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

<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">c</font>, <font color="Maroon" title="c3">b</font> be  <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:42"/><i><font color="Green" title="E25">A1</font></i>: 
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">c</font> &amp; <font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">c</font> )
 <b>and </b><br/><a NAME="E2:42"/><i><font color="Green" title="E26">A2</font></i>: 
for <font color="Olive" title="b1">d</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">d</font> holds <br/><font color="Maroon" title="c2">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">d</font>
 ;<br/>

<a NAME="E3:42"/><i><font color="Green" title="E27">A3</font></i>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c1">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="c2">c</font>
 
<b>by </b><i><a class="txt" href="xxreal_0.html#E1:42"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="xxreal_0.html#D9" target="_self" title="XXREAL_0:def.9">Def9</a></i>;<br/>
<a NAME="E4:42"/>
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T25" target="_self" title="XXREAL_0:th.25">Th25</a></i>;<br/>
<a NAME="E5:42"/><b>then </b>
<font color="Maroon" title="c2">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="xxreal_0.html#E2:42"><i><font color="Green" title="E26">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:42"/>
<font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="xxreal_0.html#E3:42"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T1" target="_self" title="XXREAL_0:th.1">Th1</a></i>;<br/>


</div>
