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

<span class="kw">set </span><font color="Maroon" title="c3">i1</font> = <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>() <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">i2</font> =  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">WHL</font> =  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>();<br/>
<span class="kw">set </span><font color="Maroon" title="c6">pWHL</font> =  <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">iWHL</font> =  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">pI</font> =  <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>();<br/>
<span class="kw">set </span><font color="Maroon" title="c9">IsI</font> =  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">b</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>();<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ] <span class="kw">means </span>for <font color="Olive" title="b1">t</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>   st <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Olive" title="b1">t</font></span>)</span>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> $1 &amp; <font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Olive" title="b1">t</font>] &amp; <font color="Olive" title="b1">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() holds <br/>(  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive" title="b1">t</font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive" title="b1">t</font> );<br/>
<a NAME="E1:37_1"/><span class="lab"><font color="Green" title="E26">A5</font></span>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c11">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:37_1_1"/><span class="lab"><font color="Green" title="E27">A6</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">k</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">t</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</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">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font></span>)</span>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font>] &amp; <font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() implies (  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive">b<sub>1</sub></font> ) )</span><br/><span class="kw">assume </span><a NAME="E1:37_1_1_1"/><span class="lab"><font color="Green" title="E28">A7</font></span>: 
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font></span>)</span>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font>] &amp; <font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() implies (  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive">b<sub>1</sub></font> ) )</span><br/><span class="kw">assume </span><a NAME="E2:37_1_1_1"/><span class="lab"><font color="Green" title="E29">A8</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font>]
 ; <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="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() implies (  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive">b<sub>1</sub></font> ) )</span><br/><span class="kw">assume </span><a NAME="E3:37_1_1_1"/><span class="lab"><font color="Green" title="E30">A9</font></span>: 
<font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:37_1_1_1_1"/>
( <font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> <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>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_1_1_1"/>
<font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:37_1_1_1_1_1"/>
(  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c12">t</font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">t</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_1_1_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="ref" href="scmpds_8.html#T20" target="_self" title="SCMPDS_8:th.20">Th20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E31">A10</font></span>: 
<font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><div class="add"><a NAME="E2:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E32">A11</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T143" title="AMI_1:th.143">AMI_1:143</a></span>;<br/><a NAME="E3:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E33">A12</font></span>: 
not <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E32">A11</font></span></a>, <a class="ref" href="scmpds_2.html#T53" title="SCMPDS_2:th.53">SCMPDS_2:53</a></span>;<br/><a NAME="E4:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E34">A13</font></span>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c12">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="txt" href="#E2:37_1_1_1"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="txt" href="#E3:37_1_1_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="txt" href="#E1:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E31">A10</font></span></a></span>;<br/><a NAME="E5:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E35">A14</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T75" title="SCMPDS_4:th.75">SCMPDS_4:75</a></span>;<br/><a NAME="E6:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E36">A15</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T143" title="AMI_1:th.143">AMI_1:143</a></span>;<br/><a NAME="E7:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E37">A16</font></span>: 
not  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T31" title="SCMPDS_4:th.31">SCMPDS_4:31</a></span>;<br/><a NAME="E8:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E38">A17</font></span>: 
 <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>() <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T51" title="SCMPDS_4:th.51">SCMPDS_4:51</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c13">t2</font> = <font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c14">t3</font> = <font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c15">t4</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1;<br/><a NAME="E9:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E39">A18</font></span>: 
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c16">m2</font> =  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c17">t5</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <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> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c18">l1</font> = <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/><a NAME="E10:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E40">A19</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T21" title="SCMPDS_6:th.21">SCMPDS_6:21</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c19">m3</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/><span class="kw">set </span><font color="Maroon" title="c20">t6</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c21">t7</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> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/><a NAME="E11:37_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <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> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/><a NAME="E12:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A20</font></span>: 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_8.html#T18" target="_self" title="SCMPDS_8:th.18">Th18</a></span>;<br/><a NAME="E13:37_1_1_1_1_2"/>
