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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="fib_fusc.html#K1" title="FIB_FUSC:func.1">Fib_Program</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">F</font> implies  for <font color="Olive" title="b1">N</font>, <font color="Olive" title="b2">k</font>, <font color="Olive" title="b3">Fk</font>, <font color="Olive" title="b4">Fk1</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  3 <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>   <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> ,<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">1</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">Fk</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">Fk1</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; <font color="Olive" title="b3">Fk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b4">Fk1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> holds <br/>( <font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Olive" title="b5">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 &amp;  ex <font color="Olive" title="b6">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b6">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:13"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
 <a href="fib_fusc.html#K1" title="FIB_FUSC:func.1">Fib_Program</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">N</font>, <font color="Olive" title="b2">k</font>, <font color="Olive" title="b3">Fk</font>, <font color="Olive" title="b4">Fk1</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  3 <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>   <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> ,<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">1</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">Fk</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">Fk1</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; <font color="Olive" title="b3">Fk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b4">Fk1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> holds <br/>( <font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Olive" title="b5">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 &amp;  ex <font color="Olive" title="b6">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b6">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) )</span><br/>

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ] <span class="kw">means </span> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">Fk</font>, <font color="Olive" title="b3">Fk1</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  3 <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>   <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> ,<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">1</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">Fk</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">Fk1</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>  st $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>  &amp; <font color="Olive" title="b2">Fk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b3">Fk1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> holds <br/>( <font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Olive" title="b4">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> $1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 &amp;  ex <font color="Olive" title="b5">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> $1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b5">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) );<br/>
<a NAME="E2:13"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
 for <font color="Olive" title="b1">N</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">N</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><font color="Maroon" title="c2">C1</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="c3">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="c4">FP</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="c5">FC</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="c6">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="c7">N</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">N</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:13_1"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">N</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/>

<a NAME="E2:13_1"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
<font color="Maroon" title="c7">N</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c8">k</font>, <font color="Maroon" title="c9">Fk</font>, <font color="Maroon" title="c10">Fk1</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being  3 <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>   <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> ,<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">1</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"><span class="p4">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="p2"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c9">Fk</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">Fk1</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>  st <font color="Maroon" title="c7">N</font> <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>  &amp; <font color="Maroon" title="c9">Fk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c8">k</font> &amp; <font color="Maroon" title="c10">Fk1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> holds <br/>( <font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Olive" title="b1">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 &amp;  ex <font color="Olive" title="b2">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b2">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c11">s</font> be  3 <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>   <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> ,<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">1</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"><span class="p4">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="p2"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c9">Fk</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">Fk1</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">N</font> <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>  &amp; <font color="Maroon" title="c9">Fk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c8">k</font> &amp; <font color="Maroon" title="c10">Fk1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> implies ( <font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c11">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 &amp;  ex <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b1">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) ) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:13_1"/>
<font color="Maroon" title="c7">N</font> <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">and </span><br/><a NAME="E4:13_1"/><span class="lab"><font color="Green" title="E23">A5</font></span>: 
<font color="Maroon" title="c9">Fk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c8">k</font>
 <span class="kw">and </span><br/><a NAME="E5:13_1"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
<font color="Maroon" title="c10">Fk1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c11">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 &amp;  ex <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b1">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) )</span><br/>

<a NAME="E6:13_1"/><span class="lab"><font color="Green" title="E25">A7</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</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> <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="#E1:13"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="fib_fusc.html#E18"><span class="lab"><font color="Green" title="E17">Lm17</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">s0</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c11">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>);<br/>
