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

<span class="kw">set </span><font color="Maroon" title="c1">c2</font> =  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">n</font> =  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">a</font> =  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">b</font> =  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">aux</font> =  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">L6</font> = 6;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">L7</font> = 7;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">L8</font> = 8;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">L0</font> =  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">L1</font> = 1;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">L2</font> = 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">L3</font> = 3;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">L4</font> = 4;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">L5</font> = 5;<br/>
<span class="kw">let </span><font color="Maroon" title="c15">N</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c15">N</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies for <font color="Olive" title="b1">s</font> being   <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="fib_fusc.html#K3" title="FIB_FUSC:func.3">Fusc_Program</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default">2</span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c15">N</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default">1</span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> holds <br/> (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Olive" title="b1">s</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p4">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:11"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<font color="Maroon" title="c15">N</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being   <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="fib_fusc.html#K3" title="FIB_FUSC:func.3">Fusc_Program</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default">2</span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c15">N</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default">1</span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> holds <br/> (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Olive" title="b1">s</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p4">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c16">k</font> = <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span>;<br/>
<a NAME="E2:11"/>
<span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D4" title="INT_1:def.4">INT_1:def 4</a></span>;<br/>
<a NAME="E3:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A2</font></span>: 
 <a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></span>;<br/>
<a NAME="E4:11"/>
<font color="Maroon" title="c15">N</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E5:11"/><span class="kw">then </span>
 <a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="power.html#K5" title="POWER:func.5">log</a> 2,1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_ff.html#T12" title="PRE_FF:th.12">PRE_FF:12</a></span>;<br/>
<a NAME="E6:11"/><span class="kw">then </span>
 <a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T59" title="POWER:th.59">POWER:59</a></span>;<br/>
<a NAME="E7:11"/><span class="kw">then </span>
<span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">k</font> = <span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a>, <a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></span>;<br/>
<a NAME="E9:11"/>
2 <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="power.html#T44" title="POWER:th.44">POWER:44</a></span>;<br/>
<a NAME="E10:11"/><span class="kw">then </span>
2 <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c15">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="power.html#D3" title="POWER:def.3">POWER:def 3</a></span>;<br/>
<a NAME="E11:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A3</font></span>: 
2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c15">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T46" title="POWER:th.46">POWER:46</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c18">S</font> be    <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="fib_fusc.html#K3" title="FIB_FUSC:func.3">Fusc_Program</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default">2</span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c15">N</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default">1</span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c18">S</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c18">S</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c18">S</font></span>)</span>,<font color="Maroon" title="c18">S</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c18">S</font></span>)</span>,<font color="Maroon" title="c18">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p4">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c19">s</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <span class="kw"> such that </span><br/><a NAME="E13:11"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">S</font>
 ;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ] <span class="kw">means </span>( $1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 implies for <font color="Olive" title="b1">u</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> $1</span>)</span> holds <br/>(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> $1</span>)</span> &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> ) );<br/>
<a NAME="E14:11"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> 8
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E15:11"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K8" title="AMI_3:func.8">SCM-goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E16:11"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4</span>)</span> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E17:11"/><span class="lab"><font color="Green" title="E25">A8</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E18:11"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E19:11"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E20:11"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4</span>)</span> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> 6
