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

<b>set </b><font color="Maroon">c<sub>17</sub></font> =  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>();<br/>
<b>set </b><font color="Maroon">c<sub>18</sub></font> =  <a href="scpinvar.html#K3" target="_self">while&lt;&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/>
<b>set </b><font color="Maroon">c<sub>19</sub></font> =  <a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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/>
<b>set </b><font color="Maroon">c<sub>20</sub></font> =  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> =  <a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>();<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></font> =  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>() <a href="scmpds_2.html#K8">&lt;&gt;0_goto</a> 2;<br/>
<b>set </b><font color="Maroon">c<sub>24</sub></font> =  <a href="scmpds_2.html#K4">goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>25</sub></font> =  <a href="scmpds_2.html#K4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  st <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <font color="Olive">b<sub>1</sub></font></span>)</span>) <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1">Dstate</a> <font color="Olive">b<sub>1</sub></font>] &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>() holds <br/>(  <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_closed_on</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_halting_on</a> <font color="Olive">b<sub>1</sub></font> );<br/>
<a NAME="E1:34_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>26</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E1:34_1_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <font color="Maroon">c<sub>26</sub></font></span>)</span>) <a href="xxreal_0.html#R1">&lt;=</a> 0 &amp; <font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1">Dstate</a> <font color="Maroon">c<sub>26</sub></font>] &amp; <font color="Maroon">c<sub>26</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>() )
 ;<br/>

<a NAME="E2:34_1_1"/>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <font color="Maroon">c<sub>26</sub></font></span>)</span>) <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<a NAME="E3:34_1_1"/><b>then </b>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <font color="Maroon">c<sub>26</sub></font></span>)</span>) <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpinvar.html#E1:34_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xreal_1.html#T1">XREAL_1:1</a></i>;<br/>
<a NAME="E4:34_1_1"/><b>then </b>
<font color="Maroon">c<sub>26</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpinvar.html#E2:34"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scpinvar.html#E1:34_1_1"><i><font color="Green">E30</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:34_1_1"/>
(  <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_closed_on</a> <font color="Maroon">c<sub>26</sub></font> &amp;  <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_halting_on</a> <font color="Maroon">c<sub>26</sub></font> )
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:34_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scpinvar.html#T16" target="_self">Th16</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:34_1"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>26</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:34_1_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>26</sub></font>]
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>27</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>assume </b><a NAME="E1:34_1_2_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <font color="Maroon">c<sub>27</sub></font></span>)</span>) <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>26</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><b>assume </b><a NAME="E2:34_1_2_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1">Dstate</a> <font color="Maroon">c<sub>27</sub></font>]
 ;<br/><b>assume </b><a NAME="E3:34_1_2_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>27</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_1_2_1_1"/>
( <font color="Maroon">c<sub>27</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>27</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:34_1_2_1_1_1"/>
<font color="Maroon">c<sub>27</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:34_1_2_1_1_1"/>
(  <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_closed_on</a> <font color="Maroon">c<sub>27</sub></font> &amp;  <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_halting_on</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="txt" href="scpinvar.html#E3:34_1_2_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scpinvar.html#T16" target="_self">Th16</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:34_1_2_1_1_2"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>27</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>29</sub></font> = <font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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/><b>set </b><font color="Maroon">c<sub>30</sub></font> =  <a href="ami_1.html#K10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>;<br/><b>set </b><font color="Maroon">c<sub>31</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1;<br/><a NAME="E2:34_1_2_1_1_2"/><i><font color="Green">E36</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">c<sub>27</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>() &amp; <font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">c<sub>27</sub></font></span>)</span></span>)</span>) <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <font color="Maroon">c<sub>27</sub></font></span>)</span>) &amp; <font color="Maroon">P<sub>1</sub></font>[ <a href="scmpds_8.html#K1">Dstate</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">c<sub>27</sub></font></span>)</span>] )