<span class="kw">set </span><font color="Maroon" title="c13">s1</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="E7:13_1"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">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="#E1:13"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="fib_fusc.html#E18"><span class="lab"><font color="Green" title="E17">Lm17</font></span></a></span>;<br/>
<a NAME="E8:13_1"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a>, <a class="ref" href="memstr_0.html#D9" title="MEMSTR_0:def.9">MEMSTR_0:def 9</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E28">A11</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> = 
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="#E6:13_1"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="ref" href="scm_1.html#T6" title="SCM_1:th.6">SCM_1:6</a></span>
<br/>.= 
4

;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">s2</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="E10:13_1"/><span class="lab"><font color="Green" title="E29">A13</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4 <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> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="fib_fusc.html#E18"><span class="lab"><font color="Green" title="E17">Lm17</font></span></a></span>;<br/>
<a NAME="E11:13_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">Fk1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T1" title="SCM_1:th.1">SCM_1:1</a></span>;<br/>
<a NAME="E12:13_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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">Fk1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E8:13_1"><span class="lab"><font color="Green" title="E27">A10</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#T6" title="SCM_1:th.6">SCM_1:6</a></span>;<br/>
<a NAME="E13:13_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A14</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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">Fk1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="scm_1.html#T10" title="SCM_1:th.10">SCM_1:10</a></span>;<br/>
<a NAME="E14:13_1"/><span class="lab"><font color="Green" title="E31">A15</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <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> 4</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="fib_fusc.html#E18"><span class="lab"><font color="Green" title="E17">Lm17</font></span></a></span>;<br/>
<a NAME="E15:13_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">Fk</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T1" title="SCM_1:th.1">SCM_1:1</a></span>;<br/>
<a NAME="E16:13_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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">Fk</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E8:13_1"><span class="lab"><font color="Green" title="E27">A10</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#T6" title="SCM_1:th.6">SCM_1:6</a></span>;<br/>
<a NAME="E17:13_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A16</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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">Fk</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="scm_1.html#T10" title="SCM_1:th.10">SCM_1:10</a></span>;<br/>
<a NAME="E18:13_1"/><span class="lab"><font color="Green" title="E33">A17</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 6 <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> 2</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> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="fib_fusc.html#E18"><span class="lab"><font color="Green" title="E17">Lm17</font></span></a></span>;<br/>
<a NAME="E19:13_1"/><span class="lab"><font color="Green" title="E34">A18</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> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T1" title="SCM_1:th.1">SCM_1:1</a></span>;<br/>
<a NAME="E20:13_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E8:13_1"><span class="lab"><font color="Green" title="E27">A10</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="ref" href="scm_1.html#T6" title="SCM_1:th.6">SCM_1:6</a></span>;<br/>
<a NAME="E21:13_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A19</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="scm_1.html#T10" title="SCM_1:th.10">SCM_1:10</a></span>;<br/>
<a NAME="E22:13_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> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T1" title="SCM_1:th.1">SCM_1:1</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E36">A20</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E19:13_1"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E8:13_1"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="scm_1.html#T6" title="SCM_1:th.6">SCM_1:6</a></span>
<br/>.= 
<font color="Maroon" title="c7">N</font>

;<br/>
<a NAME="E24:13_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A21</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="c7">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="scm_1.html#T10" title="SCM_1:th.10">SCM_1:10</a></span>;<br/>
<a NAME="E25:13_1"/><span class="lab"><font color="Green" title="E38">A22</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 5 <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> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="fib_fusc.html#E18"><span class="lab"><font color="Green" title="E17">Lm17</font></span></a></span>;<br/>
<a NAME="E26:13_1"/><span class="lab"><font color="Green" title="E39">A23</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K8" title="AMI_3:func.8">SCM-goto</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="fib_fusc.html#E18"><span class="lab"><font color="Green" title="E17">Lm17</font></span></a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_3"><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="E1:13_1_3"/>
( <font color="Maroon" title="c7">N</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="c7">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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_3_1"><span class="kw">suppose </span></a><a NAME="E1:13_1_3_1"/><span class="lab"><font color="Green" title="E40">A24</font></span>: 
<font color="Maroon" title="c7">N</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c11">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 &amp;  ex <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b1">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) )</span><br/><div class="add"><a NAME="E2:13_1_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A25</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<span class="default">1 <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="compos_1.html#K2" title="COMPOS_1:func.2">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="#E7:13_1"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E23:13_1"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="scm_1.html#T10" title="SCM_1:th.10">SCM_1:10</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_1_3_1"/>
<font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_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="extpro_1.html#T30" title="EXTPRO_1:th.30">EXTPRO_1:30</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 &amp;  ex <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b1">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) )</span><br/><a NAME="E4:13_1_3_1"/>
<font color="Maroon" title="c1">F</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">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="#E10:13_1"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="scm_1.html#T12" title="SCM_1:th.12">SCM_1:12</a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_1_3_1"/>
 <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_3_1"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="txt" href="#E2:13_1_3_1"><span class="lab"><font color="Green" title="E41">A25</font></span></a>, <a class="ref" href="extpro_1.html#T32" title="EXTPRO_1:th.32">EXTPRO_1:32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b1">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )</span><br/><span class="kw">take </span><font color="Maroon" title="c15">m</font> = <font color="Maroon" title="c8">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c15">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c15">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E6:13_1_3_1"/>
