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

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span>for <font color="Olive" title="b1">N</font>, <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</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> <br/> for <font color="Olive" title="b4">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">$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="p2"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Olive" title="b2">A</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="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Olive" title="b3">B</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>  st <font color="Olive" title="b1">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>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Olive" title="b1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> $1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">B</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p3">(<span class="default">$1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> holds <br/>(  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b4">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Olive" title="b4">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="b4">s</font></span>)</span>,<font color="Olive" title="b4">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="Olive" title="b1">N</font> &amp; ( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="b4">s</font></span>)</span>,<font color="Olive" title="b4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( $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>  implies  <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="b4">s</font></span>)</span>,<font color="Olive" title="b4">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,$1</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 ) );<br/>
<a NAME="E1:14"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( for <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">n</font>] ) holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><span class="kw">proof </span></a><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">let </span><font color="Maroon" title="c6">nn</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">nn</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] ) implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">nn</font>] )</span><br/>

<span class="kw">assume </span><a NAME="E1:14_1"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
for <font color="Olive" title="b1">n9</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">n9</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">nn</font> holds <br/>for <font color="Olive" title="b2">N</font>, <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">B</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> <br/> for <font color="Olive" title="b5">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="Olive" title="b1">n9</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"><font color="Olive" title="b3">A</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="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Olive" title="b4">B</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>  st <font color="Olive" title="b2">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>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Olive" title="b2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">A</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Olive" title="b1">n9</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">B</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">n9</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> holds <br/>(  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b5">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Olive" title="b5">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="b5">s</font></span>)</span>,<font color="Olive" title="b5">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="Olive" title="b2">N</font> &amp; ( <font color="Olive" title="b1">n9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="b5">s</font></span>)</span>,<font color="Olive" title="b5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Olive" title="b1">n9</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  <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="b5">s</font></span>)</span>,<font color="Olive" title="b5">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="Olive" title="b1">n9</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 ) )
 ; <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="c6">nn</font>]</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">n2</font> = <font color="Maroon" title="c6">nn</font> 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="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c8">N</font>, <font color="Maroon" title="c9">A</font>, <font color="Maroon" title="c10">B</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"> 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="c6">nn</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"><font color="Maroon" title="c9">A</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="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c10">B</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>  st <font color="Maroon" title="c8">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>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c8">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">A</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c6">nn</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">B</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">nn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c6">nn</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">let </span><font color="Maroon" title="c11">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="c6">nn</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"><font color="Maroon" title="c9">A</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="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c10">B</font></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"> ( <font color="Maroon" title="c8">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>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c8">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">A</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c6">nn</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">B</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">nn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> implies (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c11">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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><span class="kw">that </span><br/><a NAME="E3:14_1"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
<font color="Maroon" title="c8">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> 
 <span class="kw">and </span><br/><a NAME="E4:14_1"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c8">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">A</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c6">nn</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">B</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">nn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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"> (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c11">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="E5:14_1"/><span class="lab"><font color="Green" title="E23">A5</font></span>: 
<font color="Maroon" title="c11">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="c6">nn</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">s0</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<a NAME="E6:14_1"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
