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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:35"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="int_2.html#V1" target="_self">prime</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="int_2.html#V1" target="_self">prime</a> )
 ;<br/>

<b>assume </b><a NAME="E2:35"/>
not <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="int_2.html#R2" target="_self">are_relative_prime</a> 
 ;<br/>

<a NAME="E3:35"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 
<b>by </b><i><a class="ref" href="int_2.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E4:35"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="nat_1.html#D5">NAT_1:def 5</a></i>;<br/>
<a NAME="E5:35"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="int_2.html#E1:35"><i><font color="Green">E24</font></i></a>, <a class="txt" href="int_2.html#E3:35"><i><font color="Green">E25</font></i></a>, <a class="ref" href="int_2.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E6:35"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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