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E21:11"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K8" title="AMI_3:func.8">SCM-goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E22:11"/><span class="lab"><font color="Green" title="E30">A13</font></span>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c20">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c20">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:11_1"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
( <font color="Maroon" title="c20">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 implies for <font color="Olive" title="b1">u</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> holds <br/>(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c20">k</font></span>)</span> &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/>

<span class="kw">set </span><font color="Maroon" title="c21">t</font> = 6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">t0</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E2:11_1"/><span class="lab"><font color="Green" title="E32">A15</font></span>: 
<font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">u</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> holds <br/>(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> )</span><br/>

<a NAME="E3:11_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/>
<a NAME="E4:11_1"/><span class="kw">then </span>
2 <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c20">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 2 <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_ff.html#T10" title="PRE_FF:th.10">PRE_FF:10</a></span>;<br/>
<a NAME="E5:11_1"/><span class="kw">then </span>
2 <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c20">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="power.html#D3" title="POWER:def.3">POWER:def 3</a></span>;<br/>
<a NAME="E6:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A16</font></span>: 
2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c20">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T46" title="POWER:th.46">POWER:46</a></span>;<br/>
<a NAME="E7:11_1"/><span class="lab"><font color="Green" title="E34">A17</font></span>: 
<font color="Maroon" title="c20">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/>
<a NAME="E8:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A18</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="txt" href="#E2:11_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E9:11_1"/><span class="lab"><font color="Green" title="E36">A19</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c20">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="txt" href="#E2:11_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E7:11_1"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E10:11_1"/><span class="lab"><font color="Green" title="E37">A20</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="txt" href="#E2:11_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E7:11_1"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c23">t3</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c24">t2</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c25">t1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<a NAME="E11:11_1"/><span class="lab"><font color="Green" title="E38">A21</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
;<br/>
<a NAME="E12:11_1"/>
2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c20">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T102" title="NEWTON:th.102">NEWTON:102</a></span>;<br/>
<a NAME="E13:11_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:11_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E6:11_1"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="ref" href="pre_ff.html#T3" title="PRE_FF:th.3">PRE_FF:3</a></span>;<br/>
<a NAME="E14:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A22</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:11"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E10:11_1"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<a NAME="E15:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A23</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:11"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E11:11_1"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="ref" href="scm_1.html#T18" title="SCM_1:th.18">SCM_1:18</a></span>;<br/>
<a NAME="E16:11_1"/><span class="lab"><font color="Green" title="E41">A24</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 
;<br/>
<a NAME="E17:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A25</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:11"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:11_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="fib_fusc.html#E14"><span class="lab"><font color="Green" title="E14">Lm14</font></span></a>, <a class="ref" href="scm_1.html#T22" title="SCM_1:th.22">SCM_1:22</a></span>;<br/>
<a NAME="E18:11_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:11"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E10:11_1"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<a NAME="E19:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A26</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:11"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E14:11_1"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E11:11_1"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="txt" href="fib_fusc.html#E14"><span class="lab"><font color="Green" title="E14">Lm14</font></span></a>, <a class="ref" href="scm_1.html#T18" title="SCM_1:th.18">SCM_1:18</a></span>;<br/>
<a NAME="E20:11_1"/><span class="lab"><font color="Green" title="E44">A27</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p5">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D8" title="INT_1:def.8">INT_1:def 8</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c26">u</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c26">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> implies (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c26">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> ) )</span><br/>

<span class="kw">assume </span><a NAME="E21:11_1"/><span class="lab"><font color="Green" title="E45">A28</font></span>: 
