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<b>let </b><font color="Maroon" title="c1">V</font> be  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">antisymmetric</a> <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">u1</font>, <font color="Maroon" title="c3">u2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font>;<br/>





<a NAME="E1:38"/><i><font color="Green" title="E19">A1</font></i>: 
( <font color="Maroon" title="c2">u1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">u1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c3">u2</font> &amp; <font color="Maroon" title="c3">u2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">u1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c3">u2</font> &amp; ( for <font color="Olive" title="b1">u3</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font>  st <font color="Maroon" title="c2">u1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">u3</font> &amp; <font color="Maroon" title="c3">u2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">u3</font> holds <br/><font color="Maroon" title="c2">u1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c3">u2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">u3</font> ) )
 
<b>by </b><i><a class="txt" href="lattice3.html#E26"><i><font color="Green" title="E15">Lm1</font></i></a></i>;<br/>
<a NAME="E2:38"/>
for <font color="Olive" title="b1">u3</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font>  st <font color="Maroon" title="c3">u2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">u3</font> &amp; <font color="Maroon" title="c2">u1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">u3</font> holds <br/><font color="Maroon" title="c2">u1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c3">u2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">u3</font>
 
<b>by </b><i><a class="txt" href="lattice3.html#E26"><i><font color="Green" title="E15">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:38"/>
<font color="Maroon" title="c2">u1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c3">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">u2</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c2">u1</font>
 <b>by </b><i><a class="txt" href="lattice3.html#E1:38"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="lattice3.html#D13" target="_self" title="LATTICE3:def.13">Def13</a></i>;<br/>


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