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<b>let </b><font color="Maroon">L</font> be  <a href="waybel_1.html#V2">distributive</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">u</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:34"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">p</font> <a href="orders_2.html#R2">&lt;</a> <font color="Maroon">q</font>
 <b>and </b><br/><a NAME="E2:34"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">s</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Maroon">p</font> <a href="orders_2.html#R2">&lt;</a> <font color="Olive">s</font> holds <br/><font color="Maroon">q</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">s</font>
 <b>and </b><br/><a NAME="E3:34"/><i><font color="Green">E28</font></i>: 
not <font color="Maroon">u</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E4:34"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">u</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">q</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">p</font>
 ;<br/>

<a NAME="E5:34"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">p</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">q</font>
 
<b>by </b><i>, <a class="ref" href="orders_2.html#D10">ORDERS_2:def 10</a></i>;<br/>
<font color="Maroon">p</font> = 
<font color="Maroon">p</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">q</font></span>)</span>
<b>by </b><i><a class="ref" href="waybel16.html#T3" target="_self">Th3</a>, <a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">u</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="ref" href="waybel_1.html#T6">WAYBEL_1:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">u</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">q</font>
<b>by </b><i><a class="txt" href="waybel16.html#E1:34"><i><font color="Green">E25</font></i></a>, <a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>
<br/>.= 
<font color="Maroon">q</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">u</font></span>)</span>
<b>by </b><i>, , , </i>
<br/>.= 
<font color="Maroon">q</font>
<b>by </b><i><a class="ref" href="lattice3.html#T18">LATTICE3:18</a></i>
;<br/>
<b>hence </b><a NAME="E7:34"/>
contradiction
 <b>by </b><i/>;<br/>


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