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

<b>let </b><font color="Maroon">S</font> be   <a href="waybel_0.html#NM6">Semilattice</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">s1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>, <font color="Maroon">s2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D2" target="_self">WAYBEL_1:def 2</a><br/>





<b>assume </b><a NAME="E1:102"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">s1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s2</font>
 ;<br/>

<a NAME="E2:102"/><i><font color="Green">E35</font></i>: 
 <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">s2</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T21">YELLOW_0:21</a></i>;<br/>
<a NAME="E3:102"/><i><font color="Green">E45</font></i>: 
 <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">s1</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T21">YELLOW_0:21</a></i>;<br/>
<a NAME="E4:102"/><b>then </b>
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">s1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s1</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T19">YELLOW_0:19</a></i>;<br/>
<a NAME="E5:102"/><b>then </b>
( <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">s1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s2</font> &amp; <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">s1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> )
 
<b>by </b><i>, , <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a>, <a class="ref" href="yellow_0.html#T19">YELLOW_0:19</a></i>;<br/>
<a NAME="E6:102"/><b>then </b>
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">s1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">s2</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T19">YELLOW_0:19</a></i>;<br/>
<a NAME="E7:102"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4" target="_self">"/\"</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">s1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">s2</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:102"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4" target="_self">"/\"</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">s1</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4" target="_self">"/\"</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">s2</font>
 <b>by </b><i/>;<br/>


</div>
