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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> ;<br/>

<b>assume </b><a NAME="E1:64"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 &amp; <font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 )
 ;<br/>

<b>assume </b><a NAME="E2:64"/><i><font color="Green">E35</font></i>: 
 <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">n</font> is <a href="int_2.html#V1">prime</a>
 ;<br/>

<b>assume </b><a NAME="E3:64"/>
not <font color="Maroon">n</font> is <a href="int_2.html#V1">prime</a>
 ;<br/>

<b>then consider </b><font color="Maroon">k</font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:64"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">n</font> &amp; <font color="Maroon">k</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="ref" href="fib_num2.html#T14" target="_self">Th14</a>, <a class="ref" href="fib_num2.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E6:64"/><i><font color="Green">E65</font></i>: 
 <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="fib_num2.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E7:64"/><i><font color="Green">E66</font></i>: 
 <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="fib_num2.html#T14" target="_self">Th14</a>, , </i>;<br/>
<a NAME="E8:64"/>
 <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">k</font> <a href="nat_1.html#R1">divides</a>  <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="fib_num2.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E9:64"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="int_2.html#D5">INT_2:def 5</a></i>;<br/>


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