<font color="Maroon" title="c11">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="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">s1</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<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>;<br/>
<a NAME="E7:14_1"/><span class="lab"><font color="Green" title="E25">A7</font></span>: 
<font color="Maroon" title="c11">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="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E8:14_1"/><span class="lab"><font color="Green" title="E26">A8</font></span>: 
<font color="Maroon" title="c11">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="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E9:14_1"/><span class="lab"><font color="Green" title="E27">A9</font></span>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c11">s</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="c11">s</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<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>, <a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E10:14_1"/>
<font color="Maroon" title="c11">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> <font color="Maroon" title="c9">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E11:14_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A10</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<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> <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> <font color="Maroon" title="c9">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E9:14_1"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<a NAME="E12:14_1"/>
<font color="Maroon" title="c11">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> <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="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E13:14_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A11</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<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> <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="#E6:14_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E9:14_1"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<a NAME="E14:14_1"/><span class="lab"><font color="Green" title="E30">A12</font></span>: 
<font color="Maroon" title="c11">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="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E15:14_1"/>
<font color="Maroon" title="c11">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> <font color="Maroon" title="c10">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E16:14_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A13</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<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> <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> <font color="Maroon" title="c10">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E9:14_1"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E32">A14</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1"/><span class="lab"><font color="Green" title="E33">A15</font></span>: 
<font color="Maroon" title="c6">nn</font> <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#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c11">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="E2:14_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A16</font></span>: 
<font color="Maroon" title="c11">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<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>)</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="#E6:14_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E7:14_1"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E5:14_1"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E9:14_1"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><span class="kw">hence </span><a NAME="E3:14_1_1"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c11">s</font>
 <span class="kw">by</span> <span class="lab"><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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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">thus </span><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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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> = 
<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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<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> <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="#E2:14_1_1"><span class="lab"><font color="Green" title="E34">A16</font></span></a>, <a class="ref" href="scm_1.html#T4" title="SCM_1:th.4">SCM_1:4</a></span>
<br/>.= 
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c8">N</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E16:14_1"><span class="lab"><font color="Green" title="E31">A13</font></span></a>, <a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E33">A15</font></span></a>, <a class="ref" href="pre_ff.html#T20" title="PRE_FF:th.20">PRE_FF:20</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="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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/><div><span class="kw">hereby </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="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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>
<div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_2"/>
<font color="Maroon" title="c6">nn</font> <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#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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><a NAME="E2:14_1_1_2"/>
 <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>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="ref" href="scm_1.html#T26" title="SCM_1:th.26">SCM_1:26</a></span>;<br/><span class="kw">hence </span><a NAME="E3:14_1_1_2"/>
 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E9:14_1"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E34">A16</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/></div>
<span class="kw">end;</span></div><span class="kw">thus </span><a NAME="E6:14_1_1"/>
( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="#E1:14_1_1"><span class="lab"><font color="Green" title="E33">A15</font></span></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="E18:14_1"/><span class="lab"><font color="Green" title="E33">A17</font></span>: 
<font color="Maroon" title="c11">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="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E19:14_1"/><span class="lab"><font color="Green" title="E34">A18</font></span>: 
<font color="Maroon" title="c11">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="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E20:14_1"/><span class="lab"><font color="Green" title="E35">A19</font></span>: 
<font color="Maroon" title="c11">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="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E21:14_1"/><span class="lab"><font color="Green" title="E36">A20</font></span>: 
<font color="Maroon" title="c11">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="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E22:14_1"/><span class="lab"><font color="Green" title="E37">A21</font></span>: 
<font color="Maroon" title="c11">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="ref" href="scm_1.html#T14" title="SCM_1:th.14">SCM_1:14</a></span>;<br/>
