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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<span class="p1">(<span class="default"><a href="fib_num3.html#K2" title="FIB_NUM3:func.2">GenFib</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></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#K2" title="FIB_NUM3:func.2">GenFib</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> = 
 <a href="fib_num3.html#K2" title="FIB_NUM3:func.2">GenFib</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="fib_num3.html#T32" target="_self" title="FIB_NUM3:th.32">Th32</a></i>
<br/>.= 
 <a href="fib_num3.html#K2" title="FIB_NUM3:func.2">GenFib</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span>

;<br/>
<b>hence </b><a NAME="E2:40"/>
<span class="p1">(<span class="default"><a href="fib_num3.html#K2" title="FIB_NUM3:func.2">GenFib</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></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#K2" title="FIB_NUM3:func.2">GenFib</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">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>  <a href="fib_num3.html#K2" title="FIB_NUM3:func.2">GenFib</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span>
 ;<br/>


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