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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="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:45_1_2"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>and </b><br/><a NAME="E2:45_1_2"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/>

<a NAME="E3:45_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> is   <a href="nat_1.html#NM1">Nat</a> &amp; <font color="Maroon">c<sub>4</sub></font> is   <a href="nat_1.html#NM1">Nat</a> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E4:45_1_2"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="nat_1.html#E1:45_1_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="nat_1.html#E2:45_1_2"><i><font color="Green">E30</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:45_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="nat_1.html#T52" target="_self">Th52</a></i>;<br/>


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