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<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c1">n</font>, <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a> </span><br/>

<a NAME="E1:80"/><span class="lab"><font color="Green" title="E59">A1</font></span>: 
<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pepin.html#T1" title="PEPIN:th.1">PEPIN:1</a></span>;<br/>
<span class="p1">(<span class="default"><a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
 <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_num.html#T5" title="FIB_NUM:th.5">FIB_NUM:5</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:80"><span class="lab"><font color="Green" title="E59">A1</font></span></a>, <a class="ref" href="int_2.html#D3" title="INT_2:def.3">INT_2:def 3</a>, <a class="ref" href="pre_ff.html#T1" title="PRE_FF:th.1">PRE_FF:1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:80"/>
 <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c1">n</font>, <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#D3" title="INT_2:def.3">INT_2:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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