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

<b>let </b><font color="Maroon" title="c1">b</font>, <font color="Maroon" title="c2">a</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/>



<a NAME="E1:35"/>
<font color="Maroon" title="c2">a</font> <a href="arytm_3.html#K5" title="ARYTM_3:func.5">hcf</a> <font color="Maroon" title="c1">b</font> <a href="arytm_3.html#R2" title="ARYTM_3:pred.2">divides</a> <font color="Maroon" title="c1">b</font>
 
<b>by </b><i><a class="ref" href="arytm_3.html#D5" target="_self" title="ARYTM_3:def.5">Def5</a></i>;<br/>
<a NAME="E2:35"/><b>then </b>
<font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="arytm_3.html#K5" title="ARYTM_3:func.5">hcf</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">*^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">b</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="arytm_3.html#K5" title="ARYTM_3:func.5">hcf</a> <font color="Maroon" title="c1">b</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="arytm_3.html#T11" target="_self" title="ARYTM_3:th.11">Th11</a></i>;<br/>
<b>hence </b><a NAME="E3:35"/>
( <font color="Maroon" title="c1">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies ( <font color="Maroon" title="c2">a</font> <a href="arytm_3.html#K5" title="ARYTM_3:func.5">hcf</a> <font color="Maroon" title="c1">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c1">b</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="arytm_3.html#K5" title="ARYTM_3:func.5">hcf</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) )
 <b>by </b><i><a class="ref" href="ordinal2.html#T52" title="ORDINAL2:th.52">ORDINAL2:52</a></i>;<br/>


</div>