<font color="Maroon" title="c26">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c26">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> )</span><br/>

<a NAME="E22:11_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="txt" href="#E2:11_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E7:11_1"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E23:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A29</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:11"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E10:11_1"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<a NAME="E24:11_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:11"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E14:11_1"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E11:11_1"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="txt" href="fib_fusc.html#E13"><span class="lab"><font color="Green" title="E13">Lm13</font></span></a>, <a class="ref" href="scm_1.html#T18" title="SCM_1:th.18">SCM_1:18</a></span>;<br/>
<a NAME="E25:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A30</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:11"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:11_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E16:11_1"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="fib_fusc.html#E7"><span class="lab"><font color="Green" title="E7">Lm7</font></span></a>, <a class="txt" href="fib_fusc.html#E13"><span class="lab"><font color="Green" title="E13">Lm13</font></span></a>, <a class="txt" href="fib_fusc.html#E14"><span class="lab"><font color="Green" title="E14">Lm14</font></span></a>, <a class="ref" href="scm_1.html#T22" title="SCM_1:th.22">SCM_1:22</a></span>;<br/>
<a NAME="E26:11_1"/><span class="lab"><font color="Green" title="E48">A31</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:11"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E14:11_1"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E23:11_1"><span class="lab"><font color="Green" title="E46">A29</font></span></a>, <a class="txt" href="#E11:11_1"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="ref" href="scm_1.html#T18" title="SCM_1:th.18">SCM_1:18</a></span>;<br/>
<a NAME="E27:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A32</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:11"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:11_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E19:11_1"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="txt" href="#E16:11_1"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="fib_fusc.html#E14"><span class="lab"><font color="Green" title="E14">Lm14</font></span></a>, <a class="ref" href="scm_1.html#T22" title="SCM_1:th.22">SCM_1:22</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E50">A33</font></span>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> = 
<font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:11_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="ref" href="pre_ff.html#T5" title="PRE_FF:th.5">PRE_FF:5</a></span>
<br/>.= 
<font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T11" title="NEWTON:th.11">NEWTON:11</a></span>
;<br/>
<a NAME="E29:11_1"/><span class="lab"><font color="Green" title="E51">A34</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:11"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:11_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E26:11_1"><span class="lab"><font color="Green" title="E48">A31</font></span></a>, <a class="txt" href="#E19:11_1"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="txt" href="#E16:11_1"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="fib_fusc.html#E14"><span class="lab"><font color="Green" title="E14">Lm14</font></span></a>, <a class="ref" href="scm_1.html#T22" title="SCM_1:th.22">SCM_1:22</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c27">t6</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c28">t5</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c29">t4</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span>;<br/>
<a NAME="E30:11_1"/><span class="lab"><font color="Green" title="E52">A35</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
 
;<br/>
<a NAME="E31:11_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:11"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E10:11_1"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<a NAME="E32:11_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:11"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E14:11_1"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E11:11_1"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="txt" href="fib_fusc.html#E16"><span class="lab"><font color="Green" title="E16">Lm16</font></span></a>, <a class="ref" href="scm_1.html#T18" title="SCM_1:th.18">SCM_1:18</a></span>;<br/>
<a NAME="E33:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A36</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:11"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:11_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E16:11_1"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="fib_fusc.html#E11"><span class="lab"><font color="Green" title="E11">Lm11</font></span></a>, <a class="txt" href="fib_fusc.html#E14"><span class="lab"><font color="Green" title="E14">Lm14</font></span></a>, <a class="txt" href="fib_fusc.html#E16"><span class="lab"><font color="Green" title="E16">Lm16</font></span></a>, <a class="ref" href="scm_1.html#T22" title="SCM_1:th.22">SCM_1:22</a></span>;<br/>
<a NAME="E34:11_1"/><span class="lab"><font color="Green" title="E54">A37</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6
 
;<br/>
<a NAME="E35:11_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:11"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E10:11_1"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<a NAME="E36:11_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:11"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E14:11_1"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E11:11_1"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="txt" href="fib_fusc.html#E15"><span class="lab"><font color="Green" title="E15">Lm15</font></span></a>, <a class="ref" href="scm_1.html#T18" title="SCM_1:th.18">SCM_1:18</a></span>;<br/>
