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<b>consider </b><font color="Maroon">c<sub>1</sub></font> being  <a href="group_1.html#V6">finite</a> <a href="lattices.html#NM1">Lattice</a>;<br/>
<b>take </b>
<font color="Maroon">c<sub>1</sub></font>
;<br/>

<a NAME="E2:14_1_1"/>
<span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattice3.html#K7">~</a>  is <a href="wellfnd1.html#V1">well_founded</a>
 
<b>by </b><i><a class="txt" href="lattice6.html#E8"><i><font color="Green">Lemma6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:14_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="lattice6.html#V2" target="_self">co-noetherian</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V14">upper-bounded</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V13">lower-bounded</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="lattice3.html#V4">complete</a> )
 <b>by </b><i><a class="ref" href="lattice6.html#D4" target="_self">Def4</a></i>;<br/>


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