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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V2">with_infima</a> <a href="yellow_0.html#V1">lower-bounded</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">y</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="E1:32"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> is <a href="waybel15.html#V1" target="_self">atom</a>
 <b>and </b><br/><a NAME="E2:32"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">y</font> is <a href="waybel15.html#V1" target="_self">atom</a>
 <b>and </b><br/><a NAME="E3:32"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 <b>and </b><br/><a NAME="E4:32"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E5:32"/>
 <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T44">YELLOW_0:44</a></i>;<br/>
<a NAME="E6:32"/><b>then </b><i><font color="Green">E47</font></i>: 
 <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font> <a href="orders_2.html#R2">&lt;</a> <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="waybel15.html#T1" target="_self">Th1</a>, <a class="ref" href="orders_2.html#D10">ORDERS_2:def 10</a></i>;<br/>
<a NAME="E7:32"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">y</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>
<b>then </b><font color="Maroon">x</font> = 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">y</font>
<b>by </b><i>, , , </i>
;<br/>
<b>hence </b><a NAME="E9:32"/>
contradiction
 <b>by </b><i/>;<br/>


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