 <b>by </b><i><a class="txt" href="scpinvar.html#E4:34"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scpinvar.html#E2:34_1_2_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="scpinvar.html#E3:34_1_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scpinvar.html#E1:34_1_2_1_1_2"><i><font color="Green">E35</font></i></a></i>;<br/><a NAME="E3:34_1_2_1_1_2"/><i><font color="Green">E37</font></i>: 
 <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/><a NAME="E4:34_1_2_1_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="txt" href="scpinvar.html#E2:34_1_2_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="scmpds_6.html#D3">SCMPDS_6:def 3</a></i>;<br/><a NAME="E5:34_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="txt" href="scpinvar.html#E3:34_1_2_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>;<br/><a NAME="E6:34_1_2_1_1_2"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_6.html#D3">SCMPDS_6:def 3</a></i>;<br/><a NAME="E7:34_1_2_1_1_2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">F<sub>3</sub></font>() <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpinvar.html#E2:34_1_2_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="scmpds_6.html#T38">SCMPDS_6:38</a></i>;<br/><a NAME="E8:34_1_2_1_1_2"/><i><font color="Green">E41</font></i>: 
 <a href="scmpds_3.html#K2">inspos</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T75">SCMPDS_4:75</a></i>;<br/><a NAME="E9:34_1_2_1_1_2"/><i><font color="Green">E42</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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">=</a>  <a href="scmpds_3.html#K2">inspos</a> 0
 <b>by </b><i><a class="ref" href="scmpds_6.html#T21">SCMPDS_6:21</a></i>;<br/><a NAME="E10:34_1_2_1_1_2"/>
 <a href="scpinvar.html#K3" target="_self">while&lt;&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">=</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#K8">&lt;&gt;0_goto</a> 2</span>)</span> <a href="scmpds_4.html#K4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K4">';'</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpinvar.html#E28"><i><font color="Green">Lemma20</font></i></a></i>;<br/><a NAME="E11:34_1_2_1_1_2"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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">=</a> <font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon">F<sub>5</sub></font>() <a href="scmpds_2.html#K8">&lt;&gt;0_goto</a> 2
 <b>by </b><i><a class="ref" href="scmpds_6.html#T22">SCMPDS_6:22</a></i>;<br/><i><font color="Green">E44</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">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#K8">&lt;&gt;0_goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
<b>by </b><i><a class="txt" href="scpinvar.html#E11:34_1_2_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
;<br/><a NAME="E13:34_1_2_1_1_2"/><i><font color="Green">E45</font></i>: 
( not <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> &amp; <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#T49">SCMPDS_2:49</a>, <a class="ref" href="scmpds_4.html#T31">SCMPDS_4:31</a></i>;<br/><a NAME="E14:34_1_2_1_1_2"/><i><font color="Green">E46</font></i>: 
( not  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> &amp;  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#T49">SCMPDS_2:49</a>, <a class="ref" href="scmpds_4.html#T31">SCMPDS_4:31</a></i>;<br/><i><font color="Green">E47</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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">.</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">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E3:34_1_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scpinvar.html#E13:34_1_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">c<sub>27</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>,<font color="Maroon">F<sub>5</sub></font>()</span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E14:34_1_2_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/><i><font color="Green">E48</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>,2
<b>by </b><i><a class="txt" href="scpinvar.html#E1:34_1_2_1_1_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scpinvar.html#E12:34_1_2_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scpinvar.html#E15:34_1_2_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmpds_2.html#T67">SCMPDS_2:67</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E9:34_1_2_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="scmpds_6.html#T23">SCMPDS_6:23</a></i>
;<br/><a NAME="E17:34_1_2_1_1_2"/>
<font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span>,<font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="scmpds_4.html#T36">SCMPDS_4:36</a></i>;<br/><a NAME="E18:34_1_2_1_1_2"/><b>then </b><i><font color="Green">E49</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmpds_4.html#T24">SCMPDS_4:24</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_2_1_1_2_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>32</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>32</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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">.</a> <font color="Maroon">c<sub>32</sub></font>
