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<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:7"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">p</font> is <a href="int_2.html#V1">prime</a>
 ;<br/>

<a NAME="E2:7"/>
<font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> <font color="Maroon">p</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#D5">NAT_1:def 5</a></i>;<br/>
<a NAME="E3:7"/><b>then </b>
( <font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> )
 
<b>by </b><i>, <a class="ref" href="int_2.html#D5">INT_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:7"/>
( <font color="Maroon">m</font>,<font color="Maroon">p</font> <a href="int_2.html#R2">are_relative_prime</a>  or <font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> )
 <b>by </b><i><a class="ref" href="int_2.html#D6">INT_2:def 6</a></i>;<br/>


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