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

<b>set </b><font color="Maroon">L0</font> =  <a href="ami_3.html#K16">il.</a> 0;<br/>
<b>set </b><font color="Maroon">L1</font> =  <a href="ami_3.html#K16">il.</a> 1;<br/>
<b>set </b><font color="Maroon">L2</font> =  <a href="ami_3.html#K16">il.</a> 2;<br/>
<b>set </b><font color="Maroon">L3</font> =  <a href="ami_3.html#K16">il.</a> 3;<br/>
<b>set </b><font color="Maroon">L4</font> =  <a href="ami_3.html#K16">il.</a> 4;<br/>
<b>set </b><font color="Maroon">L5</font> =  <a href="ami_3.html#K16">il.</a> 5;<br/>
<b>set </b><font color="Maroon">L6</font> =  <a href="ami_3.html#K16">il.</a> 6;<br/>
<b>set </b><font color="Maroon">L7</font> =  <a href="ami_3.html#K16">il.</a> 7;<br/>
<b>set </b><font color="Maroon">L8</font> =  <a href="ami_3.html#K16">il.</a> 8;<br/>
<b>set </b><font color="Maroon">c2</font> =  <a href="ami_3.html#K15">dl.</a> 0;<br/>
<b>set </b><font color="Maroon">n</font> =  <a href="ami_3.html#K15">dl.</a> 1;<br/>
<b>set </b><font color="Maroon">a</font> =  <a href="ami_3.html#K15">dl.</a> 2;<br/>
<b>set </b><font color="Maroon">b</font> =  <a href="ami_3.html#K15">dl.</a> 3;<br/>
<b>set </b><font color="Maroon">aux</font> =  <a href="ami_3.html#K15">dl.</a> 4;<br/>
<b>let </b><font color="Maroon">N</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:11"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">N</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>let </b><font color="Maroon">S</font> be    <a href="scm_1.html#M1">State-consisting</a> of 0,0,0, <a href="fib_fusc.html#K3" target="_self">Fusc_Program</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="scm_1.html#K1">&lt;*</a><span class="default">2</span><a href="scm_1.html#K1">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="scm_1.html#K1">&lt;*</a><span class="default"><font color="Maroon">N</font></span><a href="scm_1.html#K1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="scm_1.html#K1">&lt;*</a><span class="default">1</span><a href="scm_1.html#K1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="scm_1.html#K1">&lt;*</a><span class="default">0</span><a href="scm_1.html#K1">*&gt;</a></span>;<br/>

<b>consider </b><font color="Maroon">s</font> being   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:11"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font>
 ;<br/>
<a NAME="E4:11"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="ami_3.html#K9">=0_goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 8</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E5:11"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="ami_3.html#K3">:=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E6:11"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 2</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7">Divide</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E7:11"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="ami_3.html#K9">=0_goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 6</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E8:11"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 4</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4">AddTo</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E9:11"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 5</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E10:11"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 6</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4">AddTo</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E11:11"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 7</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E12:11"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 8</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> 
 
<b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E13:11"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">N</font> &amp; <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E14:11"/><i><font color="Green">E58</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 implies for <font color="Olive">u</font> being  <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a>   st <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> holds <br/>(  <a href="ami_1.html#K6">IC</a> <font color="Olive">u</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">N</font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> &amp; <font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  &amp;  <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</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"><font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> ) );<br/>
<a NAME="E15:11"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 ;<br/>

<b>let </b><font color="Maroon">u</font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>assume </b><a NAME="E2:11_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> 0</span>)</span>
 ;<br/>

<a NAME="E3:11_1"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>;<br/>
<b>hence </b><a NAME="E4:11_1"/>
(  <a href="ami_1.html#K6">IC</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>

