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

<span class="kw">let </span><font color="Maroon" title="c1">i1</font>, <font color="Maroon" title="c2">i2</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being   <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <span class="p3">(<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="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>,<span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c1">i1</font></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="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c2">i2</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> holds <br/> (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Olive" title="b1">s</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">i2</font> &amp; ( for <font color="Olive" title="b2">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>   st <font color="Olive" title="b2">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b2">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b2">d</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be    <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <span class="p3">(<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="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>,<span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c1">i1</font></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="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c2">i2</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c3">s</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">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> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">i2</font> &amp; ( for <font color="Olive" title="b1">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>   st <font color="Olive" title="b1">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> ) )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c4">s0</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">s1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">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="E1:39"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>;<br/>
<a NAME="E2:39"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
( <font color="Maroon" title="c3">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> <font color="Maroon" title="c1">i1</font> &amp; <font color="Maroon" title="c3">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="c2">i2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T15" target="_self" title="SCM_1:th.15">Th15</a></span>;<br/>
<a NAME="E3:39"/><span class="lab"><font color="Green" title="E25">A3</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T15" target="_self" title="SCM_1:th.15">Th15</a></span>;<br/>
<a NAME="E4:39"/><span class="lab"><font color="Green" title="E26">A4</font></span>: 
<font color="Maroon" title="c3">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T15" target="_self" title="SCM_1:th.15">Th15</a></span>;<br/>
<a NAME="E5:39"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A5</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font>,<span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="scm_1.html#T19" target="_self" title="SCM_1:th.19">Th19</a></span>;<br/>
<a NAME="E6:39"/><span class="lab"><font color="Green" title="E28">A6</font></span>: 
<font color="Maroon" title="c3">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#T15" target="_self" title="SCM_1:th.15">Th15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:39"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c3">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:39"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="scm_1.html#T3" target="_self" title="SCM_1:th.3">Th3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">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> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">i2</font> &amp; ( for <font color="Olive" title="b1">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>   st <font color="Olive" title="b1">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E8:39"/>
 <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:39"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E5:39"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="scm_1.html#T17" target="_self" title="SCM_1:th.17">Th17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">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> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">i2</font> &amp; ( for <font color="Olive" title="b1">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>   st <font color="Olive" title="b1">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> ) )</span><br/>

<a NAME="E9:39"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="scm_1.html#T19" target="_self" title="SCM_1:th.19">Th19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:39"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">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> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">i2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:39"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E5:39"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="scm_1.html#T4" target="_self" title="SCM_1:th.4">Th4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>   st <font color="Olive" title="b1">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font> )</span><br/>

<span class="kw">assume </span><a NAME="E11:39"/><span class="lab"><font color="Green" title="E29">A7</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">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> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:39"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E5:39"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="scm_1.html#T4" target="_self" title="SCM_1:th.4">Th4</a></span>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E11:39"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="ref" href="scm_1.html#T19" target="_self" title="SCM_1:th.19">Th19</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
