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

<b>set </b><font color="Maroon">q</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,<span class="p3">(<span class="default"><a href="fib_num2.html#K2" target="_self">FIB</a>  <a href="funct_2.html#K3">.</a> 1</span>)</span></span><a href="domain_1.html#K1">]</a></span></span><a href="tarski.html#K1">}</a></span>;<br/>
<b>reconsider </b><font color="Maroon">q</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,<span class="p3">(<span class="default"><a href="fib_num2.html#K2" target="_self">FIB</a>  <a href="funct_2.html#K3">.</a> 1</span>)</span></span><a href="domain_1.html#K1">]</a></span></span><a href="tarski.html#K1">}</a></span> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i/>;<br/>
<a NAME="E2:77"/>
1 <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
;<br/>
<a NAME="E3:77"/><b>then </b><i><font color="Green">E34</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="fib_num2.html#K2" target="_self">FIB</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E4:77"/><i><font color="Green">E35</font></i>: 
<a href="fib_num2.html#K4" target="_self">OddNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:77_1"/>
<a href="fib_num2.html#K4" target="_self">OddNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:77_1_1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <a href="fib_num2.html#K4" target="_self">OddNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E2:77_1_1"/>
<a href="fib_num2.html#K4" target="_self">OddNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:77_1"/>
<span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <a href="fib_num2.html#K4" target="_self">OddNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1_2"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:77_1_2_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span>
 ;<br/><a NAME="E2:77_1_2_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 0</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:77_1_2_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="fib_num2.html#K4" target="_self">OddNAT</a> 
 ;<br/><b>hence </b><a NAME="E4:77_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="fib_num2.html#K4" target="_self">OddNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="fib_num2.html#T16" target="_self">Th16</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:77_1_2"/>
<span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <a href="fib_num2.html#K4" target="_self">OddNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div><b>end;</b></div>


</div><b>end;</b></div>
 <a href="fib_num2.html#K6" target="_self">OddFibs</a> 1 = 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="fib_num2.html#T15" target="_self">Th15</a>, , <a class="ref" href="grfunc_1.html#T89">GRFUNC_1:89</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="fib_num2.html#K2" target="_self">FIB</a>  <a href="funct_2.html#K3">.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="pnproc_1.html#T3">PNPROC_1:3</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default">1</span><a href="binarith.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="fib_num2.html#T14" target="_self">Th14</a>, <a class="ref" href="pre_ff.html#T1">PRE_FF:1</a></i>
;<br/>
<b>hence </b><a NAME="E6:77"/>
 <a href="fib_num2.html#K6" target="_self">OddFibs</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default">1</span><a href="binarith.html#K11">*&gt;</a></span>
 ;<br/>


</div>