<font color="Maroon" title="c15">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_3_1"><span class="lab"><font color="Green" title="E40">A24</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c15">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E7:13_1_3_1"/>
( <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c15">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E17:13_1"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E13:13_1"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E2:13_1_3_1"><span class="lab"><font color="Green" title="E41">A25</font></span></a>, <a class="ref" href="extpro_1.html#T31" title="EXTPRO_1:th.31">EXTPRO_1:31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="13_1_3_2"><span class="kw">suppose </span></a><a NAME="E1:13_1_3_2"/><span class="lab"><font color="Green" title="E40">A26</font></span>: 
<font color="Maroon" title="c7">N</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c11">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 &amp;  ex <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b1">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) )</span><br/><div class="add"><a NAME="E2:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A27</font></span>: 
<span class="p1">(<span class="default">6 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c7">N</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 <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="fib_fusc.html#E6"><span class="lab"><font color="Green" title="E6">Lm6</font></span></a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c15">Fk2</font> =  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c16">s6</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="c17">s5</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="c18">s4</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="c19">s3</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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/><a NAME="E3:13_1_3_2"/><span class="lab"><font color="Green" title="E42">A28</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 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="#E10:13_1"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E23:13_1"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E1:13_1_3_2"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="ref" href="scm_1.html#T10" title="SCM_1:th.10">SCM_1:10</a></span>;<br/><a NAME="E4:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A29</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 5 <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="#E25:13_1"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="ref" href="scm_1.html#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><a NAME="E5:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A30</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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 <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="#E18:13_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="scm_1.html#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><a NAME="E6:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A31</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 7 <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="#E14:13_1"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="ref" href="scm_1.html#T5" title="SCM_1:th.5">SCM_1:5</a></span>;<br/><a NAME="E7:13_1_3_2"/><span class="lab"><font color="Green" title="E46">A32</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E25:13_1"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="txt" href="#E13:13_1"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E3:13_1_3_2"><span class="lab"><font color="Green" title="E42">A28</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#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><a NAME="E8:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A33</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:13_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E4:13_1_3_2"><span class="lab"><font color="Green" title="E43">A29</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#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><a NAME="E9:13_1_3_2"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:13_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E4:13_1_3_2"><span class="lab"><font color="Green" title="E43">A29</font></span></a>, <a class="txt" href="#E7:13_1_3_2"><span class="lab"><font color="Green" title="E46">A32</font></span></a>, <a class="ref" href="scm_1.html#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><a NAME="E10:13_1_3_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E5:13_1_3_2"><span class="lab"><font color="Green" title="E44">A30</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#T5" title="SCM_1:th.5">SCM_1:5</a></span>;<br/><a NAME="E11:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A34</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:13_1"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="txt" href="#E6:13_1_3_2"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="scm_1.html#T9" title="SCM_1:th.9">SCM_1:9</a></span>;<br/><a NAME="E12:13_1_3_2"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:13_1"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="txt" href="#E21:13_1"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="txt" href="#E3:13_1_3_2"><span class="lab"><font color="Green" title="E42">A28</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#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><a NAME="E13:13_1_3_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:13_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E4:13_1_3_2"><span class="lab"><font color="Green" title="E43">A29</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#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><a NAME="E14:13_1_3_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E5:13_1_3_2"><span class="lab"><font color="Green" title="E44">A30</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#T5" title="SCM_1:th.5">SCM_1:5</a></span>;<br/><a NAME="E15:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A35</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:13_1"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="txt" href="#E6:13_1_3_2"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="scm_1.html#T9" title="SCM_1:th.9">SCM_1:9</a></span>;<br/><a NAME="E16:13_1_3_2"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c8">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E25:13_1"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="txt" href="#E17:13_1"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E3:13_1_3_2"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="scm_1.html#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><a NAME="E17:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A36</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c8">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:13_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E4:13_1_3_2"><span class="lab"><font color="Green" title="E43">A29</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#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<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="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c11">s</font>,<span class="p3">(<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="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 3</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E5:13_1_3_2"><span class="lab"><font color="Green" title="E44">A30</font></span></a>, <a class="ref" href="scm_1.html#T5" title="SCM_1:th.5">SCM_1:5</a></span>
<br/>.= 
 <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_1_3_2"><span class="lab"><font color="Green" title="E47">A33</font></span></a>, <a class="txt" href="#E17:13_1_3_2"><span class="lab"><font color="Green" title="E50">A36</font></span></a>, <a class="ref" href="pre_ff.html#T1" title="PRE_FF:th.1">PRE_FF:1</a></span>
