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<b>let </b><font color="Maroon">L</font> be  <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V2">with_infima</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>, <font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:3"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E2:3"/>
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>
<a NAME="E3:3"/><b>then </b>
( <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">y</font> &amp; <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">z</font> )
 
<b>by </b><i>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>
<b>hence </b><a NAME="E4:3"/>
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>


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