<b>by </b><i><a class="txt" href="scpinvar.html#E18:34_1_2_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>32</sub></font>
<b>by </b><i><a class="txt" href="scpinvar.html#E12:34_1_2_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="scmpds_2.html#T67">SCMPDS_2:67</a></i>
;<br/></div><b>end;</b></div><a NAME="E20:34_1_2_1_1_2"/><b>then </b><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>set </b><font color="Maroon">c<sub>32</sub></font> =  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>33</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>34</sub></font> =  <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>;<br/><a NAME="E21:34_1_2_1_1_2"/><i><font color="Green">E51</font></i>: 
 <a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#D8">SCMPDS_4:def 8</a></i>;<br/><a NAME="E22:34_1_2_1_1_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="scmpds_6.html#T1">SCMPDS_6:1</a></i>;<br/><a NAME="E23:34_1_2_1_1_2"/><b>then </b><i><font color="Green">E52</font></i>: 
not <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>;<br/><a NAME="E24:34_1_2_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 3
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E25:34_1_2_1_1_2"/><b>then </b><i><font color="Green">E53</font></i>: 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="ref" href="scpinvar.html#T13" target="_self">Th13</a></i>;<br/><a NAME="E26:34_1_2_1_1_2"/><i><font color="Green">E54</font></i>: 
 <a href="scpinvar.html#K3" target="_self">while&lt;&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">c=</a>  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="ref" href="scmpds_6.html#T17">SCMPDS_6:17</a></i>;<br/><a NAME="E27:34_1_2_1_1_2"/>
 <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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">c=</a> <font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/><a NAME="E28:34_1_2_1_1_2"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="scpinvar.html#K3" target="_self">while&lt;&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">c=</a> <font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="txt" href="scpinvar.html#E26:34_1_2_1_1_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E29:34_1_2_1_1_2"/>
 <a href="scmpds_3.html#K6">Shift</a> <font color="Maroon">F<sub>3</sub></font>(),2 <a href="tarski.html#R1">c=</a>  <a href="scpinvar.html#K3" target="_self">while&lt;&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>()
 <b>by </b><i><a class="txt" href="scpinvar.html#E33"><i><font color="Green">Lemma24</font></i></a></i>;<br/><a NAME="E30:34_1_2_1_1_2"/><b>then </b>
 <a href="scmpds_3.html#K6">Shift</a> <font color="Maroon">F<sub>3</sub></font>(),2 <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="txt" href="scpinvar.html#E28:34_1_2_1_1_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E31:34_1_2_1_1_2"/><b>then </b><i><font color="Green">E56</font></i>: 
 <a href="scmpds_3.html#K6">Shift</a> <font color="Maroon">F<sub>3</sub></font>(),2 <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1
 <b>by </b><i><a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/><a NAME="E32:34_1_2_1_1_2"/><b>then </b><i><font color="Green">E57</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:34"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scpinvar.html#E3:34_1_2_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scpinvar.html#E6:34_1_2_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scpinvar.html#E7:34_1_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scpinvar.html#E16:34_1_2_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scpinvar.html#E20:34_1_2_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmpds_7.html#T36">SCMPDS_7:36</a></i>;<br/><b>then </b><i><font color="Green">E58</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">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">.</a> <font color="Maroon">F<sub>4</sub></font>() = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">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">.</a> <font color="Maroon">F<sub>4</sub></font>()
<b>by </b><i><a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()
<b>by </b><i><a class="txt" href="scpinvar.html#E4:34_1_2_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="scmfsa6b.html#T16">SCMFSA6B:16</a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()
<b>by </b><i><a class="txt" href="scpinvar.html#E3:34_1_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scpinvar.html#E2:34_1_2_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="scpinvar.html#E21:34_1_2_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scpinvar.html#E23:34_1_2_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/><a NAME="E34:34_1_2_1_1_2"/><i><font color="Green">E59</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="scmpds_6.html#T1">SCMPDS_6:1</a></i>;<br/><i><font color="Green">E60</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
<b>by </b><i><a class="txt" href="scpinvar.html#E4:34_1_2_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scpinvar.html#E32:34_1_2_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmfsa6b.html#T16">SCMFSA6B:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
<b>by </b><i><a class="txt" href="scpinvar.html#E34:34_1_2_1_1_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="funct_4.html#T76">FUNCT_4:76</a>, <a class="ref" href="scmpds_2.html#T10">SCMPDS_2:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">c<sub>27</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