<b>thus </b><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> = 
<font color="Maroon">N</font> <a href="int_1.html#K5">div</a> 1
<b>by </b><i>, <a class="txt" href="fib_fusc.html#E4"><i><font color="Green">Lemma24</font></i></a>, <a class="ref" href="pre_ff.html#T2">PRE_FF:2</a></i>
<br/>.= 
<font color="Maroon">N</font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T9">NEWTON:9</a></i>
;<br/>

<b>thus </b><a NAME="E6:11_1"/>
<font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i>, <a class="txt" href="fib_fusc.html#E4"><i><font color="Green">Lemma24</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>

<b>thus </b><a NAME="E7:11_1"/>
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</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"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="fib_fusc.html#E4"><i><font color="Green">Lemma24</font></i></a>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E16:11"/><i><font color="Green">E64</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:11_2"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 implies for <font color="Olive">u</font> being  <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a>   st <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> holds <br/>(  <a href="ami_1.html#K6">IC</a> <font color="Olive">u</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">N</font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">k</font></span>)</span> &amp; <font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  &amp;  <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</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"><font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive">u</font> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> ) )
 ;<br/>

<b>assume </b><a NAME="E2:11_2"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 ;<br/>

<b>let </b><font color="Maroon">u</font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>assume </b><a NAME="E3:11_2"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon">t</font> = 6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font>;<br/>
<b>set </b><font color="Maroon">t0</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span>;<br/>
<a NAME="E4:11_2"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E5:11_2"/><b>then </b><i><font color="Green">E72</font></i>: 
(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">N</font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">k</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i>, <a class="txt" href="fib_fusc.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E6:11_2"/>
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="power.html#K5">log</a> 2,<font color="Maroon">N</font>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E7:11_2"/><b>then </b>
2 <a href="power.html#K3">to_power</a> <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="power.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pre_ff.html#T10">PRE_FF:10</a></i>;<br/>
<a NAME="E8:11_2"/><b>then </b>
2 <a href="power.html#K3">to_power</a> <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">N</font>
 
<b>by </b><i>, <a class="ref" href="power.html#D3">POWER:def 3</a></i>;<br/>
<a NAME="E9:11_2"/><b>then </b><i><font color="Green">E73</font></i>: 
( 2 <a href="card_4.html#K1">|^</a> <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">N</font> &amp; 2 <a href="card_4.html#K1">|^</a> <font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 
<b>by </b><i><a class="ref" href="newton.html#T102">NEWTON:102</a>, <a class="ref" href="power.html#T48">POWER:48</a></i>;<br/>
<a NAME="E10:11_2"/><b>then </b><i><font color="Green">E74</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i>, <a class="ref" href="pre_ff.html#T3">PRE_FF:3</a></i>;<br/>
<b>set </b><font color="Maroon">t1</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<a NAME="E11:11_2"/><i><font color="Green">E76</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, , <a class="txt" href="fib_fusc.html#E8"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/>
<a NAME="E12:11_2"/><i><font color="Green">E77</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> )
 
<b>by </b><i>, , <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/>
<b>set </b><font color="Maroon">t2</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>;<br/>
<a NAME="E13:11_2"/><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E14:11_2"/><b>then </b><i><font color="Green">E81</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, , <a class="ref" href="scm_1.html#T18">SCM_1:18</a></i>;<br/>
<a NAME="E15:11_2"/><i><font color="Green">E83</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i>, , , , <a class="ref" href="scm_1.html#T18">SCM_1:18</a></i>;<br/>
<a NAME="E16:11_2"/><i><font color="Green">E84</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> )
 
<b>by </b><i>, , , , , <a class="ref" href="scm_1.html#T18">SCM_1:18</a></i>;<br/>
<b>set </b><font color="Maroon">t3</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>;<br/>
<a NAME="E17:11_2"/><i><font color="Green">E85</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3
 
;<br/>
<a NAME="E18:11_2"/><b>then </b><i><font color="Green">E87</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, , , <a class="ref" href="scm_1.html#T22">SCM_1:22</a></i>;<br/>
<a NAME="E19:11_2"/><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K5">div</a> 2
 
