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<b>let </b><font color="Maroon">n</font> be  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> ;<br/>

<a NAME="E1:85"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="nat_2.html#T21">NAT_2:21</a></i>;<br/>
<b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E2:85"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/>

<b>assume </b><a NAME="E3:85"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#R1">divides</a>  <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">n</font>
 ;<br/>

<b>assume </b><a NAME="E4:85"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#R1">divides</a>  <a href="pre_ff.html#K3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 ;<br/>

<a NAME="E5:85"/>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="fib_num2.html#T18" target="_self">Th18</a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/>
<a NAME="E6:85"/><b>then </b>
 <a href="pre_ff.html#K3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>, <a href="pre_ff.html#K3">Fib</a> <font color="Maroon">n</font> <a href="int_2.html#R2">are_relative_prime</a> 
 
<b>by </b><i><a class="ref" href="fib_num2.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E7:85"/><b>then </b>
<span class="p1">(<span class="default"><a href="pre_ff.html#K3">Fib</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K10">hcf</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K3">Fib</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="int_2.html#D6">INT_2:def 6</a></i>;<br/>
<a NAME="E8:85"/><b>then </b>
<font color="Maroon">m</font> <a href="nat_1.html#R1">divides</a> 1
 
<b>by </b><i><a class="txt" href="fib_num2.html#E4:85"><i><font color="Green">E65</font></i></a>, , <a class="ref" href="nat_1.html#D5">NAT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E9:85"/>
contradiction
 <b>by </b><i>, <a class="ref" href="wsierp_1.html#T20">WSIERP_1:20</a></i>;<br/>


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