<a NAME="E37:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A38</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:11"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:11_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E16:11_1"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="fib_fusc.html#E10"><span class="lab"><font color="Green" title="E10">Lm10</font></span></a>, <a class="txt" href="fib_fusc.html#E14"><span class="lab"><font color="Green" title="E14">Lm14</font></span></a>, <a class="txt" href="fib_fusc.html#E15"><span class="lab"><font color="Green" title="E15">Lm15</font></span></a>, <a class="ref" href="scm_1.html#T22" title="SCM_1:th.22">SCM_1:22</a></span>;<br/>
<a NAME="E38:11_1"/><span class="lab"><font color="Green" title="E56">A39</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5
 
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_2"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:11_1_2"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_2_1"><span class="kw">suppose </span></a><a NAME="E1:11_1_2_1"/><span class="lab"><font color="Green" title="E57">A40</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c26">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> )</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c30">ta</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>, <font color="Maroon" title="c31">tb</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/><a NAME="E3:11_1_2_1"/><span class="lab"><font color="Green" title="E58">A41</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E17:11_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E37:11_1"><span class="lab"><font color="Green" title="E55">A38</font></span></a>, <a class="txt" href="#E30:11_1"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E4:11_1_2_1"/><span class="lab"><font color="Green" title="E59">A42</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E17:11_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E30:11_1"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="txt" href="#E1:11_1_2_1"><span class="lab"><font color="Green" title="E57">A40</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E5:11_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A43</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:11"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E38:11_1"><span class="lab"><font color="Green" title="E56">A39</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E6:11_1_2_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E17:11_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E30:11_1"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E7:11_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A44</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:11"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E38:11_1"><span class="lab"><font color="Green" title="E56">A39</font></span></a>, <a class="txt" href="#E4:11_1_2_1"><span class="lab"><font color="Green" title="E59">A42</font></span></a>, <a class="txt" href="fib_fusc.html#E11"><span class="lab"><font color="Green" title="E11">Lm11</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E8:11_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A45</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E34:11_1"><span class="lab"><font color="Green" title="E54">A37</font></span></a>, <a class="txt" href="#E5:11_1_2_1"><span class="lab"><font color="Green" title="E60">A43</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c32">un</font> = <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>, <font color="Maroon" title="c33">tn</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11_1"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E8:11_1"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="txt" href="#E27:11_1"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="ref" href="pre_ff.html#T7" title="PRE_FF:th.7">PRE_FF:7</a></span>;<br/><span class="lab"><font color="Green" title="E63">A46</font></span>: <font color="Maroon" title="c33">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p5">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p4">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11_1"><span class="lab"><font color="Green" title="E44">A27</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c32">un</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11_1"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E27:11_1"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="txt" href="#E29:11_1"><span class="lab"><font color="Green" title="E51">A34</font></span></a>, <a class="txt" href="#E1:11_1_2_1"><span class="lab"><font color="Green" title="E57">A40</font></span></a>, <a class="txt" href="#E8:11_1_2_1"><span class="lab"><font color="Green" title="E62">A45</font></span></a>, <a class="ref" href="pre_ff.html#T6" title="PRE_FF:th.6">PRE_FF:6</a></span>
;<br/><a NAME="E11:11_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A47</font></span>: 
<font color="Maroon" title="c33">tn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">un</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ;<br/><a NAME="E12:11_1_2_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E17:11_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E25:11_1"><span class="lab"><font color="Green" title="E47">A30</font></span></a>, <a class="txt" href="#E30:11_1"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E13:11_1_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:11"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E38:11_1"><span class="lab"><font color="Green" title="E56">A39</font></span></a>, <a class="txt" href="#E4:11_1_2_1"><span class="lab"><font color="Green" title="E59">A42</font></span></a>, <a class="txt" href="fib_fusc.html#E9"><span class="lab"><font color="Green" title="E9">Lm9</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><span class="kw">hence </span><a NAME="E14:11_1_2_1"/>
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c26">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E21:11_1"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E28:11_1"><span class="lab"><font color="Green" title="E50">A33</font></span></a>, <a class="txt" href="#E34:11_1"><span class="lab"><font color="Green" title="E54">A37</font></span></a>, <a class="txt" href="#E5:11_1_2_1"><span class="lab"><font color="Green" title="E60">A43</font></span></a>, <a class="txt" href="#E7:11_1_2_1"><span class="lab"><font color="Green" title="E61">A44</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E15:11_1_2_1"/>
