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<b>let </b><font color="Maroon" title="c1">W</font> be  <a href="setfam_1.html#NV3" title="SETFAM_1:NV.3">with_non-empty_element</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">L</font> being  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a> holds <br/> ( <font color="Olive" title="b1">L</font> is   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font> <a href="waybel34.html#K5" title="WAYBEL34:func.5">-SUP_category</a> </span>)</span> iff ( <font color="Olive" title="b1">L</font> is <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> &amp; <font color="Olive" title="b1">L</font> is <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> ) )</span><br/>

<a NAME="E1:30"/>
 ex <font color="Olive" title="b1">a</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#D11" title="SETFAM_1:def.11">SETFAM_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E2:30"/>
for <font color="Olive" title="b1">L</font> being  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a> holds <br/> ( <font color="Olive" title="b1">L</font> is   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font> <a href="waybel34.html#K5" title="WAYBEL34:func.5">-SUP_category</a> </span>)</span> iff ( <font color="Olive" title="b1">L</font> is <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> &amp; <font color="Olive" title="b1">L</font> is <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> ) )
 <b>by </b><i><a class="ref" href="waybel34.html#D5" target="_self" title="WAYBEL34:def.5">Def5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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