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<b>let </b><font color="Maroon">V</font> be  <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V1" target="_self">with_suprema</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">u1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/>





<a NAME="E1:38"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">u1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">u1</font> <a href="lattice3.html#K10" target="_self">"\/"</a> <font color="Maroon">u2</font> &amp; <font color="Maroon">u2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">u1</font> <a href="lattice3.html#K10" target="_self">"\/"</a> <font color="Maroon">u2</font> &amp; ( for <font color="Olive">u3</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>  st <font color="Maroon">u1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">u3</font> &amp; <font color="Maroon">u2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">u3</font> holds <br/><font color="Maroon">u1</font> <a href="lattice3.html#K10" target="_self">"\/"</a> <font color="Maroon">u2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">u3</font> ) )
 
<b>by </b><i/>;<br/>
<a NAME="E2:38"/>
for <font color="Olive">u3</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>  st <font color="Maroon">u2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">u3</font> &amp; <font color="Maroon">u1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">u3</font> holds <br/><font color="Maroon">u1</font> <a href="lattice3.html#K10" target="_self">"\/"</a> <font color="Maroon">u2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">u3</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:38"/>
<font color="Maroon">u1</font> <a href="lattice3.html#K10" target="_self">"\/"</a> <font color="Maroon">u2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u2</font> <a href="lattice3.html#K10" target="_self">"\/"</a> <font color="Maroon">u1</font>
 <b>by </b><i>, </i>;<br/>


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