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

<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:67"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">a</font> <a href="nat_1.html#K10">hcf</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">b</font> <a href="nat_1.html#K2">*</a> <font color="Maroon">c</font> )
 ;<br/>

<a NAME="E2:67"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">a</font> <a href="int_2.html#K3">gcd</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E3:67"/>
<font color="Maroon">a</font> <a href="int_1.html#R2">divides</a> <font color="Maroon">b</font> <a href="nat_1.html#K2">*</a> <font color="Maroon">c</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:67"/><b>then </b>
<font color="Maroon">a</font> <a href="int_1.html#R2">divides</a> <font color="Maroon">c</font>
 
<b>by </b><i>, <a class="txt" href="wsierp_1.html#E12"><i><font color="Green">Lemma47</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:67"/>
<font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c</font>
 <b>by </b><i/>;<br/>


</div>
