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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:13"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">k</font>
 ;<br/>

<b>assume </b><a NAME="E2:13"/><i><font color="Green">E39</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font>
 ;<br/>

<a NAME="E3:13"/><b>then </b>
1 <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E4:13"/><b>then </b><i><font color="Green">E40</font></i>: 
2 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>consider </b><font color="Maroon">p</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:13"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">p</font> is <a href="int_2.html#V1">prime</a> &amp; <font color="Maroon">p</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> )
 <b>by </b><i>, <a class="ref" href="int_2.html#T48">INT_2:48</a></i>;<br/>
<b>take </b>
<font color="Maroon">p</font>
;<br/>

<b>thus </b><a NAME="E7:13"/>
<font color="Maroon">p</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">k</font>
 <b>by </b><i>, , <a class="ref" href="nat_1.html#T51">NAT_1:51</a></i>;<br/>

<b>thus </b><a NAME="E8:13"/>
<font color="Maroon">p</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 <b>by </b><i>, , <a class="ref" href="nat_1.html#T54">NAT_1:54</a></i>;<br/>

<b>thus </b><a NAME="E9:13"/>
<font color="Maroon">p</font> is <a href="int_2.html#V1">prime</a>
 <b>by </b><i/>;<br/>


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