<a NAME="E23:14_1"/><span class="lab"><font color="Green" title="E38">A22</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<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> <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="c6">nn</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E5:14_1"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E9:14_1"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E39">A23</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c14">s6</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">5 <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="c15">s5</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">4 <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="c16">s4</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">3 <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="c17">s3</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">2 <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="c18">s2</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/><a NAME="E1:14_1_2"/><span class="lab"><font color="Green" title="E40">A24</font></span>: 
<font color="Maroon" title="c6">nn</font> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">nn</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">nn</font> <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">assume </span><a NAME="E2:14_1_2"/><span class="lab"><font color="Green" title="E41">A25</font></span>: 
<font color="Maroon" title="c6">nn</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"> (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c11">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="E3:14_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A26</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<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> <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="#E6:14_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E5:14_1"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E9:14_1"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E4:14_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A27</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">1 <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> 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="#E18:14_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="scm_1.html#T18" title="SCM_1:th.18">SCM_1:18</a></span>;<br/><a NAME="E5:14_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A28</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> 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="#E14:14_1"><span class="lab"><font color="Green" title="E30">A12</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="E6:14_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">1 <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> <font color="Maroon" title="c9">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E11:14_1"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="txt" href="#E3:14_1_2"><span class="lab"><font color="Green" title="E42">A26</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="E7:14_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> <font color="Maroon" title="c9">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:14_1"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="txt" href="#E4:14_1_2"><span class="lab"><font color="Green" title="E43">A27</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="E8:14_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">1 <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="#E18:14_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E13:14_1"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="txt" href="#E3:14_1_2"><span class="lab"><font color="Green" title="E42">A26</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="E9:14_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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="#E14:14_1"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="txt" href="#E4:14_1_2"><span class="lab"><font color="Green" title="E43">A27</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="E10:14_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">1 <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> <font color="Maroon" title="c10">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E16:14_1"><span class="lab"><font color="Green" title="E31">A13</font></span></a>, <a class="txt" href="#E3:14_1_2"><span class="lab"><font color="Green" title="E42">A26</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="E11:14_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> <font color="Maroon" title="c10">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:14_1"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="txt" href="#E4:14_1_2"><span class="lab"><font color="Green" title="E43">A27</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="E12:14_1_2"/><span class="lab"><font color="Green" title="E48">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">1 <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> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">1 <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> <font color="Maroon" title="c6">nn</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E13:14_1"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="txt" href="#E23:14_1"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="txt" href="#E3:14_1_2"><span class="lab"><font color="Green" title="E42">A26</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="E13:14_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> <font color="Maroon" title="c7">n2</font> <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="#E14:14_1"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="txt" href="#E4:14_1_2"><span class="lab"><font color="Green" title="E43">A27</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="kw">reconsider </span><font color="Maroon" title="c19">nn9</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> 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="pre_ff.html#T7" title="PRE_FF:th.7">PRE_FF:7</a></span>;<br/><a NAME="E15:14_1_2"/><span class="lab"><font color="Green" title="E50">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">nn</font> <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="#E14:14_1"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="txt" href="#E4:14_1_2"><span class="lab"><font color="Green" title="E43">A27</font></span></a>, <a class="txt" href="#E12:14_1_2"><span class="lab"><font color="Green" title="E48">A32</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/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_2_1"><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="E1:14_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> 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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> 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="14_1_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:14_1_2_1_1"/><span class="lab"><font color="Green" title="E51">A35</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> 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#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c11">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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/><div class="add"><a NAME="E2:14_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A36</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">3 <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> 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="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E3:14_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A37</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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> 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="#E20:14_1"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E4:14_1_2_1_1"/><span class="lab"><font color="Green" title="E54">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">3 <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> <font color="Maroon" title="c9">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="txt" href="#E7:14_1_2"><span class="lab"><font color="Green" title="E45">A29</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E5:14_1_2_1_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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> <font