<font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11_1"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E8:11_1"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="txt" href="#E27:11_1"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="txt" href="#E8:11_1_2_1"><span class="lab"><font color="Green" title="E62">A45</font></span></a>, <a class="ref" href="pre_ff.html#T7" title="PRE_FF:th.7">PRE_FF:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span><br/><span class="lab"><font color="Green" title="E65">A48</font></span>:  <a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">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" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p4">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> = 
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c33">tn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
<br/>.= 
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">un</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:11_1_2_1"><span class="lab"><font color="Green" title="E64">A47</font></span></a>, <a class="ref" href="pre_ff.html#T17" title="PRE_FF:th.17">PRE_FF:17</a></span>
<br/>.= 
 <a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
;<br/><a NAME="E17:11_1_2_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E17:11_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E33:11_1"><span class="lab"><font color="Green" title="E53">A36</font></span></a>, <a class="txt" href="#E30:11_1"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E18:11_1_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:11"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E38:11_1"><span class="lab"><font color="Green" title="E56">A39</font></span></a>, <a class="txt" href="#E4:11_1_2_1"><span class="lab"><font color="Green" title="E59">A42</font></span></a>, <a class="txt" href="#E3:11_1_2_1"><span class="lab"><font color="Green" title="E58">A41</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E19:11_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A49</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E34:11_1"><span class="lab"><font color="Green" title="E54">A37</font></span></a>, <a class="txt" href="#E5:11_1_2_1"><span class="lab"><font color="Green" title="E60">A43</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><span class="lab"><font color="Green" title="E67">A50</font></span>:  <a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> = 
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c33">tn</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c32">un</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c32">un</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:11_1_2_1"><span class="lab"><font color="Green" title="E63">A46</font></span></a>, <a class="ref" href="pre_ff.html#T17" title="PRE_FF:th.17">PRE_FF:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c32">un</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
;<br/><span class="kw">reconsider </span><font color="Maroon" title="c34">un</font> = <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>, <font color="Maroon" title="c35">tn</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/><a NAME="E22:11_1_2_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:11"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E38:11_1"><span class="lab"><font color="Green" title="E56">A39</font></span></a>, <a class="txt" href="#E4:11_1_2_1"><span class="lab"><font color="Green" title="E59">A42</font></span></a>, <a class="txt" href="#E3:11_1_2_1"><span class="lab"><font color="Green" title="E58">A41</font></span></a>, <a class="txt" href="fib_fusc.html#E12"><span class="lab"><font color="Green" title="E12">Lm12</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E23:11_1_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E34:11_1"><span class="lab"><font color="Green" title="E54">A37</font></span></a>, <a class="txt" href="#E5:11_1_2_1"><span class="lab"><font color="Green" title="E60">A43</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><a NAME="E24:11_1_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c30">ta</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <font color="Maroon" title="c35">tn</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">tb</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c35">tn</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <font color="Maroon" title="c34">un</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c34">un</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11_1"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E19:11_1_2_1"><span class="lab"><font color="Green" title="E66">A49</font></span></a>, <a class="txt" href="#E20:11_1_2_1"><span class="lab"><font color="Green" title="E67">A50</font></span></a>, <a class="txt" href="#E16:11_1_2_1"><span class="lab"><font color="Green" title="E65">A48</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E25:11_1_2_1"/>
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="txt" href="#E2:11_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E7:11_1"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_2_2"><span class="kw">suppose </span></a><a NAME="E1:11_1_2_2"/><span class="lab"><font color="Green" title="E57">A51</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c26">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> )</span><br/><div class="add"><a NAME="E2:11_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A52</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E17:11_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E30:11_1"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E3:11_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A53</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:11"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E38:11_1"><span class="lab"><font color="Green" title="E56">A39</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E4:11_1_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E17:11_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E30:11_1"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E5:11_1_2_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:11"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E38:11_1"><span class="lab"><font