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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:64"/><i><font color="Green" title="E48">A1</font></i>: 
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp; <font color="Maroon" title="c1">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 )
 ;<br/>

<b>assume </b><a NAME="E2:64"/><i><font color="Green" title="E49">A2</font></i>: 
 <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c1">n</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>
 ;<br/>

<b>assume </b><a NAME="E3:64"/>
not <font color="Maroon" title="c1">n</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">k</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E5:64"/><i><font color="Green" title="E50">A3</font></i>: 
( <font color="Maroon" title="c2">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Maroon" title="c2">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">k</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">n</font> )
 <b>by </b><i><a class="txt" href="fib_num2.html#E1:64"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="fib_num2.html#T51" target="_self" title="FIB_NUM2:th.51">Th51</a></i>;<br/>
<a NAME="E6:64"/><i><font color="Green" title="E51">A4</font></i>: 
 <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c2">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 
<b>by </b><i><a class="txt" href="fib_num2.html#E5:64"><i><font color="Green" title="E50">A3</font></i></a>, <a class="ref" href="fib_num2.html#T49" target="_self" title="FIB_NUM2:th.49">Th49</a></i>;<br/>
<a NAME="E7:64"/><i><font color="Green" title="E52">A5</font></i>: 
 <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c2">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="txt" href="fib_num2.html#E1:64"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="fib_num2.html#E5:64"><i><font color="Green" title="E50">A3</font></i></a>, <a class="ref" href="fib_num2.html#T50" target="_self" title="FIB_NUM2:th.50">Th50</a></i>;<br/>
<a NAME="E8:64"/>
 <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c2">k</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="txt" href="fib_num2.html#E5:64"><i><font color="Green" title="E50">A3</font></i></a>, <a class="ref" href="fib_num2.html#T44" target="_self" title="FIB_NUM2:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E9:64"/>
contradiction
 <b>by </b><i><a class="txt" href="fib_num2.html#E2:64"><i><font color="Green" title="E49">A2</font></i></a>, <a class="txt" href="fib_num2.html#E6:64"><i><font color="Green" title="E51">A4</font></i></a>, <a class="txt" href="fib_num2.html#E7:64"><i><font color="Green" title="E52">A5</font></i></a>, <a class="ref" href="int_2.html#D5" title="INT_2:def.5">INT_2:def 5</a></i>;<br/>


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