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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:3"/><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:3"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span><b>by </b><i><a class="txt" href="topreal6.html#E2:3"><i><font color="Green">E6</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1"><b>suppose </b></a><a NAME="E1:3_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:3_1_1"/><b>then </b>
 <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="absvalue.html#T7">ABSVALUE:7</a></i>;<br/><b>hence </b><a NAME="E3:3_1_1"/>
 <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="complex1.html#T132">COMPLEX1:132</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_2"><b>suppose </b></a><a NAME="E1:3_1_2"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:3_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 <b>by </b><i><a class="txt" href="topreal6.html#E1:3"><i><font color="Green">E5</font></i></a></i>;<br/><a NAME="E3:3_1_2"/><b>then </b>
(  <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="topreal6.html#E1:3_1_2"><i><font color="Green">E7</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/><b>hence </b><a NAME="E4:3_1_2"/>
 <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="topreal6.html#E1:3"><i><font color="Green">E5</font></i></a>, <a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