(  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span> &amp;  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a>, <a class="ref" href="scmpds_6.html#T17" title="SCMPDS_6:th.17">SCMPDS_6:17</a></span>;<br/><a NAME="E14:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A21</font></span>: 
 <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E15:37_1_1_1_1_2"/>
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <font color="Maroon">F<sub>3</sub></font>(),1 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()
 <span class="kw">by</span> <span class="lab"><a class="txt" href="scmpds_8.html#E30"><span class="lab"><font color="Green" title="E21">Lm4</font></span></a></span>;<br/><a NAME="E16:37_1_1_1_1_2"/><span class="kw">then </span>
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <font color="Maroon">F<sub>3</sub></font>(),1 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E42">A21</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E17:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A22</font></span>: 
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> <font color="Maroon">F<sub>3</sub></font>(),1 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T81" title="AMI_1:th.81">AMI_1:81</a></span>;<br/><span class="lab"><font color="Green" title="E44">A23</font></span>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<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> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>
<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 href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>() <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E38">A17</font></span></a>, <a class="ref" href="scmpds_6.html#T22" title="SCMPDS_6:th.22">SCMPDS_6:22</a></span>
;<br/><a NAME="E19:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E45">A24</font></span>: 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T24" title="SCMPDS_4:th.24">SCMPDS_4:24</a>, <a class="ref" href="scmpds_4.html#T36" title="SCMPDS_4:th.36">SCMPDS_4:36</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c22">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">a</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E45">A24</font></span></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E44">A23</font></span></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E21:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A25</font></span>: 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></span>;<br/><a NAME="E22:37_1_1_1_1_2"/>
<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="txt" href="#E2:37_1_1_1"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="txt" href="#E3:37_1_1_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="txt" href="#E1:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E31">A10</font></span></a></span>;<br/><a NAME="E23:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A26</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></span>;<br/><a NAME="E24:37_1_1_1_1_2"/>
<font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></span>;<br/><a NAME="E25:37_1_1_1_1_2"/><span class="kw">then </span>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E47">A26</font></span></a></span>;<br/><a NAME="E26:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A27</font></span>: 
<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></span>;<br/><a NAME="E27:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E49">A28</font></span>: 
 <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#D8" title="SCMPDS_4:def.8">SCMPDS_4:def 8</a></span>;<br/><a NAME="E28:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E50">A29</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c12">t</font></span>)</span>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="txt" href="#E2:37_1_1_1"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="txt" href="#E3:37_1_1_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="txt" href="#E1:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E31">A10</font></span></a></span>;<br/><a NAME="E29:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E51">A30</font></span>: 
<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c12">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="txt" href="#E2:37_1_1_1"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="txt" href="#E3:37_1_1_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="txt" href="#E1:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E31">A10</font></span></a></span>;<br/><a NAME="E30:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A31</font></span>: 
<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T38" title="SCMPDS_6:th.38">SCMPDS_6:38</a></span>;<br/><a NAME="E31:37_1_1_1_1_2"/>
not <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T31" title="SCMPDS_4:th.31">SCMPDS_4:31</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_1_1_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E37">A16</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A32</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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E31">A10</font></span></a>, <a class="txt" href="#E18:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E44">A23</font></span></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></span>
<br/>.= 
<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="#E10:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E40">A19</font></span></a></span>
;<br/><a NAME="E34:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A33</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> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="txt" href="#E9:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="txt" href="#E26:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E48">A27</font></span></a>, <a class="txt" href="#E30:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E52">A31</font></span></a>, <a class="txt" href="#E21:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E46">A25</font></span></a>, <a class="txt" href="#E17:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E43">A22</font></span></a>, <a class="ref" href="scmpds_7.html#T36" title="SCMPDS_7:th.36">SCMPDS_7:36</a></span>;<br/><a NAME="E35:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E55">Y</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/><a NAME="E36:37_1_1_1_1_2"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/><a NAME="E37:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A34</font></span>: 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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> <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> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A35</font></span>:  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</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="#E1:37"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="txt" href="#E9:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="txt" href="#E26:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E48">A27</font></span></a>, <a class="txt" href="#E30:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E52">A31</font></span></a>, <a class="txt" href="#E33:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E53">A32</font></span></a>, <a class="txt" href="#E21:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E46">A25</font></span></a>, <a class="txt" href="#E17:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E43">A22</font></span></a>, <a class="txt" href="#E35:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E55">Y</font></span></a>, <a class="ref" href="scmpds_7.html#T36" title="SCMPDS_7:th.36">SCMPDS_7:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</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="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</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="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</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"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</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="#E12:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E41">A20</font></span></a>, <a class="txt" href="#E14:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E42">A21</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