<b>by </b><i><a class="ref" href="scmpds_4.html#D8">SCMPDS_4:def 8</a></i>
;<br/><b>set </b><font color="Maroon">c<sub>35</sub></font> = <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1;<br/><b>set </b><font color="Maroon">c<sub>36</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/><a NAME="E36:34_1_2_1_1_2"/><i><font color="Green">E61</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">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">=</a>  <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:34"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scpinvar.html#E3:34_1_2_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scpinvar.html#E6:34_1_2_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scpinvar.html#E7:34_1_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scpinvar.html#E16:34_1_2_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scpinvar.html#E20:34_1_2_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scpinvar.html#E31:34_1_2_1_1_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="scmpds_7.html#T36">SCMPDS_7:36</a></i>;<br/><a NAME="E37:34_1_2_1_1_2"/><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>;<br/><b>then </b><i><font color="Green">E63</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">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#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E36:34_1_2_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p4">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E25:34_1_2_1_1_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scpinvar.html#E28:34_1_2_1_1_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
 <a href="scmpds_2.html#K4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scpinvar.html#T15" target="_self">Th15</a></i>
;<br/><b>set </b><font color="Maroon">c<sub>37</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/><i><font color="Green">E64</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E38:34_1_2_1_1_2"><i><font color="Green">E63</font></i></a>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
;<br/><i><font color="Green">E65</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E39:34_1_2_1_1_2"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> 0
<b>by </b><i><a class="txt" href="scpinvar.html#E36:34_1_2_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpinvar.html#E37:34_1_2_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_7.html#T1">SCMPDS_7:1</a></i>
;<br/><i><font color="Green">E66</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>() = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()
<b>by </b><i><a class="txt" href="scpinvar.html#E39:34_1_2_1_1_2"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2">.</a> <font color="Maroon">F<sub>4</sub></font>()
<b>by </b><i><a class="txt" href="scpinvar.html#E33:34_1_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><a NAME="E42:34_1_2_1_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="scmpds_2.html#T21">SCMPDS_2:21</a></i>;<br/><a NAME="E43:34_1_2_1_1_2"/><b>then </b>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K9">{</a><span class="default">0,4,5,6</span><a href="domain_1.html#K9">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/><b>then </b><i><font color="Green">E67</font></i>:  <a href="scmpds_8.html#K1">Dstate</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
 <a href="scmpds_8.html#K1">Dstate</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E39:34_1_2_1_1_2"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmpds_8.html#T3">SCMPDS_8:3</a></i>
<br/>.= 
 <a href="scmpds_8.html#K1">Dstate</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">c<sub>27</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E35:34_1_2_1_1_2"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpinvar.html#E37:34_1_2_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_8.html#T2">SCMPDS_8:2</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_2_1_1_2_12"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_1_2_1_1_2_12"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>) <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>26</sub></font>
 ;<br/><a NAME="E2:34_1_2_1_1_2_12"/>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">c<sub>27</sub></font></span>)</span></span>)</span>) <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <font color="Maroon">c<sub>27</sub></font></span>)</span>)
 <b>by </b><i><a class="txt" href="scpinvar.html#E4:34"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scpinvar.html#E2:34_1_2_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="scpinvar.html#E3:34_1_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scpinvar.html#E1:34_1_2_1_1_2"><i><font color="Green">E35</font></i></a></i>;<br/><a NAME="E3:34_1_2_1_1_2_12"/><b>then </b>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>) <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>26</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:34_1_2_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scpinvar.html#E44:34_1_2_1_1_2"><i><font color="Green">E67</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><a NAME="E4:34_1_2_1_1_2_12"/>
contradiction
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:34_1_2_1_1_2_12"><i><font color="Green">E68</font></i></a>, <a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/></div><b>end;</b></div><a NAME="E46:34_1_2_1_1_2"/><b>then </b><i><font color="Green">E68</font></i>: 
