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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/>

<a NAME="E1:49"/>
(  <a href="fib_num3.html#K2" target="_self">GenFib</a> 2,1,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="fib_num3.html#K1" target="_self">Lucas</a> <font color="Maroon">n</font> &amp;  <a href="fib_num3.html#K2" target="_self">GenFib</a> 2,1,<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="hidden.html#R1">=</a>  <a href="fib_num3.html#K1" target="_self">Lucas</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 3</span>)</span> &amp; 2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> 2,1,<span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="fib_num3.html#K1" target="_self">Lucas</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="fib_num3.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E2:49"/>
<span class="p1">(<span class="default"><a href="fib_num3.html#K1" target="_self">Lucas</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="fib_num3.html#K1" target="_self">Lucas</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="fib_num3.html#K1" target="_self">Lucas</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="fib_num3.html#E4"><i><font color="Green">Lemma31</font></i></a></i>;<br/>


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