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

<b>let </b><font color="Maroon">c</font> be  <a href="ordinal1.html#V7">natural</a> <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">a</font> be  <a href="ordinal1.html#V7">natural</a> <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">b</font> be  <a href="ordinal1.html#V7">natural</a> <a href="ordinal1.html#NM2">Ordinal</a>;<br/>





<a NAME="E1:44"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">a</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:44"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="arytm_3.html#T3" target="_self">Th3</a></i>;<br/>
<b>assume </b><a NAME="E3:44"/>
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E4:44"/><b>then </b><i><font color="Green">E15</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  implies <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i>, <a class="ref" href="ordinal3.html#T34">ORDINAL3:34</a></i>;<br/>
<a NAME="E5:44"/><i><font color="Green">E16</font></i>: 
(  <a href="arytm_3.html#K6" target="_self">RED</a> <a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <a href="xboole_0.html#K1">{}</a>  <a href="arytm_3.html#K3" target="_self">*^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <a href="xboole_0.html#K1">{}</a>  <a href="ordinal3.html#K6">div^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="ordinal2.html#T52">ORDINAL2:52</a>, <a class="ref" href="ordinal3.html#T83">ORDINAL3:83</a></i>;<br/>
<b>thus </b> <a href="arytm_3.html#K6" target="_self">RED</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font></span>)</span> <a href="ordinal3.html#K6">div^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="arytm_3.html#T2" target="_self">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ordinal3.html#K6">div^</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font></span>)</span> <a href="ordinal3.html#K6">div^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i>, <a class="txt" href="arytm_3.html#E1:44"><i><font color="Green">E13</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="ordinal3.html#K6">div^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <font color="Maroon">b</font></span>)</span> <a href="arytm_3.html#K3" target="_self">*^</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="ordinal3.html#T58">ORDINAL3:58</a></i>
<br/>.= 
 <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
<b>by </b><i>, , <a class="ref" href="ordinal3.html#T81">ORDINAL3:81</a></i>
;<br/>


</div>
