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

<b>let </b><font color="Maroon">i1</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">i2</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>



<b>thus </b><a NAME="E1:25"/>
(  not <font color="Maroon">i1</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 or ( <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:25_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">i1</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 ;<br/>

<a NAME="E2:25_1"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E3:25_1"/><b>then </b><i><font color="Green">E22</font></i>: 
( (  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> 1 ) or (  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 ) )
 
<b>by </b><i/>;<br/>
<b>thus </b><a NAME="E4:25_1"/>
( ( <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 ) )
 <b>by </b><i/>;<br/>


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

<b>assume </b><a NAME="E2:25"/>
( ( <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 ) )
 ;<br/>

<b>hence </b><a NAME="E3:25"/>
<font color="Maroon">i1</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 ;<br/>


</div>