<b>by </b><i>, , , , , , <a class="ref" href="scm_1.html#T22">SCM_1:22</a></i>;<br/>
<b>then </b><i><font color="Green">E89</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> = 
<font color="Maroon">N</font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K2">*</a> 2</span>)</span>
<b>by </b><i>, <a class="txt" href="fib_fusc.html#E7"><i><font color="Green">Lemma30</font></i></a>, <a class="ref" href="pre_ff.html#T5">PRE_FF:5</a></i>
<br/>.= 
<font color="Maroon">N</font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
;<br/>
<a NAME="E21:11_2"/><i><font color="Green">E91</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> 2
 
<b>by </b><i>, , , , , , <a class="ref" href="scm_1.html#T22">SCM_1:22</a></i>;<br/>
<a NAME="E22:11_2"/><i><font color="Green">E92</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> )
 
<b>by </b><i>, , , , , , <a class="ref" href="scm_1.html#T22">SCM_1:22</a></i>;<br/>
<b>set </b><font color="Maroon">t4</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span>;<br/>
<a NAME="E23:11_2"/><i><font color="Green">E93</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4
 
;<br/>
<b>set </b><font color="Maroon">t5</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span>;<br/>
<a NAME="E24:11_2"/><i><font color="Green">E95</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5
 
;<br/>
<b>set </b><font color="Maroon">t6</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span>;<br/>
<a NAME="E25:11_2"/><i><font color="Green">E96</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 6
 
