<?xml version="1.0"?>
<div class="add">

<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="E2:13_1_1"/>
 <a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">c<sub>1</sub></font> is <a href="wellfnd1.html#V1">well_founded</a>
 
;<br/>
<b>hence </b><a NAME="E3:13_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="lattice6.html#V1" target="_self">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#D3" target="_self">Def3</a></i>;<br/>


</div>
