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

<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/><b>let </b><font color="Maroon" title="c2">AR</font> be   <a href="alg_1.html#NM1" title="ALG_1:NM.1">Relation</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>assume </b><a NAME="E1:129"/><i><font color="Green" title="E76">A1</font></i>: 
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> holds  <font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Olive" title="b1">x</font> <a href="waybel_4.html#R1" title="WAYBEL_4:pred.1">is_directed_wrt</a> <font color="Maroon" title="c2">AR</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">X</font>, <font color="Maroon" title="c4">Z</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_4.html#D22" target="_self" title="WAYBEL_4:def.22">WAYBEL_4:def 22</a><br/>

<b>assume </b><a NAME="E2:129"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Z</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AR</font>
 ;<br/>

<a NAME="E3:129"/><b>then </b><i><font color="Green" title="E77">A2</font></i>: 
<font color="Maroon" title="c3">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c4">Z</font>
 
;<br/>
<a NAME="E4:129"/>
<font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c4">Z</font> <a href="waybel_4.html#R1" title="WAYBEL_4:pred.1">is_directed_wrt</a> <font color="Maroon" title="c2">AR</font>
 
<b>by </b><i><a class="txt" href="waybel_4.html#E1:129"><i><font color="Green" title="E76">A1</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E6:129"/><i><font color="Green" title="E78">A3</font></i>: 
( <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c4">Z</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c5">u</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AR</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c5">u</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AR</font> )
 <b>by </b><i><a class="txt" href="waybel_4.html#E3:129"><i><font color="Green" title="E77">A2</font></i></a>, <a class="ref" href="waybel_4.html#D23" target="_self" title="WAYBEL_4:def.23">Def23</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">u</font>
;<br/>

<b>thus </b><a NAME="E7:129"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c5">u</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AR</font>
 <b>by </b><i><a class="txt" href="waybel_4.html#E6:129"><i><font color="Green" title="E78">A3</font></i></a></i>;<br/>

<b>thus </b><a NAME="E8:129"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c4">Z</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AR</font>
 <b>by </b><i><a class="txt" href="waybel_4.html#E6:129"><i><font color="Green" title="E78">A3</font></i></a>, <a class="ref" href="waybel_4.html#T13" target="_self" title="WAYBEL_4:th.13">Th13</a></i>;<br/>


</div>
