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<b>consider </b><font color="Maroon" title="c1">L</font> being  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/>
<b>take </b>
<font color="Maroon" title="c1">L</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is <a href="lattice6.html#V2" title="LATTICE6:attr.2">co-noetherian</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V4" title="LATTICE3:attr.4">complete</a> )</span><br/>

<a NAME="E2:14_1_1"/>
<span class="p1">(<span class="default"><a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a>  is <a href="wellfnd1.html#V1" title="WELLFND1:attr.1">well_founded</a>
 
<b>by </b><i><a class="txt" href="lattice6.html#E8"><i><font color="Green" title="E6">Lm6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:14_1_1"/>
( <font color="Maroon" title="c1">L</font> is <a href="lattice6.html#V2" title="LATTICE6:attr.2">co-noetherian</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V4" title="LATTICE3:attr.4">complete</a> )
 <b>by </b><i><a class="ref" href="lattice6.html#D4" target="_self" title="LATTICE6:def.4">Def4</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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