 <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_8.html#T19" target="_self" title="SCMPDS_8:th.19">Th19</a></span>
;<br/><a NAME="E39:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E58">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/><span class="lab"><font color="Green" title="E59">A36</font></span>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E57">A35</font></span></a>, <a class="txt" href="#E39:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E58">T</font></span></a></span>
;<br/><span class="kw">then </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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E54">A33</font></span></a>, <a class="txt" href="#E37:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E56">A34</font></span></a>, <a class="ref" href="scmpds_7.html#T1" title="SCMPDS_7:th.1">SCMPDS_7:1</a></span>
;<br/><a NAME="E42:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A37</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <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> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_7.html#T37" title="SCMPDS_7:th.37">SCMPDS_7:37</a></span>;<br/><a NAME="E43:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E61">A38</font></span>: 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</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> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="txt" href="#E9:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="txt" href="#E26:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E48">A27</font></span></a>, <a class="txt" href="#E30:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E52">A31</font></span></a>, <a class="txt" href="#E33:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E53">A32</font></span></a>, <a class="txt" href="#E21:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E46">A25</font></span></a>, <a class="txt" href="#E17:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E43">A22</font></span></a>, <a class="ref" href="scmpds_7.html#T36" title="SCMPDS_7:th.36">SCMPDS_7:36</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A39</font></span>:  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</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> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E47">A26</font></span></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></span>
<br/>.= 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E36">A15</font></span></a>, <a class="ref" href="ami_2.html#T29" title="AMI_2:th.29">AMI_2:29</a>, <a class="ref" href="funct_4.html#T76" title="FUNCT_4:th.76">FUNCT_4:76</a>, <a class="ref" href="scmpds_2.html#T100" title="SCMPDS_2:th.100">SCMPDS_2:100</a></span>
<br/>.= 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c12">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#D8" title="SCMPDS_4:def.8">SCMPDS_4:def 8</a></span>
;<br/><a NAME="E45:37_1_1_1_1_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T21" title="SCMPDS_2:th.21">SCMPDS_2:21</a></span>;<br/><a NAME="E46:37_1_1_1_1_2"/><span class="kw">then </span>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,4,5,6</span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A40</font></span>:  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
 <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E59">A36</font></span></a>, <a class="ref" href="scmpds_8.html#T3" target="_self" title="SCMPDS_8:th.3">Th3</a></span>
<br/>.= 
 <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c12">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E62">A39</font></span></a>, <a class="txt" href="#E37:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E56">A34</font></span></a>, <a class="ref" href="scmpds_8.html#T2" target="_self" title="SCMPDS_8:th.2">Th2</a></span>
;<br/><div><span class="lab"><font color="Green" title="E64">A41</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1_1_2_10"><span class="kw">now </span></a><div class="add"><a NAME="E1:37_1_1_1_1_2_10"/>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon" title="c12">t</font></span>)</span></span>)</span>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="txt" href="#E2:37_1_1_1"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="txt" href="#E3:37_1_1_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="txt" href="#E1:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E31">A10</font></span></a></span>;<br/><a NAME="E2:37_1_1_1_1_2_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A42</font></span>: 
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1_1"><span class="lab"><font color="Green" title="E28">A7</font></span></a>, <a class="txt" href="#E47:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E63">A40</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><span class="kw">assume </span><a NAME="E3:37_1_1_1_1_2_10"/>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>) <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c11">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">hence </span><a NAME="E4:37_1_1_1_1_2_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1_1_1_1_2_10"><span class="lab"><font color="Green" title="E65">A42</font></span></a>, <a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="lab"><font color="Green" title="E65">A43</font></span>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E61">A38</font></span></a>, <a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></span>
<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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E47">A26</font></span></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></span>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_1_1_1"><span class="lab"><font color="Green" title="E30">A9</font></span></a>, <a class="txt" href="#E4:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="txt" href="#E27:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E49">A28</font></span></a>, <a class="txt" href="#E3:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E33">A12</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
;<br/><a NAME="E50:37_1_1_1_1_2"/><span class="lab"><font color="Green" title="E66">T1</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/><span class="lab"><font color="Green" title="E67">A44</font></span>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E59">A36</font></span></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></span>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E65">A43</font></span></a>, <a class="txt" href="#E50:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E66">T1</font></span></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></span>
;<br/><a NAME="E52:37_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A45</font></span>: 
