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

<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> <a href="waybel_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon" title="c2">AR</font> be  <a href="waybel_4.html#V2" title="WAYBEL_4:attr.2">auxiliary(ii)</a> <a href="waybel_4.html#V3" title="WAYBEL_4:attr.3">auxiliary(iii)</a> <a href="alg_1.html#NM1" title="ALG_1:NM.1">Relation</a> of <font color="Maroon" title="c1">L</font>;<br/><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">z</font>, <font color="Maroon" title="c6">u</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>





<b>assume </b><a NAME="E1:8"/><i><font color="Green" title="E9">A1</font></i>: 
( <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">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> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c6">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> )
 ;<br/>

<a NAME="E2:8"/><i><font color="Green" title="E10">A2</font></i>: 
( <font color="Maroon" title="c3">x</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="c4">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">y</font> )
 
;<br/>
<a NAME="E3:8"/>
( <font color="Maroon" title="c5">z</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">z</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">u</font> &amp; <font color="Maroon" title="c6">u</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">z</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">u</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/>
<a NAME="E4:8"/><b>then </b>
( <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>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">z</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">u</font></span>)</span></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="c4">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">z</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">u</font></span>)</span></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#E1:8"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="waybel_4.html#E2:8"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="waybel_4.html#D5" target="_self" title="WAYBEL_4:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E5:8"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">z</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">u</font></span>)</span></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="ref" href="waybel_4.html#D6" target="_self" title="WAYBEL_4:def.6">Def6</a></i>;<br/>


</div>
