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

<b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c4">I</font> be   <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/><b>let </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>let </b><font color="Maroon" title="c7">i</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>







<b>set </b><font color="Maroon" title="c8">d1</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font>;<br/>
<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 ;<br/>

<b>set </b><font color="Maroon" title="c9">WHL</font> =  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font>;<br/>
<b>set </b><font color="Maroon" title="c10">pWHL</font> =  <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c11">iWHL</font> =  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c12">s3</font> = <font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c13">s4</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1;<br/>
<b>set </b><font color="Maroon" title="c14">i1</font> = <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c15">i2</font> =  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c16">SAl</font> =  <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>;<br/>
<a NAME="E2:15"/><i><font color="Green" title="E15">A2</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 0
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T21" title="SCMPDS_6:th.21">SCMPDS_6:21</a></i>;<br/>
<a NAME="E3:15"/>
 <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_8.html#E12"><i><font color="Green" title="E11">Lm2</font></i></a></i>;<br/>
<a NAME="E4:15"/><b>then </b><i><font color="Green" title="E16">A3</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T22" title="SCMPDS_6:th.22">SCMPDS_6:22</a></i>;<br/>
<i><font color="Green" title="E17">A4</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_8.html#E4:15"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="ami_1.html#D18" title="AMI_1:def.18">AMI_1:def 18</a></i>
;<br/>
<a NAME="E6:15"/><i><font color="Green" title="E18">A5</font></i>: 
( not  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">s</font> )
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T49" title="SCMPDS_2:th.49">SCMPDS_2:49</a>, <a class="ref" href="scmpds_4.html#T31" title="SCMPDS_4:th.31">SCMPDS_4:31</a></i>;<br/>
<a NAME="E7:15"/>
( not <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">s</font> )
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T49" title="SCMPDS_2:th.49">SCMPDS_2:49</a>, <a class="ref" href="scmpds_4.html#T31" title="SCMPDS_4:th.31">SCMPDS_4:31</a></i>;<br/>
<b>then </b><i><font color="Green" title="E19">A6</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_8.html#E6:15"><i><font color="Green" title="E18">A5</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
;<br/>
<a NAME="E9:15"/><i><font color="Green" title="E20">A7</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T1" title="SCMPDS_6:th.1">SCMPDS_6:1</a></i>;<br/>
<a NAME="E10:15"/>
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E11:15"/><b>then </b>
 <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T57" title="SCMPDS_4:th.57">SCMPDS_4:57</a></i>;<br/>
<a NAME="E12:15"/><b>then </b><i><font color="Green" title="E21">A8</font></i>: 
 <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1
 
<b>by </b><i><a class="ref" href="ami_3.html#T38" title="AMI_3:th.38">AMI_3:38</a></i>;<br/>
<a NAME="E13:15"/><i><font color="Green" title="E22">A9</font></i>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<b>by </b><i><a class="ref" href="scmpds_8.html#T6" target="_self" title="SCMPDS_8:th.6">Th6</a></i>;<br/>
<a NAME="E14:15"/><b>then </b><i><font color="Green" title="E23">A10</font></i>: 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T25" title="SCMPDS_6:th.25">SCMPDS_6:25</a></i>;<br/>
<i><font color="Green" title="E24">A11</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15" title="AMI_1:def.15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmpds_8.html#E1:15"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="scmpds_8.html#E5:15"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="scmpds_8.html#E8:15"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_8.html#E2:15"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="scmpds_6.html#T23" title="SCMPDS_6:th.23">SCMPDS_6:23</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_8.html#E12:15"><i><font color="Green" title="E21">A8</font></i></a>, <a class="txt" href="scmpds_8.html#E14:15"><i><font color="Green" title="E23">A10</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
<b>by </b><i><a class="txt" href="scmpds_8.html#E13:15"><i><font color="Green" title="E22">A9</font></i></a>, <a class="ref" href="scmpds_6.html#T25" title="SCMPDS_6:th.25">SCMPDS_6:25</a></i>
;<br/>
<a NAME="E17:15"/><b>then </b><i><font color="Green" title="E25">A12</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<b>by </b><i><a class="txt" href="scmpds_8.html#E15:15"><i><font color="Green" title="E24">A11</font></i></a>, <a class="ref" href="ami_1.html#D17" title="AMI_1:def.17">AMI_1:def 17</a></i>;<br/>
<a NAME="E18:15"/><b>then </b><i><font color="Green" title="E26">A13</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a>
 
<b>by </b><i><a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c17">l</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:15_5"/>
<font color="Maroon" title="c17">l</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ;<br/><a NAME="E2:15_5"/><b>then </b>
<font color="Maroon" title="c17">l</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E3:15_5"/><b>then </b>
<font color="Maroon" title="c17">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><a NAME="E4:15_5"/><b>then </b>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c17">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>;<br/><b>hence </b><a NAME="E5:15_5"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c17">l</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmpds_8.html#E4:15"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="scmpds_6.html#T31" title="SCMPDS_6:th.31">SCMPDS_6:31</a></i>;<br/></div><b>end;</b></div>
<a NAME="E20:15"/><b>then </b>
for <font color="Olive" title="b1">l</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b1">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  holds <br/>1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">l</font>
 
