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

<a NAME="E1:18_1_1"/>
(  <a href="lfuzzy_0.html#K2" title="LFUZZY_0:func.2">max</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="lfuzzy_0.html#K2" title="LFUZZY_0:func.2">max</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></i>;<br/>
<a NAME="E2:18_1_1"/><b>then </b><i><font color="Green" title="E7">A1</font></i>: 
(  <a href="lfuzzy_0.html#K2" title="LFUZZY_0:func.2">max</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="lfuzzy_0.html#NR2" title="LFUZZY_0:NR.2">&gt;&gt;=</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="lfuzzy_0.html#K2" title="LFUZZY_0:func.2">max</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="lfuzzy_0.html#NR2" title="LFUZZY_0:NR.2">&gt;&gt;=</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="lfuzzy_0.html#T3" target="_self" title="LFUZZY_0:th.3">Th3</a></i>;<br/>
<a NAME="E3:18_1_1"/>
for <font color="Olive" title="b1">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b1">d</font> <a href="lfuzzy_0.html#NR2" title="LFUZZY_0:NR.2">&gt;&gt;=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Olive" title="b1">d</font> <a href="lfuzzy_0.html#NR2" title="LFUZZY_0:NR.2">&gt;&gt;=</a> <font color="Maroon" title="c3">b</font> holds <br/> <a href="lfuzzy_0.html#K2" title="LFUZZY_0:func.2">max</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="lfuzzy_0.html#NR1" title="LFUZZY_0:NR.1">&lt;&lt;=</a> <font color="Olive" title="b1">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>;<br/>

<b>assume </b><a NAME="E1:18_1_1_1"/>
( <font color="Maroon" title="c4">d</font> <a href="lfuzzy_0.html#NR2" title="LFUZZY_0:NR.2">&gt;&gt;=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c4">d</font> <a href="lfuzzy_0.html#NR2" title="LFUZZY_0:NR.2">&gt;&gt;=</a> <font color="Maroon" title="c3">b</font> )
 ;<br/>

<a NAME="E2:18_1_1_1"/><b>then </b>
( <font color="Maroon" title="c4">d</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c4">d</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="lfuzzy_0.html#T3" target="_self" title="LFUZZY_0:th.3">Th3</a></i>;<br/>
<a NAME="E3:18_1_1_1"/><b>then </b>
 <a href="lfuzzy_0.html#K2" title="LFUZZY_0:func.2">max</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">d</font>
 
<b>by </b><i><a class="ref" href="square_1.html#T50" title="SQUARE_1:th.50">SQUARE_1:50</a></i>;<br/>
<b>hence </b><a NAME="E4:18_1_1_1"/>
 <a href="lfuzzy_0.html#K2" title="LFUZZY_0:func.2">max</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="lfuzzy_0.html#NR1" title="LFUZZY_0:NR.1">&lt;&lt;=</a> <font color="Maroon" title="c4">d</font>
 <b>by </b><i><a class="ref" href="lfuzzy_0.html#T3" target="_self" title="LFUZZY_0:th.3">Th3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:18_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lfuzzy_0.html#K2" title="LFUZZY_0:func.2">max</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="lfuzzy_0.html#E2:18_1_1"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/>


</div>
