<?xml version="1.0"?>
<div class="add">

<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/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <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> ] <b>means </b> <a href="fib_num2.html#K6" title="FIB_NUM2:func.6">OddFibs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> $1</span>)</span> <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> <span class="p1">(<span class="default"><a href="fib_num2.html#K6" title="FIB_NUM2:func.6">OddFibs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> $1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">^</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> $1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span>;<br/>
<a NAME="E1:81"/><i><font color="Green" title="E61">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i><a class="ref" href="fib_num2.html#T24" target="_self" title="FIB_NUM2:th.24">Th24</a>, <a class="ref" href="fib_num2.html#T62" target="_self" title="FIB_NUM2:th.62">Th62</a>, <a class="ref" href="fib_num2.html#T63" target="_self" title="FIB_NUM2:th.63">Th63</a></i>;<br/>
<a NAME="E2:81"/><i><font color="Green" title="E62">A2</font></i>: 
for <font color="Olive" title="b1">k</font> being   <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>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">k</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/>

<b>assume </b><a NAME="E1:81_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">k</font>]
 ;<br/>

<b>set </b><font color="Maroon" title="c3">LEFTk</font> =  <a href="fib_num2.html#K6" title="FIB_NUM2:func.6">OddFibs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k</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> 3</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c4">RIGHTk</font> = <span class="p1">(<span class="default"><a href="fib_num2.html#K6" title="FIB_NUM2:func.6">OddFibs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">k</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> 1</span>)</span></span>)</span> <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">^</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">k</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> 3</span>)</span></span>)</span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">RS</font> = <a href="fib_num2.html#K2" title="FIB_NUM2:func.2">FIB</a>  <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fib_num2.html#K4" title="FIB_NUM2:func.4">OddNAT</a>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span></span>)</span> as   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c6">ARR</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,<span class="p3">(<span class="default"><a href="fib_num2.html#K2" title="FIB_NUM2:func.2">FIB</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5</span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> <b>by </b><i><a class="ref" href="fib_num2.html#T19" target="_self" title="FIB_NUM2:th.19">Th19</a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">RR</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c6">ARR</font>;<br/>
<a NAME="E4:81_1"/><i><font color="Green" title="E63">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">RS</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="fib_num2.html#K4" title="FIB_NUM2:func.4">OddNAT</a>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T87" title="RELAT_1:th.87">RELAT_1:87</a></i>;<br/>
<a NAME="E5:81_1"/>
<a href="fib_num2.html#K4" title="FIB_NUM2:func.4">OddNAT</a>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E6:81_1"/><b>then </b><i><font color="Green" title="E64">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">RS</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_num2.html#E4:81_1"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E7:81_1"/>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">p1</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E9:81_1"/><i><font color="Green" title="E65">A5</font></i>: 
( <font color="Maroon" title="c5">RS</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">p1</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> )
 <b>by </b><i><a class="txt" href="fib_num2.html#E6:81_1"><i><font color="Green" title="E64">A4</font></i></a>, <a class="ref" href="fib_num2.html#T21" target="_self" title="FIB_NUM2:th.21">Th21</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">p2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E11:81_1"/><i><font color="Green" title="E66">A6</font></i>: 
<font color="Maroon" title="c6">ARR</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">p2</font>
 <b>by </b><i><a class="ref" href="fib_num2.html#T22" target="_self" title="FIB_NUM2:th.22">Th22</a></i>;<br/>
<a NAME="E12:81_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
 
<b>by </b><i><a class="txt" href="fib_num2.html#E9:81_1"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c10">RSR</font> being   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a><b> such that </b><br/><a NAME="E14:81_1"/><i><font color="Green" title="E67">A7</font></i>: 
<font color="Maroon" title="c10">RSR</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">RS</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c6">ARR</font></span>)</span>
 <b>and </b><br/><a NAME="E15:81_1"/><i><font color="Green" title="E68">A8</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c5">RS</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c6">ARR</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c10">RSR</font>
 <b>by </b><i><a class="txt" href="fib_num2.html#E9:81_1"><i><font color="Green" title="E65">A5</font></i></a>, <a class="txt" href="fib_num2.html#E11:81_1"><i><font color="Green" title="E66">A6</font></i></a>, <a class="ref" href="pnproc_1.html#T82" title="PNPROC_1:th.82">PNPROC_1:82</a></i>;<br/>
<a NAME="E16:81_1"/>
1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5
 
;<br/>
<a NAME="E17:81_1"/><b>then </b><i><font color="Green" title="E69">A9</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c6">ARR</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5</span>)</span>,<span class="p3">(<span class="default"><a href="fib_num2.html#K2" title="FIB_NUM2:func.2">FIB</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5</span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="fib_num2.html#T20" target="_self" title="FIB_NUM2:th.20">Th20</a></i>;<br/>
<span class="p1">(<span class="default"><a href="fib_num2.html#K6" title="FIB_NUM2:func.6">OddFibs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">k</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> 1</span>)</span></span>)</span> <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">^</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">k</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> 3</span>)</span></span>)</span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <span class="p2">(<span class="default"><a href="fib_num2.html#K2" title="FIB_NUM2:func.2">FIB</a>  <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p3">(<span class="default"><a href="fib_num2.html#K4" title="FIB_NUM2:func.4">OddNAT</a>  <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="fib_num2.html#K2" title="FIB_NUM2:func.2">FIB</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5</span>)</span></span>)</span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="fib_num2.html#D2" target="_self" title="FIB_NUM2:def.2">Def2</a></i>
<br/>.= 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c10">RSR</font>
<b>by </b><i><a class="txt" href="fib_num2.html#E15:81_1"><i><font color="Green" title="E68">A8</font></i></a>, <a class="ref" href="pnproc_1.html#T3" title="PNPROC_1:th.3">PNPROC_1:3</a></i>
<br/>.= 
 <a href="fib_num2.html#K6" title="FIB_NUM2:func.6">OddFibs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k</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> 3</span>)</span>
<b>by </b><i><a class="txt" href="fib_num2.html#E14:81_1"><i><font color="Green" title="E67">A7</font></i></a>, <a class="txt" href="fib_num2.html#E17:81_1"><i><font color="Green" title="E69">A9</font></i></a>, <a class="ref" href="fib_num2.html#T65" target="_self" title="FIB_NUM2:th.65">Th65</a></i>
;<br/>
<b>hence </b><a NAME="E19:81_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:81"/>
for <font color="Olive" title="b1">k</font> being   <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>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="fib_num2.html#E1:81"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="fib_num2.html#E2:81"><i><font color="Green" title="E62">A2</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:81"/>
 <a href="fib_num2.html#K6" title="FIB_NUM2:func.6">OddFibs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <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> <span class="p1">(<span class="default"><a href="fib_num2.html#K6" title="FIB_NUM2:func.6">OddFibs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">^</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span>
 ;<br/>


</div>
