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

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

<b>assume </b><a NAME="E1:5"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E2:5"/>
<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K6">mod</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="nat_1.html#T63">NAT_1:63</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="nat_1.html#K5">div</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K5">div</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="ref" href="nat_1.html#T69">NAT_1:69</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K5">div</a> <font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font>
<b>by </b><i>, <a class="ref" href="nat_1.html#T68">NAT_1:68</a></i>
;<br/><br/>


</div>