;<br/>
<a NAME="E26:11_2"/><i><font color="Green">E98</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K6">mod</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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K5">div</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="int_1.html#D8">INT_1:def 8</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:11_2_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#R1">=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_2_1"><b>suppose </b></a><a NAME="E1:11_2_2_1"/><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:11_2_2_1"/><b>then </b><i><font color="Green">E100</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , , <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/><a NAME="E3:11_2_2_1"/><i><font color="Green">E101</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> )
 <b>by </b><i>, , , , <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/><a NAME="E4:11_2_2_1"/><i><font color="Green">E102</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E1"><i><font color="Green">Lemma16</font></i></a>, , <a class="txt" href="fib_fusc.html#E7:11"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E5:11_2_2_1"/><i><font color="Green">E104</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E1"><i><font color="Green">Lemma16</font></i></a>, , <a class="txt" href="fib_fusc.html#E7:11"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fib_fusc.html#E8:11"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E6:11_2_2_1"/><i><font color="Green">E105</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E1"><i><font color="Green">Lemma16</font></i></a>, , <a class="txt" href="fib_fusc.html#E7:11"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fib_fusc.html#E8:11"><i><font color="Green">E50</font></i></a>, , <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E7:11_2_2_1"/><b>then </b><i><font color="Green">E106</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E2"><i><font color="Green">Lemma17</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E9:11"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><a NAME="E8:11_2_2_1"/><i><font color="Green">E120</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E2"><i><font color="Green">Lemma17</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E9:11"><i><font color="Green">E51</font></i></a>, <a class="txt" href="fib_fusc.html#E10:11"><i><font color="Green">E52</font></i></a>, <a class="txt" href="fib_fusc.html#E11:11"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><b>thus </b><a NAME="E9:11_2_2_1"/>
(  <a href="ami_1.html#K6">IC</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">N</font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E2"><i><font color="Green">Lemma17</font></i></a>, <a class="txt" href="fib_fusc.html#E6"><i><font color="Green">Lemma27</font></i></a>, , <a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E9:11"><i><font color="Green">E51</font></i></a>, <a class="txt" href="fib_fusc.html#E11:11"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><b>thus </b><a NAME="E10:11_2_2_1"/>
<font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="txt" href="fib_fusc.html#E6"><i><font color="Green">Lemma27</font></i></a>, , , <a class="txt" href="fib_fusc.html#E12:11"><i><font color="Green">E54</font></i></a>, <a class="ref" href="pre_ff.html#T7">PRE_FF:7</a></i>;<br/><b>reconsider </b><font color="Maroon">un</font> = <font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>, <font color="Maroon">tn</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="txt" href="fib_fusc.html#E6"><i><font color="Green">Lemma27</font></i></a>, , , <a class="txt" href="fib_fusc.html#E12:11"><i><font color="Green">E54</font></i></a>, <a class="ref" href="pre_ff.html#T7">PRE_FF:7</a></i>;<br/><i><font color="Green">E123</font></i>: <font color="Maroon">tn</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K5">div</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E5:11"><i><font color="Green">E47</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">un</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="fib_fusc.html#E6"><i><font color="Green">Lemma27</font></i></a>, , <a class="txt" href="fib_fusc.html#E12:11"><i><font color="Green">E54</font></i></a>, , <a class="txt" href="fib_fusc.html#E6:11"><i><font color="Green">E48</font></i></a>, <a class="ref" href="pre_ff.html#T6">PRE_FF:6</a></i>
;<br/><a NAME="E13:11_2_2_1"/><b>then </b><i><font color="Green">E124</font></i>: 
<font color="Maroon">tn</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">un</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><i><font color="Green">E125</font></i>:  <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> = 
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">tn</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">un</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <span class="p2">(<span class="default"><font color="Maroon">un</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E13:11"><i><font color="Green">E56</font></i></a>, <a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <span class="p2">(<span class="default"><font color="Maroon">un</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i/>
;<br/><i><font color="Green">E126</font></i>:  <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> = 
 <a href="pre_ff.html#K5">Fusc</a> <span class="p1">(<span class="default"><font color="Maroon">tn</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="pre_ff.html#K5">Fusc</a> <span class="p1">(<span class="default"><font color="Maroon">un</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
<br/>.= 
 <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i/>
;<br/><b>reconsider </b><font color="Maroon">un</font> = <font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>, <font color="Maroon">tn</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> as   <a href="int_1.html#NM1">Integer</a> ;<br/><b>reconsider </b><font color="Maroon">ta</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span>, <font color="Maroon">tb</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> as   <a href="int_1.html#NM1">Integer</a> ;<br/><a NAME="E18:11_2_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">ta</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">tn</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">tb</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">tn</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">un</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">un</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E14:11"><i><font color="Green">E58</font></i></a>, , <a class="txt" href="fib_fusc.html#E6"><i><font color="Green">Lemma27</font></i></a>, </i>;<br/><b>hence </b><a NAME="E19:11_2_2_1"/>