(  <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_closed_on</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp;  <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_halting_on</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:34_1_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scpinvar.html#E2:34_1_2_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="scpinvar.html#E41:34_1_2_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpinvar.html#E44:34_1_2_1_1_2"><i><font color="Green">E67</font></i></a></i>;<br/><a NAME="E47:34_1_2_1_1_2"/><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="scpinvar.html#E40:34_1_2_1_1_2"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scmpds_7.html#T37">SCMPDS_7:37</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_2_1_1_2_13"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>38</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_2_13_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_1_2_1_1_2_13_1"/>
( <font color="Maroon">c<sub>38</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">c<sub>38</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_2_13_1_1"><b>suppose </b></a><a NAME="E1:34_1_2_1_1_2_13_1_1"/>
<font color="Maroon">c<sub>38</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:34_1_2_1_1_2_13_1_1"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>38</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_2_13_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_1_2_1_1_2_13_1_1_1_1"/>
( <font color="Maroon">c<sub>38</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="scpinvar.html#E2:34_1_2_1_1_2_13_1_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_2_13_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:34_1_2_1_1_2_13_1_1_1_1_1"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>38</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_2_13_1_1_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_1_2_1_1_2_13_1_1_1_1_1_1_1"/>
( <font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_2_13_1_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:34_1_2_1_1_2_13_1_1_1_1_1_1_1_1"/>
<font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:34_1_2_1_1_2_13_1_1_1_1_1_1_1_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="txt" href="scpinvar.html#E8:34_1_2_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scpinvar.html#E9:34_1_2_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/>
<font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>39</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>39</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/><a NAME="E4:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/>
<font color="Maroon">c<sub>39</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>38</sub></font>
 <b>by </b><i><a class="txt" href="scpinvar.html#E3:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E5:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>39</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:34_1_2_1_1_2_13_1_1_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E6:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E73</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>39</sub></font></span>)</span></span>)</span> <a href="scmpds_3.html#K3">+</a> 2 <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> 1</span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>39</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:34"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scpinvar.html#E3:34_1_2_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scpinvar.html#E6:34_1_2_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scpinvar.html#E7:34_1_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scpinvar.html#E16:34_1_2_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scpinvar.html#E20:34_1_2_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scpinvar.html#E31:34_1_2_1_1_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="scmpds_7.html#T34">SCMPDS_7:34</a></i>;<br/><a NAME="E7:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/><i><font color="Green">E74</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>39</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>
 <b>by </b><i><a class="txt" href="scpinvar.html#E2:34_1_2_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="scmpds_6.html#D2">SCMPDS_6:def 2</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>40</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E9:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/><i><font color="Green">E75</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>39</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">c<sub>40</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T32">SCMPDS_3:32</a></i>;<br/><a NAME="E10:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/>
<font color="Maroon">c<sub>40</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>
 <b>by </b><i><a class="txt" href="scpinvar.html#E7:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scpinvar.html#E9:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/><a NAME="E11:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>40</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="scmpds_5.html#T7">SCMPDS_5:7</a></i>;<br/><a NAME="E12:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>40</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E13:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 4
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E14:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>40</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 4