color="Green" title="E56">A39</font></span></a>, <a class="txt" href="#E2:11_1_2_2"><span class="lab"><font color="Green" title="E58">A52</font></span></a>, <a class="txt" href="fib_fusc.html#E10"><span class="lab"><font color="Green" title="E10">Lm10</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E6:11_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A54</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:11"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E34:11_1"><span class="lab"><font color="Green" title="E54">A37</font></span></a>, <a class="txt" href="#E3:11_1_2_2"><span class="lab"><font color="Green" title="E59">A53</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c30">un</font> = <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>, <font color="Maroon" title="c31">tn</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11_1"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E8:11_1"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="txt" href="#E27:11_1"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="ref" href="pre_ff.html#T7" title="PRE_FF:th.7">PRE_FF:7</a></span>;<br/><span class="lab"><font color="Green" title="E61">A55</font></span>:  <a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">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" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p4">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> = 
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">tn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c30">un</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c30">un</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11_1"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E27:11_1"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="txt" href="#E29:11_1"><span class="lab"><font color="Green" title="E51">A34</font></span></a>, <a class="txt" href="#E20:11_1"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="txt" href="#E1:11_1_2_2"><span class="lab"><font color="Green" title="E57">A51</font></span></a>, <a class="txt" href="#E6:11_1_2_2"><span class="lab"><font color="Green" title="E60">A54</font></span></a>, <a class="ref" href="pre_ff.html#T17" title="PRE_FF:th.17">PRE_FF:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c30">un</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
;<br/><a NAME="E9:11_1_2_2"/><span class="lab"><font color="Green" title="E62">A56</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E17:11_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E33:11_1"><span class="lab"><font color="Green" title="E53">A36</font></span></a>, <a class="txt" href="#E30:11_1"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E10:11_1_2_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:11"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E38:11_1"><span class="lab"><font color="Green" title="E56">A39</font></span></a>, <a class="txt" href="#E2:11_1_2_2"><span class="lab"><font color="Green" title="E58">A52</font></span></a>, <a class="txt" href="fib_fusc.html#E12"><span class="lab"><font color="Green" title="E12">Lm12</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E11:11_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A57</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:11"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E34:11_1"><span class="lab"><font color="Green" title="E54">A37</font></span></a>, <a class="txt" href="#E3:11_1_2_2"><span class="lab"><font color="Green" title="E59">A53</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><a NAME="E12:11_1_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E17:11_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E25:11_1"><span class="lab"><font color="Green" title="E47">A30</font></span></a>, <a class="txt" href="#E30:11_1"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E13:11_1_2_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:11"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E38:11_1"><span class="lab"><font color="Green" title="E56">A39</font></span></a>, <a class="txt" href="#E2:11_1_2_2"><span class="lab"><font color="Green" title="E58">A52</font></span></a>, <a class="txt" href="fib_fusc.html#E8"><span class="lab"><font color="Green" title="E8">Lm8</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><span class="kw">hence </span><a NAME="E14:11_1_2_2"/>
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c26">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c20">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:11"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E21:11_1"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E8:11_1"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="txt" href="#E27:11_1"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="txt" href="#E28:11_1"><span class="lab"><font color="Green" title="E50">A33</font></span></a>, <a class="txt" href="#E34:11_1"><span class="lab"><font color="Green" title="E54">A37</font></span></a>, <a class="txt" href="#E3:11_1_2_2"><span class="lab"><font color="Green" title="E59">A53</font></span></a>, <a class="txt" href="#E6:11_1_2_2"><span class="lab"><font color="Green" title="E60">A54</font></span></a>, <a class="ref" href="pre_ff.html#T7" title="PRE_FF:th.7">PRE_FF:7</a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span><br/><span class="lab"><font color="Green" title="E64">A58</font></span>:  <a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> = 
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c31">tn</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
<br/>.= 
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c30">un</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:11_1"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E27:11_1"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="txt" href="#E29:11_1"><span class="lab"><font color="Green" title="E51">A34</font></span></a>, <a class="txt" href="#E20:11_1"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="txt" href="#E1:11_1_2_2"><span class="lab"><font color="Green" title="E57">A51</font></span></a>, <a class="txt" href="#E6:11_1_2_2"><span class="lab"><font color="Green" title="E60">A54</font></span></a>, <a class="ref" href="pre_ff.html#T17" title="PRE_FF:th.17">PRE_FF:17</a></span>
<br/>.= 
 <a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
