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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="orders_2.html#V4" title="ORDERS_2:attr.4">antisymmetric</a> <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">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/>



<b>assume </b><b>that </b><br/><a NAME="E1:32"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c2">x</font> is <a href="waybel15.html#V1" title="WAYBEL15:attr.1">atom</a>
 <b>and </b><br/><a NAME="E2:32"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c3">y</font> is <a href="waybel15.html#V1" title="WAYBEL15:attr.1">atom</a>
 <b>and </b><br/><a NAME="E3:32"/><i><font color="Green" title="E27">A3</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font>
 <b>and </b><br/><a NAME="E4:32"/><i><font color="Green" title="E28">A4</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font>
 ;<br/>

<a NAME="E5:32"/>
 <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T44" title="YELLOW_0:th.44">YELLOW_0:44</a></i>;<br/>
<a NAME="E6:32"/><b>then </b><i><font color="Green" title="E29">A5</font></i>: 
 <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="txt" href="waybel15.html#E4:32"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="orders_2.html#D10" title="ORDERS_2:def.10">ORDERS_2:def 10</a></i>;<br/>
<a NAME="E7:32"/><i><font color="Green" title="E30">A6</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c3">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/>
<b>then </b><font color="Maroon" title="c2">x</font> = 
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">y</font>
<b>by </b><i><a class="txt" href="waybel15.html#E1:32"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="waybel15.html#E6:32"><i><font color="Green" title="E29">A5</font></i></a>, <a class="ref" href="waybel15.html#D1" target="_self" title="WAYBEL15:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c3">y</font>
<b>by </b><i><a class="txt" href="waybel15.html#E2:32"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="waybel15.html#E6:32"><i><font color="Green" title="E29">A5</font></i></a>, <a class="txt" href="waybel15.html#E7:32"><i><font color="Green" title="E30">A6</font></i></a>, <a class="ref" href="waybel15.html#D1" target="_self" title="WAYBEL15:def.1">Def1</a></i>
;<br/>
<b>hence </b><a NAME="E9:32"/>
contradiction
 <b>by </b><i><a class="txt" href="waybel15.html#E3:32"><i><font color="Green" title="E27">A3</font></i></a></i>;<br/>


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