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

<b>let </b><font color="Maroon" title="c13">term</font> be   <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">aux</font>, <font color="Olive" title="b2">n</font>, <font color="Olive" title="b3">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <br/> for <font color="Olive" title="b4">s</font> being   <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of <font color="Olive" title="b2">n</font>,<font color="Olive" title="b2">n</font>,<font color="Olive" title="b3">k</font>,<span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Olive" title="b1">aux</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span>, <a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b1">aux</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="scm_comp.html#K17" title="SCM_COMP:func.17">max_Data-Loc_in</a> <font color="Maroon" title="c13">term</font> holds <br/>( <font color="Olive" title="b4">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <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> <font color="Olive" title="b1">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Olive" title="b4">s</font> &amp;  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Olive" title="b4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Olive" title="b1">aux</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c14">aux</font>, <font color="Maroon" title="c15">n</font>, <font color="Maroon" title="c16">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being   <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of <font color="Maroon" title="c15">n</font>,<font color="Maroon" title="c15">n</font>,<font color="Maroon" title="c16">k</font>,<span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span>, <a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Maroon" title="c14">aux</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="scm_comp.html#K17" title="SCM_COMP:func.17">max_Data-Loc_in</a> <font color="Maroon" title="c13">term</font> holds <br/>( <font color="Olive" title="b1">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <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> <font color="Maroon" title="c14">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Olive" title="b1">s</font> &amp;  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c17">s</font> be    <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of <font color="Maroon" title="c15">n</font>,<font color="Maroon" title="c15">n</font>,<font color="Maroon" title="c16">k</font>,<span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span>, <a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c14">aux</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="scm_comp.html#K17" title="SCM_COMP:func.17">max_Data-Loc_in</a> <font color="Maroon" title="c13">term</font> implies ( <font color="Maroon" title="c17">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c17">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> <font color="Maroon" title="c14">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c17">s</font> &amp;  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c17">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span> ) )</span><br/>





<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c14">aux</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="scm_comp.html#K17" title="SCM_COMP:func.17">max_Data-Loc_in</a> <font color="Maroon" title="c13">term</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c17">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c17">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> <font color="Maroon" title="c14">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c17">s</font> &amp;  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c17">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span> )</span><br/>

<a NAME="E2:31"/>
<font color="Maroon" title="c17">s</font> is    <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of <font color="Maroon" title="c15">n</font>,<font color="Maroon" title="c15">n</font>,<font color="Maroon" title="c16">k</font>, <a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font>, <a href="lang1.html#K2" title="LANG1:func.2">&lt;*&gt;</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<b>by </b><i><a class="ref" href="scm_comp.html#T1" target="_self" title="SCM_COMP:th.1">Th1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c18">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <font color="Maroon" title="c19">u</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <b> such that </b><br/><a NAME="E4:31"/><i><font color="Green" title="E28">A2</font></i>: 
( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c18">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span> &amp;  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s</font>,<font color="Maroon" title="c18">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c18">i</font></span>)</span> &amp;  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c19">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c18">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon" title="c19">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Maroon" title="c14">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c17">s</font> &amp; ( for <font color="Olive" title="b1">dn</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Olive" title="b1">dn</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c14">aux</font> holds <br/><font color="Maroon" title="c17">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> <font color="Olive" title="b1">dn</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Olive" title="b1">dn</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scm_comp.html#E1:31"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="scm_comp.html#T14" target="_self" title="SCM_COMP:th.14">Th14</a></i>;<br/>
<a NAME="E5:31"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>;<br/>
<a NAME="E6:31"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">i</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
 
<b>by </b><i><a class="txt" href="scm_comp.html#E4:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E7:31"/><b>then </b>
<font color="Maroon" title="c18">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>then </b><i><font color="Green" title="E29">A3</font></i>: <font color="Maroon" title="c17">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c18">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">i</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>
<b>by </b><i><a class="ref" href="scm_1.html#D1" title="SCM_1:def.1">SCM_1:def 1</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
<b>by </b><i><a class="txt" href="scm_comp.html#E4:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="finseq_1.html#T59" title="FINSEQ_1:th.59">FINSEQ_1:59</a></i>
;<br/>
<b>hence </b><a NAME="E9:31"/>
<font color="Maroon" title="c17">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 <b>by </b><i><a class="txt" href="scm_comp.html#E4:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="scm_1.html#T3" title="SCM_1:th.3">SCM_1:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c17">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> <font color="Maroon" title="c14">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c17">s</font> &amp;  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c17">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span> )</span><br/>

<b>thus </b><a NAME="E10:31"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c17">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> <font color="Maroon" title="c14">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c17">s</font>
 <b>by </b><i><a class="txt" href="scm_comp.html#E4:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="scm_comp.html#E8:31"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="scm_1.html#T4" title="SCM_1:th.4">SCM_1:4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c17">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span></span><br/>

<a NAME="E11:31"/>
(  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c18">i</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c18">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c15">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c18">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )
 
;<br/>
<b>hence </b><a NAME="E12:31"/>
 <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c17">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c13">term</font>,<font color="Maroon" title="c14">aux</font></span>)</span>
 <b>by </b><i><a class="txt" href="scm_comp.html#E4:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="scm_comp.html#E8:31"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="scm_1.html#T17" title="SCM_1:th.17">SCM_1:17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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