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<b>let </b><font color="Maroon">A</font> be  <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">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font>;<br/>



<a NAME="E1:35"/>
 ex <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font> st <br/>( <font color="Maroon">a</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">x</font> &amp; <font color="Maroon">b</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">x</font> &amp; ( for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font>  st <font color="Maroon">a</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">c</font> &amp; <font color="Maroon">b</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">c</font> holds <br/><font color="Olive">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">c</font> ) )
 
<b>by </b><i><a class="ref" href="lattice3.html#D11">LATTICE3:def 11</a></i>;<br/>
<b>hence </b><a NAME="E2:35"/>
for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font> holds <br/> ( <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font> iff ( <font color="Olive">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a</font> &amp; <font color="Olive">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font> &amp; ( for <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font>  st <font color="Olive">d</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a</font> &amp; <font color="Olive">d</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font> holds <br/><font color="Olive">c</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">d</font> ) ) )
 <b>by </b><i><a class="ref" href="lattice3.html#D14">LATTICE3:def 14</a></i>;<br/>


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