color="Maroon" title="c9">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="txt" href="#E2:14_1_2_1_1"><span class="lab"><font color="Green" title="E52">A36</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="E6:14_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A39</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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> <font color="Maroon" title="c9">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E3:14_1_2_1_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><a NAME="E7:14_1_2_1_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">3 <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> <font color="Maroon" title="c10">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="txt" href="#E11:14_1_2"><span class="lab"><font color="Green" title="E47">A31</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E8:14_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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> <font color="Maroon" title="c10">B</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="txt" href="#E2:14_1_2_1_1"><span class="lab"><font color="Green" title="E52">A36</font></span></a>, <a class="txt" href="#E4:14_1_2_1_1"><span class="lab"><font color="Green" title="E54">A38</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E9:14_1_2_1_1"/><span class="lab"><font color="Green" title="E57">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:14_1_2"><span class="lab"><font color="Green" title="E50">A34</font></span></a>, <a class="txt" href="#E1:14_1_2_1_1"><span class="lab"><font color="Green" title="E51">A35</font></span></a>, <a class="ref" href="pre_ff.html#T6" title="PRE_FF:th.6">PRE_FF:6</a></span>;<br/><a NAME="E10:14_1_2_1_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">3 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E11:14_1_2_1_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="txt" href="#E2:14_1_2_1_1"><span class="lab"><font color="Green" title="E52">A36</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="E12:14_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A42</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E3:14_1_2_1_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><a NAME="E13:14_1_2_1_1"/><span class="lab"><font color="Green" title="E59">A43</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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 &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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="#E6:14_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E18:14_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/><a NAME="E14:14_1_2_1_1"/><span class="lab"><font color="Green" title="E60">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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="#E7:14_1"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/><a NAME="E15:14_1_2_1_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">3 <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="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="txt" href="#E9:14_1_2"><span class="lab"><font color="Green" title="E46">A30</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E16:14_1_2_1_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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="#E20:14_1"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="txt" href="#E2:14_1_2_1_1"><span class="lab"><font color="Green" title="E52">A36</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/><a NAME="E17:14_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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="#E19:14_1"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E3:14_1_2_1_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><a NAME="E18:14_1_2_1_1"/><span class="lab"><font color="Green" title="E62">A46</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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> &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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="#E22:14_1"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E21:14_1"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/><a NAME="E19:14_1_2_1_1"/><span class="lab"><font color="Green" title="E63">A47</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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> &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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="#E20:14_1"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="txt" href="#E19:14_1"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/><a NAME="E20:14_1_2_1_1"/><span class="lab"><font color="Green" title="E64">A48</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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> &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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="#E14:14_1"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="txt" href="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/><a NAME="E21:14_1_2_1_1"/>
(  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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>  &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E3:14_1_2_1_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><a NAME="E22:14_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A49</font></span>: 
 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> is    <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="c19">nn9</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"><font color="Maroon" title="c9">A</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="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">B</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">A</font></span>)</span></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_1_2_1_1"><span class="lab"><font color="Green" title="E56">A40</font></span></a>, <a class="txt" href="#E17:14_1_2_1_1"><span class="lab"><font color="Green" title="E61">A45</font></span></a>, <a class="txt" href="#E12:14_1_2_1_1"><span class="lab"><font color="Green" title="E58">A42</font></span></a>, <a class="txt" href="#E6:14_1_2_1_1"><span class="lab"><font color="Green" title="E55">A39</font></span></a>, <a class="txt" href="#E13:14_1_2_1_1"><span class="lab"><font color="Green" title="E59">A43</font></span></a>, <a class="txt" href="#E20:14_1_2_1_1"><span class="lab"><font color="Green" title="E64">A48</font></span></a>, <a class="txt" href="#E19:14_1_2_1_1"><span class="lab"><font color="Green" title="E63">A47</font></span></a>, <a class="txt" href="#E18:14_1_2_1_1"><span class="lab"><font color="Green" title="E62">A46</font></span></a>, <a class="txt" href="#E14:14_1_2_1_1"><span class="lab"><font color="Green" title="E60">A44</font></span></a>, <a class="ref" href="scm_1.html#T30" title="SCM_1:th.30">SCM_1:30</a></span>;<br/><a NAME="E23:14_1_2_1_1"/><span class="lab"><font color="Green" title="E66">A50</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">nn</font> <a href="int_1.html#K6" title="INT_1:func.6">mod</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"><font color="Maroon" title="c6">nn</font> <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="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">nn</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_2"><span class="lab"><font color="Green" title="E40">A24</font></span></a></span>;<br/><a NAME="E24:14_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A51</font></span>: 
