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<b>let </b><font color="Maroon" title="c1">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/>

<b>reconsider </b><font color="Maroon" title="c2">c</font> = <font color="Maroon" title="c1">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E2:22"/>
( <font color="Maroon" title="c2">c</font> <a href="arytm_3.html#R2" title="ARYTM_3:pred.2">divides</a> <font color="Maroon" title="c1">a</font> &amp; ( for <font color="Olive" title="b1">b</font> being <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b1">b</font> <a href="arytm_3.html#R2" title="ARYTM_3:pred.2">divides</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Olive" title="b1">b</font> <a href="arytm_3.html#R2" title="ARYTM_3:pred.2">divides</a> <font color="Maroon" title="c1">a</font> holds <br/><font color="Olive" title="b1">b</font> <a href="arytm_3.html#R2" title="ARYTM_3:pred.2">divides</a> <font color="Maroon" title="c2">c</font> ) )
 
;<br/>
<b>hence </b><a NAME="E3:22"/>
<font color="Maroon" title="c1">a</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</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="E4:22"/>
( <font color="Maroon" title="c1">a</font> <a href="arytm_3.html#R2" title="ARYTM_3:pred.2">divides</a> <font color="Maroon" title="c2">c</font> &amp; ( for <font color="Olive" title="b1">b</font> being <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Maroon" title="c1">a</font> <a href="arytm_3.html#R2" title="ARYTM_3:pred.2">divides</a> <font color="Olive" title="b1">b</font> &amp; <font color="Maroon" title="c1">a</font> <a href="arytm_3.html#R2" title="ARYTM_3:pred.2">divides</a> <font color="Olive" title="b1">b</font> holds <br/><font color="Maroon" title="c2">c</font> <a href="arytm_3.html#R2" title="ARYTM_3:pred.2">divides</a> <font color="Olive" title="b1">b</font> ) )
 
;<br/>
<b>hence </b><a NAME="E5:22"/>
<font color="Maroon" title="c1">a</font> <a href="arytm_3.html#K2" title="ARYTM_3:func.2">lcm</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="ref" href="arytm_3.html#D4" target="_self" title="ARYTM_3:def.4">Def4</a></i>;<br/>


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