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</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"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="fib_fusc.html#E5"><i><font color="Green">Lemma26</font></i></a>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_2_2"><b>suppose </b></a><a NAME="E1:11_2_2_2"/><i><font color="Green">E129</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:11_2_2_2"/><b>then </b><i><font color="Green">E130</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 6
 <b>by </b><i>, , , <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/><a NAME="E3:11_2_2_2"/><i><font color="Green">E131</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> )
 <b>by </b><i>, , , , <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/><a NAME="E4:11_2_2_2"/><i><font color="Green">E132</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , <a class="txt" href="fib_fusc.html#E7:11"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E5:11_2_2_2"/><i><font color="Green">E133</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span>
 <b>by </b><i>, , <a class="txt" href="fib_fusc.html#E7:11"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fib_fusc.html#E8:11"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E6:11_2_2_2"/><i><font color="Green">E134</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> )
 <b>by </b><i>, , <a class="txt" href="fib_fusc.html#E7:11"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fib_fusc.html#E8:11"><i><font color="Green">E50</font></i></a>, , <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E7:11_2_2_2"/><b>then </b><i><font color="Green">E135</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> )
 <b>by </b><i>, <a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E9:11"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><a NAME="E8:11_2_2_2"/><i><font color="Green">E136</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> )
 <b>by </b><i>, <a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E9:11"><i><font color="Green">E51</font></i></a>, <a class="txt" href="fib_fusc.html#E10:11"><i><font color="Green">E52</font></i></a>, <a class="txt" href="fib_fusc.html#E11:11"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><b>thus </b><a NAME="E9:11_2_2_2"/>
(  <a href="ami_1.html#K6">IC</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">N</font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  )
 <b>by </b><i>, <a class="txt" href="fib_fusc.html#E6"><i><font color="Green">Lemma27</font></i></a>, , , , <a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E9:11"><i><font color="Green">E51</font></i></a>, <a class="txt" href="fib_fusc.html#E12:11"><i><font color="Green">E54</font></i></a>, <a class="ref" href="pre_ff.html#T7">PRE_FF:7</a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><b>reconsider </b><font color="Maroon">un</font> = <font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>, <font color="Maroon">tn</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="txt" href="fib_fusc.html#E6"><i><font color="Green">Lemma27</font></i></a>, , , <a class="txt" href="fib_fusc.html#E12:11"><i><font color="Green">E54</font></i></a>, <a class="ref" href="pre_ff.html#T7">PRE_FF:7</a></i>;<br/><a NAME="E11:11_2_2_2"/><i><font color="Green">E137</font></i>: 
<font color="Maroon">tn</font> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <font color="Maroon">un</font>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E6"><i><font color="Green">Lemma27</font></i></a>, , , <a class="txt" href="fib_fusc.html#E5:11"><i><font color="Green">E47</font></i></a>, <a class="txt" href="fib_fusc.html#E6:11"><i><font color="Green">E48</font></i></a>, <a class="txt" href="fib_fusc.html#E12:11"><i><font color="Green">E54</font></i></a></i>;<br/><i><font color="Green">E138</font></i>:  <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> = 
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">tn</font>
<b>by </b><i/>
<br/>.= 
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">un</font>
<b>by </b><i><a class="txt" href="fib_fusc.html#E13:11"><i><font color="Green">E56</font></i></a>, <a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
<br/>.= 
 <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span>
<b>by </b><i/>
;<br/><i><font color="Green">E139</font></i>:  <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> = 
 <a href="pre_ff.html#K5">Fusc</a> <span class="p1">(<span class="default"><font color="Maroon">tn</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">un</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <span class="p2">(<span class="default"><font color="Maroon">un</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E13:11"><i><font color="Green">E56</font></i></a>, <a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">un</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i/>
;<br/><b>reconsider </b><font color="Maroon">un</font> = <font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>, <font color="Maroon">tn</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>, <font color="Maroon">ta</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span>, <font color="Maroon">tb</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> as   <a href="int_1.html#NM1">Integer</a> ;<br/><a NAME="E15:11_2_2_2"/>
<span class="p1">(<span class="default"><font color="Maroon">ta</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">tn</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">tb</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">tn</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">ta</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">tb</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">un</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">tb</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">un</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="fib_fusc.html#E14:11"><i><font color="Green">E58</font></i></a></i>;<br/><b>hence </b><a NAME="E16:11_2_2_2"/>
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</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"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">u</font> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="fib_fusc.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="txt" href="fib_fusc.html#E6"><i><font color="Green">Lemma27</font></i></a>, , , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E17:11"/><i><font color="Green">E140</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E23</font></i></a>, <a class="txt" href="fib_fusc.html#E4"><i><font color="Green">Lemma24</font></i></a>);<br/></i>
<b>set </b><font color="Maroon">k</font> = <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span></span><a href="int_1.html#K1">/]</a></span>;<br/>
<a NAME="E18:11"/><i><font color="Green">E141</font></i>: 
<span class="p1">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span></span><a href="int_1.html#K1">/]</a></span>
 