<font color="Maroon" title="c19">nn9</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">nn</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14_1_2"><span class="lab"><font color="Green" title="E49">A33</font></span></a>, <a class="txt" href="#E15:14_1_2"><span class="lab"><font color="Green" title="E50">A34</font></span></a>, <a class="txt" href="#E9:14_1_2_1_1"><span class="lab"><font color="Green" title="E57">A41</font></span></a>, <a class="ref" href="pre_ff.html#T19" title="PRE_FF:th.19">PRE_FF:19</a></span>;<br/><a NAME="E25:14_1_2_1_1"/><span class="lab"><font color="Green" title="E68">A52</font></span>: 
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c8">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">A</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c19">nn9</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">B</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">A</font></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">nn9</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E13:14_1_2"><span class="lab"><font color="Green" title="E49">A33</font></span></a>, <a class="txt" href="#E15:14_1_2"><span class="lab"><font color="Green" title="E50">A34</font></span></a>, <a class="txt" href="#E9:14_1_2_1_1"><span class="lab"><font color="Green" title="E57">A41</font></span></a>, <a class="txt" href="#E23:14_1_2_1_1"><span class="lab"><font color="Green" title="E66">A50</font></span></a>, <a class="ref" href="pre_ff.html#T21" title="PRE_FF:th.21">PRE_FF:21</a></span>;<br/><a NAME="E26:14_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A53</font></span>: 
( <font color="Maroon" title="c19">nn9</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  <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> <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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> <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="c19">nn9</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="#E1:14_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E22:14_1_2_1_1"><span class="lab"><font color="Green" title="E65">A49</font></span></a>, <a class="txt" href="#E24:14_1_2_1_1"><span class="lab"><font color="Green" title="E67">A51</font></span></a></span>;<br/><a NAME="E27:14_1_2_1_1"/><span class="lab"><font color="Green" title="E70">A54</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">5 <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="#E1:14_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E22:14_1_2_1_1"><span class="lab"><font color="Green" title="E65">A49</font></span></a>, <a class="txt" href="#E24:14_1_2_1_1"><span class="lab"><font color="Green" title="E67">A51</font></span></a>, <a class="txt" href="#E25:14_1_2_1_1"><span class="lab"><font color="Green" title="E68">A52</font></span></a></span>;<br/><a NAME="E28:14_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">Y</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">5 <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="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/><span class="kw">hence </span><a NAME="E29:14_1_2_1_1"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c11">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T93" title="AMI_1:th.93">AMI_1:93</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="E30:14_1_2_1_1"/><span class="lab"><font color="Green" title="E72">X</font></span>: 
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:14_1_2_1_1"><span class="lab"><font color="Green" title="E71">Y</font></span></a>, <a class="ref" href="scm_1.html#T29" title="SCM_1:th.29">SCM_1:29</a></span>;<br/><a NAME="E31:14_1_2_1_1"/>
<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> <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p4">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<span class="default">5 <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> <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="c8">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E22:14_1_2_1_1"><span class="lab"><font color="Green" title="E65">A49</font></span></a>, <a class="txt" href="#E24:14_1_2_1_1"><span class="lab"><font color="Green" title="E67">A51</font></span></a>, <a class="txt" href="#E25:14_1_2_1_1"><span class="lab"><font color="Green" title="E68">A52</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E32:14_1_2_1_1"/>
<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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_2_1_1"><span class="lab"><font color="Green" title="E72">X</font></span></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="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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">thus </span><a NAME="E33:14_1_2_1_1"/>
( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_2"><span class="lab"><font color="Green" title="E41">A25</font></span></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="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="E34:14_1_2_1_1"/><span class="lab"><font color="Green" title="E73">A55</font></span>: 
( <font color="Maroon" title="c19">nn9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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> <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E13:14_1_2"><span class="lab"><font color="Green" title="E49">A33</font></span></a>, <a class="txt" href="#E15:14_1_2"><span class="lab"><font color="Green" title="E50">A34</font></span></a>, <a class="txt" href="#E1:14_1_2"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="txt" href="#E9:14_1_2_1_1"><span class="lab"><font color="Green" title="E57">A41</font></span></a>, <a class="txt" href="#E22:14_1_2_1_1"><span class="lab"><font color="Green" title="E65">A49</font></span></a>, <a class="txt" href="#E25:14_1_2_1_1"><span class="lab"><font color="Green" title="E68">A52</font></span></a></span>;<br/><span class="kw">thus </span><a NAME="E35:14_1_2_1_1"/>
( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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 )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_2_1_1_1"/>
<font color="Maroon" title="c6">nn</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">  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_2_1_1_1_1"><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="E1:14_1_2_1_1_1_1"/>
( <font color="Maroon" title="c19">nn9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c19">nn9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="14_1_2_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:14_1_2_1_1_1_1_1"/>
<font color="Maroon" title="c19">nn9</font> <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#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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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/><div class="add"><span class="kw">hence </span><a NAME="E2:14_1_2_1_1_1_1_1"/>
 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="#E13:14_1_2"><span class="lab"><font color="Green" title="E49">A33</font></span></a>, <a class="txt" href="#E15:14_1_2"><span class="lab"><font color="Green" title="E50">A34</font></span></a>, <a class="txt" href="#E1:14_1_2"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="txt" href="#E9:14_1_2_1_1"><span class="lab"><font color="Green" title="E57">A41</font></span></a>, <a class="txt" href="#E27:14_1_2_1_1"><span class="lab"><font color="Green" title="E70">A54</font></span></a>, <a class="txt" href="#E34:14_1_2_1_1"><span class="lab"><font color="Green" title="E73">A55</font></span></a>, <a class="txt" href="fib_fusc.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="scm_1.html#T28" title="SCM_1:th.28">SCM_1:28</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="14_1_2_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:14_1_2_1_1_1_1_2"/><span class="lab"><font color="Green" title="E74">A56</font></span>: 
<font color="Maroon" title="c19">nn9</font> <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#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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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/><div class="add"><a NAME="E2:14_1_2_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A57</font></span>: 
