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

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

<b>assume </b><a NAME="E1:126"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">b</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 ;<br/>

<b>thus </b><font color="Maroon">a</font> <a href="int_2.html#K3">gcd</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">a</font></span>)</span> <a href="nat_1.html#K10">hcf</a> <span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="int_2.html#D3">INT_2:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">a</font></span>)</span> <a href="nat_1.html#K10">hcf</a> <span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">a</font></span>)</span> <a href="nat_1.html#K10">hcf</a> <span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">a</font></span>)</span> <a href="nat_1.html#K10">hcf</a> <span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="int_2.html#K3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="int_2.html#D3">INT_2:def 3</a></i>
;<br/>


</div>
