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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:11"/><i><font color="Green" title="E12">A1</font></i>: 
( <font color="Maroon" title="c1">p</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> &amp; <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">n</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a>  )
 ;<br/>

<b>assume </b><a NAME="E2:11"/>
<font color="Maroon" title="c1">p</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">n</font>
 ;<br/>

<a NAME="E3:11"/><b>then </b>
<font color="Maroon" title="c2">n</font> <a href="nat_d.html#K6" title="NAT_D:func.6">hcf</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="newton.html#T62" title="NEWTON:th.62">NEWTON:62</a></i>;<br/>
<a NAME="E4:11"/><b>then </b>
<font color="Maroon" title="c2">n</font> <a href="nat_d.html#K6" title="NAT_D:func.6">hcf</a> <font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="int_4.html#E1:11"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="int_2.html#D5" title="INT_2:def.5">INT_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:11"/>
contradiction
 <b>by </b><i><a class="txt" href="int_4.html#E1:11"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="int_2.html#D4" title="INT_2:def.4">INT_2:def 4</a></i>;<br/>


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