<font color="Maroon" title="c19">nn9</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="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">F</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="c19">nn9</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="txt" href="fib_fusc.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/><a NAME="E4:14_1_2_1_1_1_1_2"/>
<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">F</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 <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="#E2:14_1_2_1_1_1_1_2"><span class="lab"><font color="Green" title="E75">A57</font></span></a>, <a class="txt" href="fib_fusc.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/><span class="kw">hence </span> <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> = 
6 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <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="c20">F</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E27:14_1_2_1_1"><span class="lab"><font color="Green" title="E70">A54</font></span></a>, <a class="txt" href="#E26:14_1_2_1_1"><span class="lab"><font color="Green" title="E69">A53</font></span></a>, <a class="txt" href="#E1:14_1_2_1_1_1_1_2"><span class="lab"><font color="Green" title="E74">A56</font></span></a>, <a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a>, <a class="ref" href="scm_1.html#T28" title="SCM_1:th.28">SCM_1:28</a></span>
<br/>.= 
<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="c6">nn</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="#E13:14_1_2"><span class="lab"><font color="Green" title="E49">A33</font></span></a>, <a class="txt" href="#E15:14_1_2"><span class="lab"><font color="Green" title="E50">A34</font></span></a>, <a class="txt" href="#E9:14_1_2_1_1"><span class="lab"><font color="Green" title="E57">A41</font></span></a>, <a class="txt" href="#E23:14_1_2_1_1"><span class="lab"><font color="Green" title="E66">A50</font></span></a>, <a class="txt" href="#E2:14_1_2_1_1_1_1_2"><span class="lab"><font color="Green" title="E75">A57</font></span></a>, <a class="txt" href="fib_fusc.html#E3"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>
;<br/> <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></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:14_1_2_1_2"/><span class="lab"><font color="Green" title="E51">A58</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> 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#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c11">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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/><div class="add"><a NAME="E2:14_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A59</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">3 <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> 6
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E3:14_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A60</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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> 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="#E22:14_1"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="ref" href="scm_1.html#T19" title="SCM_1:th.19">SCM_1:19</a></span>;<br/><a NAME="E4:14_1_2_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">3 <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="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="txt" href="#E9:14_1_2"><span class="lab"><font color="Green" title="E46">A30</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E5:14_1_2_1_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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="#E22:14_1"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E2:14_1_2_1_2"><span class="lab"><font color="Green" title="E52">A59</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/><a NAME="E6:14_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A61</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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="#E21:14_1"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="txt" href="#E3:14_1_2_1_2"><span class="lab"><font color="Green" title="E53">A60</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><a NAME="E7:14_1_2_1_2"/><span class="lab"><font color="Green" title="E55">A62</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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> &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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="#E22:14_1"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E21:14_1"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/><a NAME="E8:14_1_2_1_2"/><span class="lab"><font color="Green" title="E56">A63</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">3 <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> <font color="Maroon" title="c10">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="txt" href="#E11:14_1_2"><span class="lab"><font color="Green" title="E47">A31</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E9:14_1_2_1_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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> <font color="Maroon" title="c10">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14_1"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E2:14_1_2_1_2"><span class="lab"><font color="Green" title="E52">A59</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="E10:14_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A64</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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> <font color="Maroon" title="c10">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14_1"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="txt" href="#E3:14_1_2_1_2"><span class="lab"><font color="Green" title="E53">A60</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><a NAME="E11:14_1_2_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">3 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E12:14_1_2_1_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14_1"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E2:14_1_2_1_2"><span class="lab"><font color="Green" title="E52">A59</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="E13:14_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A65</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14_1"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="txt" href="#E3:14_1_2_1_2"><span class="lab"><font color="Green" title="E53">A60</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><a NAME="E14:14_1_2_1_2"/><span class="lab"><font color="Green" title="E59">A66</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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> &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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="#E20:14_1"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="txt" href="#E19:14_1"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/><a NAME="E15:14_1_2_1_2"/><span class="lab"><font color="Green" title="E60">A67</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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> &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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="#E14:14_1"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="txt" href="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/><a NAME="E16:14_1_2_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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">3 <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> <font color="Maroon" title="c9">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_1"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="txt" href="#E7:14_1_2"><span class="lab"><font color="Green" title="E45">A29</font></span></a>, <a