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

<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a> <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</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">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</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">a</font> <a href="yellow_5.html#R2" title="YELLOW_5:pred.2">meets</a> <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b1">a</font> <a href="yellow_5.html#R2" title="YELLOW_5:pred.2">meets</a> <font color="Olive" title="b2">b</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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">a</font> <a href="yellow_5.html#R2" title="YELLOW_5:pred.2">meets</a> <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">c</font> implies <font color="Maroon" title="c2">a</font> <a href="yellow_5.html#R2" title="YELLOW_5:pred.2">meets</a> <font color="Maroon" title="c3">b</font> )</span><br/>



<b>assume </b><a NAME="E1:32"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="yellow_5.html#R2" title="YELLOW_5:pred.2">meets</a> <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">c</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">a</font> <a href="yellow_5.html#R2" title="YELLOW_5:pred.2">meets</a> <font color="Maroon" title="c3">b</font></span><br/>

<b>assume </b><a NAME="E2:32"/><i><font color="Green" title="E14">A2</font></i>: 
not <font color="Maroon" title="c2">a</font> <a href="yellow_5.html#R2" title="YELLOW_5:pred.2">meets</a> <font color="Maroon" title="c3">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="ref" href="lattice3.html#T16" title="LATTICE3:th.16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="yellow_5.html#E2:32"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="yellow_5.html#D3" target="_self" title="YELLOW_5:def.3">Def3</a></i>
<br/>.= 
 <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font>
<b>by </b><i><a class="ref" href="yellow_5.html#T28" target="_self" title="YELLOW_5:th.28">Th28</a></i>
;<br/>
<b>hence </b><a NAME="E4:32"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow_5.html#E1:32"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="yellow_5.html#D3" target="_self" title="YELLOW_5:def.3">Def3</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>