 <b>by </b><i><a class="txt" href="scpinvar.html#E12:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E15:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>40</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="txt" href="scpinvar.html#E24"><i><font color="Green">Lemma16</font></i></a></i>;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">c<sub>40</sub></font></span>)</span> <a href="scmpds_3.html#K3">+</a> 2
<b>by </b><i><a class="txt" href="scpinvar.html#E3:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scpinvar.html#E6:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scpinvar.html#E9:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"><i><font color="Green">E75</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>40</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#D3">SCMPDS_3:def 3</a></i>
;<br/><b>hence </b><a NAME="E17:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="txt" href="scpinvar.html#E15:34_1_2_1_1_2_13_1_1_1_1_1_1_1_2"><i><font color="Green">E77</font></i></a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_2_13_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:34_1_2_1_1_2_13_1_1_1_1_2"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:34_1_2_1_1_2_13_1_1_1_1_2"/>
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="txt" href="scpinvar.html#E25:34_1_2_1_1_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scmpds_6.html#T18">SCMPDS_6:18</a></i>;<br/><b>hence </b><a NAME="E3:34_1_2_1_1_2_13_1_1_1_1_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:34"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scpinvar.html#E3:34_1_2_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scpinvar.html#E6:34_1_2_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scpinvar.html#E7:34_1_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scpinvar.html#E16:34_1_2_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scpinvar.html#E20:34_1_2_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scpinvar.html#E31:34_1_2_1_1_2"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scpinvar.html#E37:34_1_2_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpinvar.html#E1:34_1_2_1_1_2_13_1_1_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_7.html#T36">SCMPDS_7:36</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2_1_1_2_13_1_2"><b>suppose </b></a><a NAME="E1:34_1_2_1_1_2_13_1_2"/>
<font color="Maroon">c<sub>38</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>39</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:34_1_2_1_1_2_13_1_2"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>39</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/><a NAME="E4:34_1_2_1_1_2_13_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>39</sub></font>
 <b>by </b><i><a class="txt" href="scpinvar.html#E47:34_1_2_1_1_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpinvar.html#E3:34_1_2_1_1_2_13_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>;<br/><b>hence </b><a NAME="E5:34_1_2_1_1_2_13_1_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p0">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>38</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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>
 <b>by </b><i><a class="txt" href="scpinvar.html#E46:34_1_2_1_1_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_6.html#D2">SCMPDS_6:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E49:34_1_2_1_1_2"/>
 <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_closed_on</a> <font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_6.html#D2">SCMPDS_6:def 2</a></i>;<br/><a NAME="E50:34_1_2_1_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p5">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="txt" href="scpinvar.html#E46:34_1_2_1_1_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpinvar.html#E47:34_1_2_1_1_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmpds_6.html#D3">SCMPDS_6:def 3</a></i>;<br/><a NAME="E51:34_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>27</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scpinvar.html#K3" target="_self">while&lt;&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> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="ref" href="scm_1.html#T27">SCM_1:27</a></i>;<br/><b>hence </b><a NAME="E52:34_1_2_1_1_2"/>
 <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_halting_on</a> <font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="ref" href="scmpds_6.html#D3">SCMPDS_6:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:34_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>26</sub></font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:34_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="scpinvar.html#E1:34_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scpinvar.html#E2:34_1"><i><font color="Green">E30</font></i></a>);<br/></i>
<b>set </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="scmpds_8.html#K1">Dstate</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span>);<br/>
<a NAME="E4:34_1"/>
<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">Dstate</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span>)]
 
<b>by </b><i><a class="txt" href="scpinvar.html#E3:34_1"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:34_1"/>
(  <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_closed_on</a> <font color="Maroon">F<sub>2</sub></font>() &amp;  <a href="scpinvar.html#K3" target="_self">while&lt;&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">is_halting_on</a> <font color="Maroon">F<sub>2</sub></font>() )
 <b>by </b><i><a class="txt" href="scpinvar.html#E3:34"><i><font color="Green">E27</font></i></a></i>;<br/>


</div>