<b>by </b><i><a class="ref" href="int_1.html#D4">INT_1:def 4</a></i>;<br/>
<a NAME="E19:11"/>
<font color="Maroon">N</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E20:11"/><b>then </b>
 <a href="power.html#K5">log</a> 2,<font color="Maroon">N</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="power.html#K6">log</a> 2,1
 
<b>by </b><i><a class="ref" href="pre_ff.html#T12">PRE_FF:12</a></i>;<br/>
<a NAME="E21:11"/><b>then </b><i><font color="Green">E142</font></i>: 
(  <a href="power.html#K5">log</a> 2,<font color="Maroon">N</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp;  <a href="power.html#K5">log</a> 2,<font color="Maroon">N</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1 )
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="power.html#T59">POWER:59</a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/>
<a NAME="E22:11"/><b>then </b>
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E23:11"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span></span><a href="int_1.html#K1">/]</a></span>
 
<b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">k</font> = <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<b>set </b><font color="Maroon">u</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/>
<a NAME="E25:11"/>
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="power.html#K5">log</a> 2,<font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="int_1.html#D4">INT_1:def 4</a></i>;<br/>
<a NAME="E26:11"/><b>then </b>
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E27:11"/><b>then </b><i><font color="Green">E143</font></i>: 
(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">N</font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp;  <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p0">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p0">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E28:11"/>
2 <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 <a href="power.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E6"><i><font color="Green">Lemma27</font></i></a>, <a class="ref" href="power.html#T44">POWER:44</a></i>;<br/>
<a NAME="E29:11"/><b>then </b>
2 <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">N</font>
 
<b>by </b><i>, <a class="ref" href="power.html#D3">POWER:def 3</a></i>;<br/>
<a NAME="E30:11"/><b>then </b>
2 <a href="card_4.html#K1">|^</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="power.html#T48">POWER:48</a></i>;<br/>
<a NAME="E31:11"/><b>then </b><i><font color="Green">E144</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E1:11"><i><font color="Green">E22</font></i></a>, , <a class="ref" href="pre_ff.html#T4">PRE_FF:4</a></i>;<br/>
<b>then </b><i><font color="Green">E145</font></i>: <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p0">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p0">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> = 
<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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <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="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p0">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
;<br/>
<b>set </b><font color="Maroon">h</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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> 1</span>)</span>;<br/>
<a NAME="E33:11"/><i><font color="Green">E147</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 8
 
<b>by </b><i>, , , <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/>
<a NAME="E34:11"/><i><font color="Green">E148</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span>
 
<b>by </b><i>, , <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/>
<b>thus </b><a NAME="E35:11"/>
<font color="Maroon">S</font> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i>, <a class="txt" href="fib_fusc.html#E3"><i><font color="Green">Lemma20</font></i></a>, <a class="txt" href="fib_fusc.html#E8"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="scm_1.html#T3">SCM_1:3</a></i>;<br/>

<b>thus </b><a NAME="E36:11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">S</font></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">N</font>
 <b>by </b><i>, <a class="txt" href="fib_fusc.html#E3"><i><font color="Green">Lemma20</font></i></a>, , <a class="txt" href="fib_fusc.html#E7"><i><font color="Green">Lemma30</font></i></a>, <a class="txt" href="fib_fusc.html#E8"><i><font color="Green">Lemma31</font></i></a>, , <a class="ref" href="scm_1.html#T4">SCM_1:4</a></i>;<br/>

<a NAME="E37:11"/>
( <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a>  &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <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="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a>  )
 
<b>by </b><i>, , , <a class="txt" href="fib_fusc.html#E8"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a>, <a class="ref" href="scm_1.html#T26">SCM_1:26</a></i>;<br/>
<b>hence </b><a NAME="E38:11"/>
 <a href="scm_1.html#K2">Complexity</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="int_1.html#K1">[\</a><span class="default"><span class="p4">(<span class="default"><a href="power.html#K5">log</a> 2,<font color="Maroon">N</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i>, <a class="ref" href="scm_1.html#T17">SCM_1:17</a></i>;<br/>


</div>