 <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="txt" href="#E28:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E50">A29</font></span></a>, <a class="txt" href="#E47:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E63">A40</font></span></a>, <a class="txt" href="#E48:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E64">A41</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1_1_2_13"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c22">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2_13_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:37_1_1_1_1_2_13_1"/>
( <font color="Maroon" title="c22">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c22">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2_13_1_1"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_1_1_2_13_1_1"/>
<font color="Maroon" title="c22">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:37_1_1_1_1_2_13_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A46</font></span>: 
<font color="Maroon" title="c22">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></span>;<br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2_13_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:37_1_1_1_1_2_13_1_1_1_1"/>
( <font color="Maroon" title="c22">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> or <font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1_1_1_1_2_13_1_1"><span class="lab"><font color="Green" title="E69">A46</font></span></a>, <a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2_13_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_1_1_2_13_1_1_1_1_1"/><span class="lab"><font color="Green" title="E70">A47</font></span>: 
<font color="Maroon" title="c22">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span><br/><div class="add"><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2_13_1_1_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:37_1_1_1_1_2_13_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c22">k</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="c22">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2_13_1_1_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_1_1_2_13_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:37_1_1_1_1_2_13_1_1_1_1_1_1_1_1"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="txt" href="#E10:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E40">A19</font></span></a>, <a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c22">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">kn</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E71">A48</font></span>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">kn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c24">kn</font> = <font color="Maroon" title="c23">kn</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c25">lm</font> =  <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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c24">kn</font></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  ;<br/><a NAME="E6:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E72">t</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/><a NAME="E7:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c24">kn</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c22">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E71">A48</font></span></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></span>;<br/><a NAME="E8:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">kn</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1_1_1_2_13_1_1_1_1_1"><span class="lab"><font color="Green" title="E70">A47</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E9:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c24">kn</font></span>)</span></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>  <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> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,1</span>)</span>,<font color="Maroon" title="c24">kn</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="txt" href="#E9:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="txt" href="#E26:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E48">A27</font></span></a>, <a class="txt" href="#E30:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E52">A31</font></span></a>, <a class="txt" href="#E33:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E53">A32</font></span></a>, <a class="txt" href="#E21:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E46">A25</font></span></a>, <a class="txt" href="#E17:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E43">A22</font></span></a>, <a class="ref" href="scmpds_7.html#T34" title="SCMPDS_7:th.34">SCMPDS_7:34</a></span>;<br/><a NAME="E10:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A49</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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">lm</font> <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="#E3:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E71">A48</font></span></a>, <a class="txt" href="#E6:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E72">t</font></span></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></span>;<br/><a NAME="E11:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c24">kn</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E51">A30</font></span></a>, <a class="ref" href="scmpds_6.html#D2" title="SCMPDS_6:def.2">SCMPDS_6:def 2</a></span>;<br/><a NAME="E12:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c25">lm</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/><a NAME="E13:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c25">lm</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T7" title="SCMPDS_5:th.7">SCMPDS_5:7</a></span>;<br/><a NAME="E14:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A50</font></span>: 
<font color="Maroon" title="c25">lm</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></span>;<br/><a NAME="E15:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <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> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/><a NAME="E16:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c25">lm</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> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E74">A50</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E17:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c25">lm</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="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="scmpds_8.html#E23"><span class="lab"><font color="Green" title="E16">Lm3</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E18:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:37_1_1_1_1_2_13_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E73">A49</font></span></a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2_13_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_1_1_2_13_1_1_1_1_2"/><span class="lab"><font color="Green" title="E70">A51</font></span>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:37_1_1_1_1_2_13_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E41">A20</font></span></a>, <a class="ref" href="scmpds_6.html#T18" title="SCMPDS_6:th.18">SCMPDS_6:18</a></span>;<br/><span class="kw">hence </span><a NAME="E3:37_1_1_1_1_2_13_1_1_1_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="txt" href="#E9:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="txt" href="#E26:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E48">A27</font></span></a>, <a class="txt" href="#E30:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E52">A31</font></span></a>, <a class="txt" href="#E33:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E53">A32</font></span></a>, <a class="txt" href="#E21:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E46">A25</font></span></a>, <a class="txt" href="#E17:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E43">A22</font></span></a>, <a class="txt" href="#E37:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E56">A34</font></span></a>, <a class="txt" href="#E1:37_1_1_1_1_2_13_1_1_1_1_2"><span class="lab"><font color="Green" title="E70">A51</font></span></a>, <a class="ref" href="scmpds_7.html#T36" title="SCMPDS_7:th.36">SCMPDS_7:36</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2_13_1_2"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_1_1_2_13_1_2"/>
