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<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>reconsider </b><font color="Maroon">e</font> = <font color="Maroon">a</font>, <font color="Maroon">c</font> =  <a href="xboole_0.html#K1">{}</a>  as    <a href="subset_1.html#M1">Element</a> of  <a href="ordinal1.html#K5">omega</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E2:31"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">e</font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">a</font> &amp; <font color="Maroon">e</font> <a href="arytm_3.html#R2" target="_self">divides</a>  <a href="xboole_0.html#K1">{}</a>  &amp; ( for <font color="Olive">n</font> being <a href="ordinal1.html#V7">natural</a> <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">n</font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">a</font> &amp; <font color="Olive">n</font> <a href="arytm_3.html#R2" target="_self">divides</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/><font color="Olive">n</font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">e</font> ) )
 
<b>by </b><i/>;<br/>
<a NAME="E3:31"/>
( <font color="Maroon">a</font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c</font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c</font> &amp; ( for <font color="Olive">b</font> being <a href="ordinal1.html#V7">natural</a> <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Maroon">a</font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Olive">b</font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Olive">b</font> holds <br/><font color="Maroon">c</font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Olive">b</font> ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:31"/>
( <font color="Maroon">a</font> <a href="arytm_3.html#K5" target="_self">hcf</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="arytm_3.html#K4" target="_self">lcm</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, , </i>;<br/>


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