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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/>

<a NAME="E1:49"/>
(  <a href="fib_num3.html#K2" title="FIB_NUM3:func.2">GenFib</a> 2,1,<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fib_num3.html#K1" title="FIB_NUM3:func.1">Lucas</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="fib_num3.html#K2" title="FIB_NUM3:func.2">GenFib</a> 2,1,<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fib_num3.html#K1" title="FIB_NUM3:func.1">Lucas</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span> &amp; 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p1">(<span class="default"><a href="fib_num3.html#K2" title="FIB_NUM3:func.2">GenFib</a> 2,1,<span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p1">(<span class="default"><a href="fib_num3.html#K1" title="FIB_NUM3:func.1">Lucas</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="fib_num3.html#T38" target="_self" title="FIB_NUM3:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E2:49"/>
<span class="p1">(<span class="default"><a href="fib_num3.html#K1" title="FIB_NUM3:func.1">Lucas</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="fib_num3.html#K1" title="FIB_NUM3:func.1">Lucas</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p1">(<span class="default"><a href="fib_num3.html#K1" title="FIB_NUM3:func.1">Lucas</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="fib_num3.html#T39" target="_self" title="FIB_NUM3:th.39">Th39</a></i>;<br/>


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