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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="nat_1.html#NM1">Nat</a>;<br/>



<a NAME="E1:14"/>
( <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="int_2.html#R2">are_relative_prime</a>  iff <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> 1 )
 
<b>by </b><i><a class="ref" href="int_2.html#D6">INT_2:def 6</a></i>;<br/>
<a NAME="E2:14"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="int_2.html#R2">are_relative_prime</a>  iff <font color="Maroon">c<sub>1</sub></font> <a href="int_2.html#K3">gcd</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i><a class="txt" href="wsierp_1.html#E18"><i><font color="Green">Lemma13</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:14"/>
( <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="int_2.html#R2">are_relative_prime</a>  iff <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="int_2.html#R1">are_relative_prime</a>  )
 <b>by </b><i><a class="ref" href="int_2.html#D4">INT_2:def 4</a></i>;<br/>


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