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

<b>let </b><font color="Maroon">a</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E1:2"/>
( 0 <a href="nat_1.html#R1">divides</a> <font color="Maroon">a</font> implies <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:2_1"/>
0 <a href="nat_1.html#R1">divides</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E2:2_1"/><b>then </b>
 ex <font color="Olive">b</font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#D3">NAT_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:2"/>
( 0 <a href="nat_1.html#R1">divides</a> <font color="Maroon">a</font> iff <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>


</div>
