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<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>set </b><font color="Maroon">a1</font> =  <a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">b1</font> =  <a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="prepower.html#K3">|^</a> 2 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="prepower.html#K3">|^</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="wsierp_1.html#T2">WSIERP_1:2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="prepower.html#K3">|^</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="prepower.html#K3">|^</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="wsierp_1.html#T2">WSIERP_1:2</a></i>
;<br/>
<b>hence </b><a NAME="E2:38"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="prepower.html#K3">|^</a> 2 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="prepower.html#K3">|^</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fib_num3.html#K2" target="_self">GenFib</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="prepower.html#K3">|^</a> 2</span>)</span>
 ;<br/>


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