;<br/><a NAME="E16:11_1_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E17:11_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E37:11_1"><span class="lab"><font color="Green" title="E55">A38</font></span></a>, <a class="txt" href="#E30:11_1"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E17:11_1_2_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:11"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E38:11_1"><span class="lab"><font color="Green" title="E56">A39</font></span></a>, <a class="txt" href="#E2:11_1_2_2"><span class="lab"><font color="Green" title="E58">A52</font></span></a>, <a class="txt" href="#E9:11_1_2_2"><span class="lab"><font color="Green" title="E62">A56</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E18:11_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A59</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:11"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E34:11_1"><span class="lab"><font color="Green" title="E54">A37</font></span></a>, <a class="txt" href="#E3:11_1_2_2"><span class="lab"><font color="Green" title="E59">A53</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c32">un</font> = <font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>, <font color="Maroon" title="c33">tn</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>, <font color="Maroon" title="c34">ta</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>, <font color="Maroon" title="c35">tb</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c20">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/><a NAME="E20:11_1_2_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c34">ta</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <font color="Maroon" title="c33">tn</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c35">tb</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c33">tn</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c34">ta</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c35">tb</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <font color="Maroon" title="c32">un</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c35">tb</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c32">un</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:11_1_2_2"><span class="lab"><font color="Green" title="E64">A58</font></span></a>, <a class="txt" href="#E8:11_1_2_2"><span class="lab"><font color="Green" title="E61">A55</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E21:11_1_2_2"/>
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c26">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="txt" href="#E2:11_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E21:11_1"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E7:11_1"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="txt" href="#E18:11_1_2_2"><span class="lab"><font color="Green" title="E65">A59</font></span></a>, <a class="txt" href="#E11:11_1_2_2"><span class="lab"><font color="Green" title="E63">A57</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c20">h</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">u</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>;<br/>
<a NAME="E23:11"/><span class="lab"><font color="Green" title="E31">A60</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E24:11"/><span class="lab"><font color="Green" title="E32">A61</font></span>: 
( <font color="Maroon" title="c19">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c19">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E25:11"/><span class="lab"><font color="Green" title="E33">A62</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:11_2"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">u</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> holds <br/>(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c22">u</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c22">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> implies (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c22">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:11_2"/>
<font color="Maroon" title="c22">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c22">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> )</span><br/>

<a NAME="E3:11_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A63</font></span>: 
<font color="Maroon" title="c22">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:11_2"/>
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c22">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> = 
<font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:11"><span class="lab"><font color="Green" title="E31">A60</font></span></a>, <a class="txt" href="#E3:11_2"><span class="lab"><font color="Green" title="E34">A63</font></span></a>, <a class="ref" href="pre_ff.html#T2" title="PRE_FF:th.2">PRE_FF:2</a></span>
<br/>.= 
<font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T9" title="NEWTON:th.9">NEWTON:9</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E6:11_2"/>
<font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E3:11_2"><span class="lab"><font color="Green" title="E34">A63</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span><br/>

<span class="kw">thus </span><a NAME="E7:11_2"/>
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c22">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:11"><span class="lab"><font color="Green" title="E31">A60</font></span></a>, <a class="txt" href="#E24:11"><span class="lab"><font color="Green" title="E32">A61</font></span></a>, <a class="txt" href="#E3:11_2"><span class="lab"><font color="Green" title="E34">A63</font></span></a>, <a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E26:11"/><span class="lab"><font color="Green" title="E34">A64</font></span>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E25:11"><span class="lab"><font color="Green" title="E33">A62</font></span></a>, <a class="txt" href="#E22:11"><span class="lab"><font color="Green" title="E30">A13</font></span></a>);<br/></span>
<a NAME="E27:11"/>
<span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D4" title="INT_1:def.4">INT_1:def 4</a></span>;<br/>
<a NAME="E28:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A65</font></span>: 
<font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/>
<a NAME="E29:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A66</font></span>: 
