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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="ordinal1.html#K5">omega</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:30_1_2"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="ordinal1.html#V7">natural</a> <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Olive">b<sub>1</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font> ) )
 <b>and </b><br/><a NAME="E2:30_1_2"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="ordinal1.html#V7">natural</a> <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Olive">b<sub>1</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> ) )
 ;<br/>

<a NAME="E3:30_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="arytm_3.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="arytm_3.html#E1:30_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="arytm_3.html#E2:30_1_2"><i><font color="Green">E23</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:30_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="arytm_3.html#T13" target="_self">Th13</a></i>;<br/>


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