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

<b>let </b><font color="Maroon" title="c8">r</font>, <font color="Maroon" title="c9">s</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>



<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c8">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c9">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<a NAME="E2:17"/><b>then </b><i><font color="Green" title="E24">A2</font></i>: 
<font color="Maroon" title="c8">r</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">s</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">s</font>
 
<b>by </b><i><a class="txt" href="xreal_0.html#E25"><i><font color="Green" title="E19">Lm18</font></i></a></i>;<br/>
<b>assume </b><a NAME="E3:17"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c8">r</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">s</font>
 ;<br/>

<a NAME="E4:17"/><b>then </b>
<font color="Maroon" title="c8">r</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="xreal_0.html#E2:17"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="xreal_0.html#E5"><i><font color="Green" title="E5">Lm4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:17"/>
contradiction
 <b>by </b><i><a class="txt" href="xreal_0.html#E1:17"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="xreal_0.html#E27"><i><font color="Green" title="E21">Lm20</font></i></a></i>;<br/>


</div>