<font color="Maroon" title="c22">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <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> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">nn</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:37_1_1_1_1_2_13_1_2"/><span class="lab"><font color="Green" title="E69">A52</font></span>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c23">nn</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></span>;<br/><a NAME="E4:37_1_1_1_1_2_13_1_2"/><span class="lab"><font color="Green" title="E70">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/><a NAME="E5:37_1_1_1_1_2_13_1_2"/><span class="lab"><font color="Green" title="E71">A53</font></span>: 
<font color="Maroon" title="c23">nn</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><a NAME="E6:37_1_1_1_1_2_13_1_2"/><span class="kw">then </span>
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">k</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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c23">nn</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E60">A37</font></span></a>, <a class="txt" href="#E3:37_1_1_1_1_2_13_1_2"><span class="lab"><font color="Green" title="E69">A52</font></span></a>, <a class="txt" href="#E4:37_1_1_1_1_2_13_1_2"><span class="lab"><font color="Green" title="E70">T</font></span></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></span>;<br/><span class="kw">hence </span><a NAME="E7:37_1_1_1_1_2_13_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E68">A45</font></span></a>, <a class="txt" href="#E5:37_1_1_1_1_2_13_1_2"><span class="lab"><font color="Green" title="E71">A53</font></span></a>, <a class="ref" href="scmpds_6.html#D2" title="SCMPDS_6:def.2">SCMPDS_6:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E54:37_1_1_1_1_2"/>
 <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c12">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#D2" title="SCMPDS_6:def.2">SCMPDS_6:def 2</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="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">t</font></span><br/><a NAME="E55:37_1_1_1_1_2"/>
 <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1"><span class="lab"><font color="Green" title="E27">A6</font></span></a>, <a class="txt" href="#E28:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E50">A29</font></span></a>, <a class="txt" href="#E51:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E67">A44</font></span></a>, <a class="txt" href="#E47:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E63">A40</font></span></a>, <a class="txt" href="#E48:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E64">A41</font></span></a></span>;<br/><a NAME="E56:37_1_1_1_1_2"/><span class="kw">then </span>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:37_1_1_1_1_2"><span class="lab"><font color="Green" title="E60">A37</font></span></a>, <a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></span>;<br/><a NAME="E57:37_1_1_1_1_2"/><span class="kw">then </span>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/><a NAME="E58:37_1_1_1_1_2"/><span class="kw">then </span>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c12">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T93" title="AMI_1:th.93">AMI_1:93</a></span>;<br/><span class="kw">hence </span><a NAME="E59:37_1_1_1_1_2"/>
 <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:37_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c11">n</font> = <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span>);<br/>
<span class="kw">thus </span><a NAME="E2:37_1"/>
( <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">F<sub>2</sub></font>()) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">F<sub>2</sub></font>()) or <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>2</sub></font>()] )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon">F<sub>2</sub></font>() &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon">F<sub>2</sub></font>() )</span><br/>

<a NAME="E3:37_1"/><span class="lab"><font color="Green" title="E27">A54</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c12">t</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</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">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font></span>)</span>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font>] &amp; <font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() implies (  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c12">t</font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">t</font> ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:37_1_2"/><span class="lab"><font color="Green" title="E28">A55</font></span>: 
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font></span>)</span>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E2:37_1_2"/><span class="lab"><font color="Green" title="E29">A56</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font>]
 <span class="kw">and </span><br/><a NAME="E3:37_1_2"/><span class="lab"><font color="Green" title="E30">A57</font></span>: 
<font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c12">t</font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">t</font> )</span><br/>

<a NAME="E4:37_1_2"/>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon" title="c12">t</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_2"><span class="lab"><font color="Green" title="E28">A55</font></span></a></span>;<br/>
<a NAME="E5:37_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E2:37_1_2"><span class="lab"><font color="Green" title="E29">A56</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:37_1_2"/>
(  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c12">t</font> &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">t</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_1_2"><span class="lab"><font color="Green" title="E30">A57</font></span></a>, <a class="ref" href="scmpds_8.html#T20" target="_self" title="SCMPDS_8:th.20">Th20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E4:37_1"/>
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E3:37_1"><span class="lab"><font color="Green" title="E27">A54</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E26">A5</font></span></a>);<br/></span>
<a NAME="E5:37_1"/><span class="kw">then </span>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">Dstate</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span>)]
 
;<br/>
<span class="kw">hence </span><a NAME="E6:37_1"/>
(  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon">F<sub>2</sub></font>() &amp;  <a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon">F<sub>2</sub></font>() )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E24">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
