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

<b>assume </b><a NAME="E1:9"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:9_1"/>
( <font color="Maroon">n</font> is   <a href="newton.html#NM1">Prime</a> or  not <font color="Maroon">n</font> is   <a href="newton.html#NM1">Prime</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1"><b>suppose </b></a><a NAME="E1:9_1_1"/>
<font color="Maroon">n</font> is   <a href="newton.html#NM1">Prime</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:9_1_1"/>
 ex <font color="Olive">p</font> being  <a href="newton.html#NM1">Prime</a> st <font color="Olive">p</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_2"><b>suppose </b></a><a NAME="E1:9_1_2"/>
<font color="Maroon">n</font> is  not   <a href="newton.html#NM1">Prime</a>
 ;<br/><div class="add"><a NAME="E2:9_1_2"/><b>then </b>
 ex <font color="Olive">p</font> being  <a href="newton.html#NM1">Prime</a> st <br/>( <font color="Olive">p</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> &amp; <font color="Olive">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">n</font> )
 <b>by </b><i>, , <a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/><b>hence </b><a NAME="E3:9_1_2"/>
 ex <font color="Olive">p</font> being  <a href="newton.html#NM1">Prime</a> st <font color="Olive">p</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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