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

<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM6" title="WAYBEL_0:NM.6">Semilattice</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">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">x</font> is <a href="waybel16.html#V1" title="WAYBEL16:attr.1">completely-irreducible</a> holds <br/><font color="Olive" title="b1">x</font> is <a href="waybel_6.html#V2" title="WAYBEL_6:attr.2">meet-irreducible</a></span><br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <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="c2">x</font> is <a href="waybel16.html#V1" title="WAYBEL16:attr.1">completely-irreducible</a> implies <font color="Maroon" title="c2">x</font> is <a href="waybel_6.html#V2" title="WAYBEL_6:attr.2">meet-irreducible</a> )</span><br/>



<a NAME="E1:29"/><i><font color="Green" title="E16">A1</font></i>: 
 <a href="waybel16.html#K1" title="WAYBEL16:func.1">Irr</a> <font color="Maroon" title="c1">L</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="waybel_6.html#K3" title="WAYBEL_6:func.3">IRR</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="waybel16.html#T22" target="_self" title="WAYBEL16:th.22">Th22</a></i>;<br/>
<b>assume </b><a NAME="E2:29"/>
<font color="Maroon" title="c2">x</font> is <a href="waybel16.html#V1" title="WAYBEL16:attr.1">completely-irreducible</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> is <a href="waybel_6.html#V2" title="WAYBEL_6:attr.2">meet-irreducible</a></span><br/>

<a NAME="E3:29"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel16.html#K1" title="WAYBEL16:func.1">Irr</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="waybel16.html#D4" target="_self" title="WAYBEL16:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E4:29"/>
<font color="Maroon" title="c2">x</font> is <a href="waybel_6.html#V2" title="WAYBEL_6:attr.2">meet-irreducible</a>
 <b>by </b><i><a class="txt" href="waybel16.html#E1:29"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="waybel_6.html#D4" title="WAYBEL_6:def.4">WAYBEL_6:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
