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

<b>let </b><font color="Maroon">L</font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_3.html#V3">continuous</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>set </b><font color="Maroon">R</font> = <font color="Maroon">L</font> <a href="waybel_4.html#K1" target="_self">-waybelow</a> ;<br/>
<b>thus </b><a NAME="E1:114"/>
<font color="Maroon">L</font> <a href="waybel_4.html#K1" target="_self">-waybelow</a>  <a href="waybel_4.html#NR1" target="_self">satisfies_SI</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_4.html#D21" target="_self">WAYBEL_4:def 21</a><br/>

<b>assume </b><a NAME="E1:114_1"/><i><font color="Green">E31</font></i>: 
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> <a href="waybel_4.html#K1" target="_self">-waybelow</a>  &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">z</font> )
 ;<br/>

<a NAME="E2:114_1"/><b>then </b>
<font color="Maroon">x</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">z</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:114_1"/>
 ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> <a href="waybel_4.html#K1" target="_self">-waybelow</a>  &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> <a href="waybel_4.html#K1" target="_self">-waybelow</a>  &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">y</font> )
 <b>by </b><i><a class="ref" href="waybel_4.html#T10" target="_self">Th10</a>, <a class="ref" href="waybel_4.html#T8" target="_self">Th8</a></i>;<br/>


</div><b>end;</b></div>


</div>