;<br/><a NAME="E19:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A37</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:13_1"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="txt" href="#E6:13_1_3_2"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="scm_1.html#T9" title="SCM_1:th.9">SCM_1:9</a></span>;<br/><a NAME="E20:13_1_3_2"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:13_1"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="txt" href="#E24:13_1"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E3:13_1_3_2"><span class="lab"><font color="Green" title="E42">A28</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#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><a NAME="E21:13_1_3_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> <font color="Maroon" title="c7">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:13_1"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E4:13_1_3_2"><span class="lab"><font color="Green" title="E43">A29</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#T4" title="SCM_1:th.4">SCM_1:4</a></span>;<br/><a NAME="E22:13_1_3_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> <font color="Maroon" title="c7">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E5:13_1_3_2"><span class="lab"><font color="Green" title="E44">A30</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#T5" title="SCM_1:th.5">SCM_1:5</a></span>;<br/><a NAME="E23:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A38</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> <font color="Maroon" title="c7">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:13_1"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="txt" href="#E6:13_1_3_2"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="scm_1.html#T9" title="SCM_1:th.9">SCM_1:9</a></span>;<br/><a NAME="E24:13_1_3_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:13_1"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="txt" href="#E6:13_1_3_2"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="scm_1.html#T9" title="SCM_1:th.9">SCM_1:9</a></span>;<br/><a NAME="E25:13_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A39</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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  3 <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>   <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> ,<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">1</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="c7">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="Maroon" title="c10">Fk1</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"><a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="#E5:13_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E15:13_1_3_2"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="txt" href="#E23:13_1_3_2"><span class="lab"><font color="Green" title="E52">A38</font></span></a>, <a class="txt" href="#E11:13_1_3_2"><span class="lab"><font color="Green" title="E48">A34</font></span></a>, <a class="txt" href="#E19:13_1_3_2"><span class="lab"><font color="Green" title="E51">A37</font></span></a>, <a class="ref" href="memstr_0.html#D9" title="MEMSTR_0:def.9">MEMSTR_0:def 9</a>, <a class="ref" href="scm_1.html#T13" title="SCM_1:th.13">SCM_1:13</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">m</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> <span class="kw"> such that </span><br/><a NAME="E27:13_1_3_2"/><span class="lab"><font color="Green" title="E54">A40</font></span>: 
<font color="Maroon" title="c20">m</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="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">N</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <span class="kw">and </span><br/><a NAME="E28:13_1_3_2"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c20">m</font>
 <span class="kw">and </span><br/><a NAME="E29:13_1_3_2"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c20">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E1:13_1_3_2"><span class="lab"><font color="Green" title="E40">A26</font></span></a></span>;<br/><a NAME="E30:13_1_3_2"/><span class="lab"><font color="Green" title="E55">A41</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="#E1:13_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E1:13_1_3_2"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E25:13_1_3_2"><span class="lab"><font color="Green" title="E53">A39</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E31:13_1_3_2"/>
<font color="Maroon" title="c1">F</font> <a href="extpro_1.html#R1" title="EXTPRO_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="extpro_1.html#T22" title="EXTPRO_1:th.22">EXTPRO_1:22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4 &amp;  ex <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b1">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) )</span><br/><a NAME="E32:13_1_3_2"/>
 <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c7">N</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E1:13_1_3_2"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E25:13_1_3_2"><span class="lab"><font color="Green" title="E53">A39</font></span></a></span>;<br/><span class="kw">hence </span> <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c11">s</font>) = 
6 <a href="xcmplx_0.html#K2" title="XCMPLX_0: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> <font color="Maroon" title="c7">N</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:13_1_3_2"><span class="lab"><font color="Green" title="E55">A41</font></span></a>, <a class="txt" href="#E2:13_1_3_2"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="ref" href="extpro_1.html#T34" title="EXTPRO_1:th.34">EXTPRO_1:34</a></span>
<br/>.= 
<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="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 4

;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b1">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )</span><br/><span class="kw">take </span>
<font color="Maroon" title="c20">m</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c20">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c20">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c20">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E34:13_1_3_2"/>
<font color="Maroon" title="c20">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:13_1_3_2"><span class="lab"><font color="Green" title="E54">A40</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c20">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c20">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )</span><br/><a NAME="E35:13_1_3_2"/>
 ex <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">m</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="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">N</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Olive" title="b1">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E1:13_1_3_2"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E25:13_1_3_2"><span class="lab"><font color="Green" title="E53">A39</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E36:13_1_3_2"/>
( <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K3" title="PRE_FF:func.3">Fib</a> <font color="Maroon" title="c20">m</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c1">F</font>,<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#K3" title="PRE_FF:func.3">Fib</a> <span class="p1">(<span class="default"><font color="Maroon" title="c20">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:13_1_3_2"><span class="lab"><font color="Green" title="E54">A40</font></span></a>, <a class="txt" href="#E30:13_1_3_2"><span class="lab"><font color="Green" title="E55">A41</font></span></a>, <a class="ref" href="extpro_1.html#T35" title="EXTPRO_1:th.35">EXTPRO_1:35</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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>
<a NAME="E3:13"/><span class="lab"><font color="Green" title="E21">A42</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
;<br/>
<span class="kw">thus </span><a NAME="E4:13"/>
 for <font color="Olive" title="b1">N</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">N</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E21">A42</font></span></a>, <a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E20">A2</font></span></a>);</span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
