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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</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="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">l</font> is <a href="waybel_6.html#V5" title="WAYBEL_6:attr.5">prime</a> holds <br/><font color="Olive" title="b1">l</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">l</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">l</font> is <a href="waybel_6.html#V5" title="WAYBEL_6:attr.5">prime</a> implies <font color="Maroon" title="c2">l</font> is <a href="waybel_6.html#V2" title="WAYBEL_6:attr.2">meet-irreducible</a> )</span><br/>



<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c2">l</font> is <a href="waybel_6.html#V5" title="WAYBEL_6:attr.5">prime</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">l</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="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_6.html#D2" target="_self" title="WAYBEL_6:def.2">WAYBEL_6:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c4">y</font> or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> or <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> )</span><br/>

<b>assume </b><a NAME="E2:43"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> or <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> )</span><br/>

<a NAME="E3:43"/><b>then </b><i><font color="Green" title="E28">A3</font></i>: 
( <font color="Maroon" title="c2">l</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c2">l</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">y</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/>
<a NAME="E4:43"/>
<font color="Maroon" title="c3">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">l</font>
 
<b>by </b><i><a class="txt" href="waybel_6.html#E2:43"><i><font color="Green" title="E27">A2</font></i></a></i>;<br/>
<a NAME="E5:43"/><b>then </b>
( <font color="Maroon" title="c3">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">l</font> or <font color="Maroon" title="c4">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">l</font> )
 
<b>by </b><i><a class="txt" href="waybel_6.html#E1:43"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="waybel_6.html#D6" target="_self" title="WAYBEL_6:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E6:43"/>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> or <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> )
 <b>by </b><i><a class="txt" href="waybel_6.html#E3:43"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="orders_2.html#T25" title="ORDERS_2:th.25">ORDERS_2:25</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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