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

<b>let </b><font color="Maroon">k</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">m</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">n</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">m1</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">n1</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>









<b>assume </b><a NAME="E1:12"/>
( <font color="Maroon">k</font> <a href="int_1.html#R2">divides</a> <font color="Maroon">m</font> &amp; <font color="Maroon">k</font> <a href="int_1.html#R2">divides</a> <font color="Maroon">n</font> )
 ;<br/>

<a NAME="E2:12"/><b>then </b>
( <font color="Maroon">k</font> <a href="int_1.html#R2">divides</a> <font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m1</font> &amp; <font color="Maroon">k</font> <a href="int_1.html#R2">divides</a> <font color="Maroon">n</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n1</font> )
 
<b>by </b><i><a class="ref" href="int_2.html#T12">INT_2:12</a></i>;<br/>
<b>hence </b><a NAME="E3:12"/>
<font color="Maroon">k</font> <a href="int_1.html#R2">divides</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n1</font></span>)</span>
 <b>by </b><i/>;<br/>


</div>