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p4">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p5">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p4">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">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" title="AMI_1:func.10">Comput</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p0">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:11"><span class="lab"><font color="Green" title="E34">A64</font></span></a></span>;<br/>
<a NAME="E30:11"/><span class="lab"><font color="Green" title="E37">A67</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:11"><span class="lab"><font color="Green" title="E34">A64</font></span></a>, <a class="txt" href="#E28:11"><span class="lab"><font color="Green" title="E35">A65</font></span></a></span>;<br/>
<a NAME="E31:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A68</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:11"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<a NAME="E32:11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">N</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default">2 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:11"><span class="lab"><font color="Green" title="E34">A64</font></span></a>, <a class="txt" href="#E28:11"><span class="lab"><font color="Green" title="E35">A65</font></span></a></span>;<br/>
<a NAME="E33:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A69</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:11"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a>, <a class="ref" href="pre_ff.html#T4" title="PRE_FF:th.4">PRE_FF:4</a></span>;<br/>
<a NAME="E34:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A70</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:11"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E30:11"><span class="lab"><font color="Green" title="E37">A67</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<a NAME="E35:11"/><span class="lab"><font color="Green" title="E41">A71</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:11"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E30:11"><span class="lab"><font color="Green" title="E37">A67</font></span></a>, <a class="ref" href="scm_1.html#T26" title="SCM_1:th.26">SCM_1:26</a></span>;<br/>
<a NAME="E36:11"/><span class="lab"><font color="Green" title="E42">A72</font></span>: 
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E37:11"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c18">S</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c18">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E34:11"><span class="lab"><font color="Green" title="E40">A70</font></span></a>, <a class="ref" href="scm_1.html#T3" title="SCM_1:th.3">SCM_1:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c18">S</font></span>)</span>,<font color="Maroon" title="c18">S</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c18">S</font></span>)</span>,<font color="Maroon" title="c18">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p4">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 )</span><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" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p4">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p5">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p4">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">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" title="AMI_1:func.10">Comput</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p0">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p4">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p4">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" title="FIB_FUSC:func.2">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" title="AMI_1:func.10">Comput</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p0">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:11"><span class="lab"><font color="Green" title="E39">A69</font></span></a>, <a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a>, <a class="ref" href="pre_ff.html#T17" title="PRE_FF:th.17">PRE_FF:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:11"><span class="lab"><font color="Green" title="E39">A69</font></span></a>, <a class="ref" href="fib_fusc.html#D2" target="_self" title="FIB_FUSC:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p2">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_ff.html#T17" title="PRE_FF:th.17">PRE_FF:17</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E39:11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c18">S</font></span>)</span>,<font color="Maroon" title="c18">S</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c15">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E36:11"><span class="lab"><font color="Green" title="E42">A72</font></span></a>, <a class="txt" href="#E29:11"><span class="lab"><font color="Green" title="E36">A66</font></span></a>, <a class="txt" href="#E34:11"><span class="lab"><font color="Green" title="E40">A70</font></span></a>, <a class="txt" href="#E31:11"><span class="lab"><font color="Green" title="E38">A68</font></span></a>, <a class="ref" href="scm_1.html#T4" title="SCM_1:th.4">SCM_1:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c18">S</font></span>)</span>,<font color="Maroon" title="c18">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p4">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span><br/>

<a NAME="E40:11"/>
<font color="Maroon" title="c19">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c19">s</font></span>)</span>,<font color="Maroon" title="c19">s</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c17">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E34:11"><span class="lab"><font color="Green" title="E40">A70</font></span></a>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E41:11"/>
 <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c18">S</font></span>)</span>,<font color="Maroon" title="c18">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p4">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c15">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E35:11"><span class="lab"><font color="Green" title="E41">A71</font></span></a>, <a class="ref" href="scm_1.html#T17" title="SCM_1:th.17">SCM_1:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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