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<b>let </b><font color="Maroon">W</font> be  <a href="setfam_1.html#V2">with_non-empty_element</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">L</font> be   <a href="waybel_0.html#NM8">LATTICE</a>;<br/>



<a NAME="E1:52"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">L</font> <a href="yellow21.html#K1" target="_self">as_1-sorted</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E2:52"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font>
 ;<br/>

<a NAME="E3:52"/><b>then </b>
( <font color="Maroon">L</font> <a href="hidden.html#R2">in</a>  <a href="yellow21.html#K2" target="_self">POSETS</a> <font color="Maroon">W</font> iff <font color="Maroon">L</font> is <a href="orders_2.html#V1">strict</a> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:52"/>
( <font color="Maroon">L</font> is   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="yellow21.html#K6" target="_self">-UPS_category</a> </span>)</span> iff ( <font color="Maroon">L</font> is <a href="orders_2.html#V1">strict</a> &amp; <font color="Maroon">L</font> is <a href="lattice3.html#V3">complete</a> ) )
 <b>by </b><i/>;<br/>


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