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

<b>set </b><font color="Maroon">c<sub>1</sub></font> = <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> ;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="scmfsa7b.html#V1">good</a> <a href="scm_halt.html#V2">InitHalting</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/>



<b>assume </b><a NAME="E1:29"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font>
 ;<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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Olive">b<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/> <a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R2">is_halting_onInit</a> <font color="Olive">b<sub>1</sub></font>;<br/>
<a NAME="E2:29"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i><a class="ref" href="scmisort.html#T16" target="_self">Th16</a></i>;<br/>
<div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:29_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>4</sub></font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>assume </b><a NAME="E1:29_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1_1"><b>suppose </b></a><a NAME="E1:29_1_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:29_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmisort.html#E1:29_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E3:29_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><b>hence </b><a NAME="E4:29_1_1_1_1"/>
 <a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R2">is_halting_onInit</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:29_1"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1_2"><b>suppose </b></a><a NAME="E1:29_1_1_1_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:29_1_1_1_2"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><a NAME="E3:29_1_1_1_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R1">is_closed_onInit</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="scm_halt.html#T35">SCM_HALT:35</a></i>;<br/><a NAME="E4:29_1_1_1_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R2">is_halting_onInit</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="scm_halt.html#T36">SCM_HALT:36</a></i>;<br/><b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="scmfsa6a.html#K3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>9</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>10</sub></font> = the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>set </b><font color="Maroon">c<sub>11</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>;<br/><a NAME="E5:29_1_1_1_2"/><i><font color="Green">E28</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> 0 &amp; <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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="scmisort.html#E2:29_1_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmisort.html#E3:29_1_1_1_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmisort.html#E4:29_1_1_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scmisort.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E6:29_1_1_1_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="txt" href="scmisort.html#E4:29_1_1_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scm_halt.html#D5">SCM_HALT:def 5</a></i>;<br/><b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="scmfsa_2.html#K4">intloc</a> 0;<br/><a NAME="E7:29_1_1_1_2"/>
not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T84">SCMFSA_2:84</a></i>;<br/><a NAME="E8:29_1_1_1_2"/><b>then </b>
not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E9:29_1_1_1_2"/><b>then </b><i><font color="Green">E30</font></i>: 
(  <a href="scmfsa_2.html#K4">intloc</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="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> &amp; not  <a href="scmfsa_2.html#K4">intloc</a> 0 <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>5</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a>, <a class="ref" href="scmfsa_2.html#T66">SCMFSA_2:66</a></i>;<br/><i><font color="Green">E31</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E5:29_1_1_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E6:29_1_1_1_2"><i><font color="Green">E29</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmisort.html#E9:29_1_1_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#D1">SCMFSA6B:def 1</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="scm_halt.html#T17">SCM_HALT:17</a></i>
;<br/><a NAME="E11:29_1_1_1_2"/><i><font color="Green">E32</font></i>: 
 <a href="scmfsa6a.html#K3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</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="E12:29_1_1_1_2"/>
 <a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="scmfsa6a.html#K3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T26">SCMFSA6A:26</a></i>;<br/><a NAME="E13:29_1_1_1_2"/><b>then </b>
 <a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E11:29_1_1_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E14:29_1_1_1_2"/><b>then </b>
 <a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/><a NAME="E15:29_1_1_1_2"/><b>then </b>
<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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>;<br/><a NAME="E16:29_1_1_1_2"/><b>then </b><i><font color="Green">E33</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E5:29_1_1_1_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmisort.html#E10:29_1_1_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmisort.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E17:29_1_1_1_2"/>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T84">SCMFSA_2:84</a></i>;<br/><a NAME="E18:29_1_1_1_2"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E19:29_1_1_1_2"/><b>then </b><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>3</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="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> &amp; not <font color="Maroon">c<sub>3</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>5</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a>, <a class="ref" href="scmfsa_2.html#T66">SCMFSA_2:66</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="scmisort.html#E5:29_1_1_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="scmisort.html#E6:29_1_1_1_2"><i><font color="Green">E29</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="scmisort.html#E19:29_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="scmfsa6b.html#D1">SCMFSA6B:def 1</a></i>
;<br/><a NAME="E21:29_1_1_1_2"/><b>then </b>
<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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmisort.html#E1:29"><i><font color="Green">E19</font></i></a>, <a class="txt" href="scmisort.html#E1:29_1_1_1_2"><i><font color="Green">E24</font></i></a></i>;<br/><a NAME="E22:29_1_1_1_2"/><b>then </b>
<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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><a NAME="E23:29_1_1_1_2"/><b>then </b>
 <a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R2">is_halting_onInit</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="txt" href="scmisort.html#E1:29_1"><i><font color="Green">E22</font></i></a></i>;<br/><a NAME="E24:29_1_1_1_2"/><b>then </b><i><font color="Green">E35</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="ref" href="scm_halt.html#D5">SCM_HALT:def 5</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_1_2_3"><b>now </b></a><div class="add"><b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E2:29_1_1_1_2_3"/><i><font color="Green">E36</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"><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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="scmisort.html#E16:29_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="scmisort.html#E24:29_1_1_1_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/><b>take </b><font color="Maroon">c<sub>14</sub></font> = <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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>13</sub></font>;<br/><b>thus </b><a NAME="E3:29_1_1_1_2_3"/>
 <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>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="scmisort.html#E2:29_1_1_1_2_3"><i><font color="Green">E36</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>;<br/></div><b>end;</b></div><a NAME="E26:29_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/><b>hence </b><a NAME="E27:29_1_1_1_2"/>
 <a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R2">is_halting_onInit</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="scm_halt.html#D5">SCM_HALT:def 5</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:29_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E4:29"/><i><font color="Green">E22</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="scmisort.html#E2:29"><i><font color="Green">E20</font></i></a>, <a class="txt" href="scmisort.html#E3:29"><i><font color="Green">E21</font></i></a>);<br/></i>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_2_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 or <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_2_1_1"><b>suppose </b></a><a NAME="E1:29_2_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:29_2_1_1"/>
 <a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R2">is_halting_onInit</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="scmisort.html#T16" target="_self">Th16</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_2_1_2"><b>suppose </b></a><a NAME="E1:29_2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E3:29_2_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>5</sub></font>]
 <b>by </b><i><a class="txt" href="scmisort.html#E4:29"><i><font color="Green">E22</font></i></a></i>;<br/><b>hence </b><a NAME="E4:29_2_1_2"/>
 <a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R2">is_halting_onInit</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:29"/>
 <a href="scmfsa_9.html#K2">while&gt;0</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="scm_halt.html#V2">InitHalting</a>
 <b>by </b><i><a class="ref" href="scm_halt.html#T36">SCM_HALT:36</a></i>;<br/>


</div>
