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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="scmfsa6b.html#V1">paraclosed</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>



<b>assume </b><a NAME="E1:110"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:110"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="ami_1.html#V9">halting</a>
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means ( <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>1</sub></font> implies <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</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>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  );<br/>
<a NAME="E3:110"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <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>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>;<br/>
<a NAME="E4:110"/><b>then </b><i><font color="Green">E95</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T27">SCMFSA6A:27</a></i>;<br/>
<a NAME="E5:110"/><i><font color="Green">E96</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:110_1"/><i><font color="Green">E97</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>1</sub></font> implies <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</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>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 ;<br/>

<b>assume </b><a NAME="E2:110_1"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:110_1"/><b>then </b><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="ami_1.html#K10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<i><font color="Green">E100</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
;<br/>
<i><font color="Green">E101</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</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"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
;<br/>
<a NAME="E6:110_1"/><i><font color="Green">E102</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E1:110_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="scmfsa8c.html#E2:110_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a>, <a class="ref" href="scmfsa6a.html#T29">SCMFSA6A:29</a></i>;<br/>
<a NAME="E7:110_1"/><i><font color="Green">E103</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E1:110"><i><font color="Green">E93</font></i></a>, <a class="ref" href="scmfsa6b.html#D2">SCMFSA6B:def 2</a></i>;<br/>
<a NAME="E8:110_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="sf_mastr.html#T64">SF_MASTR:64</a></i>;<br/>
<a NAME="E9:110_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T33">FUNCT_4:33</a></i>;<br/>
<a NAME="E10:110_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E1:110"><i><font color="Green">E93</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E11:110_1"/><b>then </b><i><font color="Green">E104</font></i>: 
<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/>
<a NAME="E12:110_1"/>
 <a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E13:110_1"/><b>then </b><i><font color="Green">E105</font></i>: 
 <a href="scmfsa8c.html#K1" target="_self">loop</a> <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>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/>
<a NAME="E14:110_1"/><i><font color="Green">E106</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E7:110_1"><i><font color="Green">E103</font></i></a>, <a class="ref" href="scmfsa8c.html#T106" target="_self">Th106</a></i>;<br/>
<i><font color="Green">E107</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E7:110_1"><i><font color="Green">E103</font></i></a>, <a class="txt" href="scmfsa8c.html#E11:110_1"><i><font color="Green">E104</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/>
<a NAME="E16:110_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</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="scmfsa8c.html#E2:110"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa8c.html#E3:110_1"><i><font color="Green">E99</font></i></a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/>
<b>then </b> <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E15:110_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa8c.html#T108" target="_self">Th108</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>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E13:110_1"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa8c.html#E14:110_1"><i><font color="Green">E106</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
 <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>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E6:110_1"><i><font color="Green">E102</font></i></a>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
;<br/>
<b>hence </b><a NAME="E18:110_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" target="_self">loop</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"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="funct_7.html#R1">equal_outside</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="txt" href="scmfsa8c.html#E1:110_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="scmfsa8c.html#E2:110_1"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa8c.html#E4:110_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="scmfsa8c.html#E5:110_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a>, <a class="ref" href="scmfsa6a.html#T32">SCMFSA6A:32</a></i>;<br/>


</div><b>end;</b></div>
<b>thus </b><a NAME="E6:110"/>
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="scmfsa8c.html#E4:110"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa8c.html#E5:110"><i><font color="Green">E96</font></i></a>);</i><br/>


</div>