;<br/>
<a NAME="E21:15"/><b>then </b>
 <a href="scm_1.html#NK3" title="SCM_1:NK.3">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="scmpds_8.html#E17:15"><i><font color="Green" title="E25">A12</font></i></a>, <a class="txt" href="scmpds_8.html#E18:15"><i><font color="Green" title="E26">A13</font></i></a>, <a class="ref" href="scm_1.html#D2" title="SCM_1:def.2">SCM_1:def 2</a></i>;<br/>
<a NAME="E22:15"/><b>then </b><i><font color="Green" title="E27">A14</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_8.html#E18:15"><i><font color="Green" title="E26">A13</font></i></a>, <a class="ref" href="scmfsa6b.html#T16" title="SCMFSA6B:th.16">SCMFSA6B:16</a></i>;<br/>
<i><font color="Green" title="E28">A15</font></i>:  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> = 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
<b>by </b><i><a class="ref" href="ami_3.html#T36" title="AMI_3:th.36">AMI_3:36</a></i>
<br/>.= 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p3">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T36" title="AMI_3:th.36">AMI_3:36</a></i>
;<br/>
<a NAME="E24:15"/><i><font color="Green" title="E29">A16</font></i>: 
 <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#D8" title="SCMPDS_4:def.8">SCMPDS_4:def 8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c17">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:15_7"/><i><font color="Green" title="E30">A17</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span>
 ;<br/><a NAME="E2:15_7"/><i><font color="Green" title="E31">A18</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p2">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_7_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_7_1"/>
( <font color="Maroon" title="c17">x</font> is    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  or <font color="Maroon" title="c17">x</font> is   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  )
 </span><b>by </b><i><a class="txt" href="scmpds_8.html#E1:15_7"><i><font color="Green" title="E30">A17</font></i></a>, <a class="ref" href="scmpds_4.html#T20" title="SCMPDS_4:th.20">SCMPDS_4:20</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_7_1_1"><b>suppose </b></a><a NAME="E1:15_7_1_1"/><i><font color="Green" title="E32">A19</font></i>: 
<font color="Maroon" title="c17">x</font> is    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> 
 ;<br/><div class="add"><a NAME="E2:15_7_1_1"/><b>then </b>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="scmpds_2.html#T52" title="SCMPDS_2:th.52">SCMPDS_2:52</a></i>;<br/><a NAME="E3:15_7_1_1"/><b>then </b><i><font color="Green" title="E33">A20</font></i>: 
not <font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p2">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_8.html#E2:15_7"><i><font color="Green" title="E31">A18</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E4:15_7_1_1"/>
not <font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_8.html#E9:15"><i><font color="Green" title="E20">A7</font></i></a>, <a class="txt" href="scmpds_8.html#E1:15_7_1_1"><i><font color="Green" title="E32">A19</font></i></a>, <a class="ref" href="scmpds_2.html#T53" title="SCMPDS_2:th.53">SCMPDS_2:53</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font>
<b>by </b><i><a class="txt" href="scmpds_8.html#E22:15"><i><font color="Green" title="E27">A14</font></i></a>, <a class="txt" href="scmpds_8.html#E24:15"><i><font color="Green" title="E29">A16</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font>
<b>by </b><i><a class="txt" href="scmpds_8.html#E5:15"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="scmpds_8.html#E1:15_7_1_1"><i><font color="Green" title="E32">A19</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font>
<b>by </b><i><a class="txt" href="scmpds_8.html#E1:15_7_1_1"><i><font color="Green" title="E32">A19</font></i></a>, <a class="ref" href="scmpds_5.html#T19" title="SCMPDS_5:th.19">SCMPDS_5:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p3">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font>
<b>by </b><i><a class="txt" href="scmpds_8.html#E3:15_7_1_1"><i><font color="Green" title="E33">A20</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_7_1_2"><b>suppose </b></a><a NAME="E1:15_7_1_2"/><i><font color="Green" title="E32">A21</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 ;<br/><div class="add"><a NAME="E2:15_7_1_2"/><b>then </b>
( <font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> &amp; not <font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="scmpds_8.html#E9:15"><i><font color="Green" title="E20">A7</font></i></a>, <a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a>, <a class="ref" href="ami_5.html#T25" title="AMI_5:th.25">AMI_5:25</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p0">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font>
<b>by </b><i><a class="txt" href="scmpds_8.html#E22:15"><i><font color="Green" title="E27">A14</font></i></a>, <a class="txt" href="scmpds_8.html#E24:15"><i><font color="Green" title="E29">A16</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmpds_8.html#E15:15"><i><font color="Green" title="E24">A11</font></i></a>, <a class="txt" href="scmpds_8.html#E1:15_7_1_2"><i><font color="Green" title="E32">A21</font></i></a>, <a class="ref" href="ami_1.html#D15" title="AMI_1:def.15">AMI_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p3">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font>
<b>by </b><i><a class="txt" href="scmpds_8.html#E1:15_7_1_2"><i><font color="Green" title="E32">A21</font></i></a>, <a class="ref" href="scmpds_7.html#T12" title="SCMPDS_7:th.12">SCMPDS_7:12</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_7_1_3"><b>suppose </b></a><a NAME="E1:15_7_1_3"/>
<font color="Maroon" title="c17">x</font> is   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_7_1_3"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p3">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font>
 <b>by </b><i><a class="ref" href="scmpds_6.html#T27" title="SCMPDS_6:th.27">SCMPDS_6:27</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E26:15"/>
 <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p2">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_8.html#E23:15"><i><font color="Green" title="E28">A15</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>


</div>