class="ref" href="scm_1.html#T24" title="SCM_1:th.24">SCM_1:24</a></span>;<br/><a NAME="E17:14_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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> <font color="Maroon" title="c9">A</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14_1"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E2:14_1_2_1_2"><span class="lab"><font color="Green" title="E52">A59</font></span></a>, <a class="txt" href="#E8:14_1_2_1_2"><span class="lab"><font color="Green" title="E56">A63</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">reconsider </span><font color="Maroon" title="c20">nn9</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">2 <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> 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="#E13:14_1_2"><span class="lab"><font color="Green" title="E49">A33</font></span></a>, <a class="ref" href="pre_ff.html#T7" title="PRE_FF:th.7">PRE_FF:7</a></span>;<br/><a NAME="E19:14_1_2_1_2"/><span class="lab"><font color="Green" title="E62">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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="#E7:14_1"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/><a NAME="E20:14_1_2_1_2"/><span class="lab"><font color="Green" title="E63">A70</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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 &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <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="#E6:14_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E18:14_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/><a NAME="E21:14_1_2_1_2"/>
(  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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>  &amp; <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">4 <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14_1"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="txt" href="#E3:14_1_2_1_2"><span class="lab"><font color="Green" title="E53">A60</font></span></a>, <a class="ref" href="scm_1.html#T23" title="SCM_1:th.23">SCM_1:23</a></span>;<br/><a NAME="E22:14_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A71</font></span>: 
 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> is    <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="c20">nn9</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"><span class="p3">(<span class="default"><font color="Maroon" title="c9">A</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">B</font></span>)</span></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"><font color="Maroon" title="c10">B</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:14_1_2_1_2"><span class="lab"><font color="Green" title="E61">A68</font></span></a>, <a class="txt" href="#E6:14_1_2_1_2"><span class="lab"><font color="Green" title="E54">A61</font></span></a>, <a class="txt" href="#E13:14_1_2_1_2"><span class="lab"><font color="Green" title="E58">A65</font></span></a>, <a class="txt" href="#E10:14_1_2_1_2"><span class="lab"><font color="Green" title="E57">A64</font></span></a>, <a class="txt" href="#E20:14_1_2_1_2"><span class="lab"><font color="Green" title="E63">A70</font></span></a>, <a class="txt" href="#E15:14_1_2_1_2"><span class="lab"><font color="Green" title="E60">A67</font></span></a>, <a class="txt" href="#E14:14_1_2_1_2"><span class="lab"><font color="Green" title="E59">A66</font></span></a>, <a class="txt" href="#E7:14_1_2_1_2"><span class="lab"><font color="Green" title="E55">A62</font></span></a>, <a class="txt" href="#E19:14_1_2_1_2"><span class="lab"><font color="Green" title="E62">A69</font></span></a>, <a class="ref" href="scm_1.html#T30" title="SCM_1:th.30">SCM_1:30</a></span>;<br/><a NAME="E23:14_1_2_1_2"/><span class="lab"><font color="Green" title="E65">A72</font></span>: 
( <font color="Maroon" title="c20">nn9</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">nn</font> &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c8">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="c9">A</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c10">B</font></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c20">nn9</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">B</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c20">nn9</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E2:14_1_2"><span class="lab"><font color="Green" title="E41">A25</font></span></a>, <a class="txt" href="#E13:14_1_2"><span class="lab"><font color="Green" title="E49">A33</font></span></a>, <a class="txt" href="#E15:14_1_2"><span class="lab"><font color="Green" title="E50">A34</font></span></a>, <a class="txt" href="#E1:14_1_2"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="txt" href="#E1:14_1_2_1_2"><span class="lab"><font color="Green" title="E51">A58</font></span></a>, <a class="ref" href="pre_ff.html#T18" title="PRE_FF:th.18">PRE_FF:18</a>, <a class="ref" href="pre_ff.html#T22" title="PRE_FF:th.22">PRE_FF:22</a></span>;<br/><a NAME="E24:14_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A73</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">5 <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="#E1:14_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E22:14_1_2_1_2"><span class="lab"><font color="Green" title="E64">A71</font></span></a></span>;<br/><a NAME="E25:14_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">Y</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p1">(<span class="default">5 <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="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/><span class="kw">hence </span><a NAME="E26:14_1_2_1_2"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c11">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T93" title="AMI_1:th.93">AMI_1:93</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="E27:14_1_2_1_2"/><span class="lab"><font color="Green" title="E68">X</font></span>: 
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:14_1_2_1_2"><span class="lab"><font color="Green" title="E67">Y</font></span></a>, <a class="ref" href="scm_1.html#T29" title="SCM_1:th.29">SCM_1:29</a></span>;<br/><a NAME="E28:14_1_2_1_2"/>
<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> <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p4">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<span class="default">5 <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> <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="c8">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E22:14_1_2_1_2"><span class="lab"><font color="Green" title="E64">A71</font></span></a>, <a class="txt" href="#E23:14_1_2_1_2"><span class="lab"><font color="Green" title="E65">A72</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E29:14_1_2_1_2"/>
<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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:14_1_2_1_2"><span class="lab"><font color="Green" title="E68">X</font></span></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="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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">thus </span><a NAME="E30:14_1_2_1_2"/>
( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_2"><span class="lab"><font color="Green" title="E41">A25</font></span></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="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="E31:14_1_2_1_2"/><span class="lab"><font color="Green" title="E69">A74</font></span>: 
( <font color="Maroon" title="c20">nn9</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  <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> <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font>,<span class="p2">(<span class="default">5 <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> <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="c20">nn9</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="#E1:14_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E22:14_1_2_1_2"><span class="lab"><font color="Green" title="E64">A71</font></span></a>, <a class="txt" href="#E23:14_1_2_1_2"><span class="lab"><font color="Green" title="E65">A72</font></span></a></span>;<br/><span class="kw">thus </span><a NAME="E32:14_1_2_1_2"/>
( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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 )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_2_1_2_1"/>
<font color="Maroon" title="c6">nn</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">  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_2_1_2_1_1"><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="E1:14_1_2_1_2_1_1"/>
( <font color="Maroon" title="c20">nn9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c20">nn9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="14_1_2_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:14_1_2_1_2_1_1_1"/>
<font color="Maroon" title="c20">nn9</font> <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#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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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/><div class="add"><span class="kw">hence </span><a NAME="E2:14_1_2_1_2_1_1_1"/>
 <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="#E14:14_1"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="txt" href="#E2:14_1_2"><span class="lab"><font color="Green" title="E41">A25</font></span></a>, <a class="txt" href="#E4:14_1_2"><span class="lab"><font color="Green" title="E43">A27</font></span></a>, <a class="txt" href="#E12:14_1_2"><span class="lab"><font color="Green" title="E48">A32</font></span></a>, <a class="txt" href="#E13:14_1_2"><span class="lab"><font color="Green" title="E49">A33</font></span></a>, <a class="txt" href="#E1:14_1_2"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="txt" href="#E1:14_1_2_1_2"><span class="lab"><font color="Green" title="E51">A58</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>; <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="14_1_2_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:14_1_2_1_2_1_1_2"/><span class="lab"><font color="Green" title="E70">A75</font></span>: 
<font color="Maroon" title="c20">nn9</font> <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#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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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/><div class="add"><a NAME="E2:14_1_2_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A76</font></span>: 
<font color="Maroon" title="c20">nn9</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="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c21">F</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="c20">nn9</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="txt" href="fib_fusc.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/><a NAME="E4:14_1_2_1_2_1_1_2"/>
<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="c21">F</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 <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="#E2:14_1_2_1_2_1_1_2"><span class="lab"><font color="Green" title="E71">A76</font></span></a>, <a class="txt" href="fib_fusc.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/><span class="kw">hence </span> <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> = 
6 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <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="c21">F</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_2_1_2"><span class="lab"><font color="Green" title="E66">A73</font></span></a>, <a class="txt" href="#E31:14_1_2_1_2"><span class="lab"><font color="Green" title="E69">A74</font></span></a>, <a class="txt" href="#E1:14_1_2_1_2_1_1_2"><span class="lab"><font color="Green" title="E70">A75</font></span></a>, <a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a>, <a class="ref" href="scm_1.html#T28" title="SCM_1:th.28">SCM_1:28</a></span>
<br/>.= 
<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="c6">nn</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="#E13:14_1_2"><span class="lab"><font color="Green" title="E49">A33</font></span></a>, <a class="txt" href="#E15:14_1_2"><span class="lab"><font color="Green" title="E50">A34</font></span></a>, <a class="txt" href="#E1:14_1_2"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="txt" href="#E1:14_1_2_1_2"><span class="lab"><font color="Green" title="E51">A58</font></span></a>, <a class="txt" href="#E2:14_1_2_1_2_1_1_2"><span class="lab"><font color="Green" title="E71">A76</font></span></a>, <a class="txt" href="fib_fusc.html#E5"><span class="lab"><font color="Green" title="E5">Lm5</font></span></a></span>
;<br/> <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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E25:14_1"/>
<font color="Maroon" title="c6">nn</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="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E26:14_1"/>
(  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c11">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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c8">N</font> &amp; ( <font color="Maroon" title="c6">nn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c6">nn</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  <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="c11">s</font></span>)</span>,<font color="Maroon" title="c11">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="c6">nn</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="#E17:14_1"><span class="lab"><font color="Green" title="E32">A14</font></span></a>, <a class="txt" href="#E24:14_1"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</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="E2:14"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S4" title="NAT_1:sch.4">NAT_1:sch 4</a>(<a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E19">A1</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E3:14"/>
for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">N</font>, <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">B</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> <br/> for <font color="Olive" title="b5">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="Olive" title="b1">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"><font color="Olive" title="b3">A</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="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Olive" title="b4">B</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>  st <font color="Olive" title="b2">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>  &amp;  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Olive" title="b2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">A</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">B</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> holds <br/>(  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b5">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Olive" title="b5">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="b5">s</font></span>)</span>,<font color="Olive" title="b5">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="Olive" title="b2">N</font> &amp; ( <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <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="b5">s</font></span>)</span>,<font color="Olive" title="b5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Olive" title="b1">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  <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="b5">s</font></span>)</span>,<font color="Olive" title="b5">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="Olive" title="b1">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 ) )
 ; <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>
