</a></i>
<br/>.= 
<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> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">y</font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E4:140"><i><font color="Green" title="E84">A3</font></i></a>, <a class="ref" href="waybel_1.html#D23" target="_self" title="WAYBEL_1:def.23">Def23</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">y</font>
<b>by </b><i><a class="ref" href="waybel_1.html#T4" target="_self" title="WAYBEL_1:th.4">Th4</a></i>
;<br/>
<b>hence </b><a NAME="E6:140"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">x'</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">x'</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x'</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x'</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">x</font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E1:140"><i><font color="Green" title="E82">A1</font></i></a>, <a class="ref" href="waybel_1.html#T6" target="_self" title="WAYBEL_1:th.6">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x'</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E4:140"><i><font color="Green" title="E84">A3</font></i></a>, <a class="ref" href="waybel_1.html#D23" target="_self" title="WAYBEL_1:def.23">Def23</a></i>
<br/>.= 
<font color="Maroon" title="c3">x'</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y</font>
<b>by </b><i><a class="ref" href="waybel_1.html#T5" target="_self" title="WAYBEL_1:th.5">Th5</a></i>
;<br/>
<b>hence </b><a NAME="E8:140"/>
<font color="Maroon" title="c4">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">x'</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/>


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