<?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="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/>





<b>assume </b><a NAME="E1:90"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="scmfsa7b.html#R4">does_not_destroy</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<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="E2:90"/><i><font color="Green">E78</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>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</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>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E3:90"/><i><font color="Green">E79</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> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E4:90"/>
 <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="E5:90"/><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="E6:90"/><b>then </b><i><font color="Green">E80</font></i>: 
<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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E3:90"><i><font color="Green">E79</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<a NAME="E7:90"/>
<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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></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> <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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <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> <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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E2:90"><i><font color="Green">E78</font></i></a>, <a class="txt" href="scmfsa8c.html#E6:90"><i><font color="Green">E80</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E8:90"/><b>then </b>
<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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></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> <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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E2:90"><i><font color="Green">E78</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E9:90"/><b>then </b><i><font color="Green">E81</font></i>: 
<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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></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> <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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E1:90"><i><font color="Green">E77</font></i></a>, <a class="ref" href="scmfsa7b.html#D4">SCMFSA7B:def 4</a></i>;<br/>
<b>thus </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>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</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"><a href="ami_1.html#K9">Following</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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></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="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8">CurInstr</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>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></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="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></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="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,<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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></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="ref" href="ami_1.html#T54">AMI_1:54</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"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</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="txt" href="scmfsa8c.html#E9:90"><i><font color="Green">E81</font></i></a>, <a class="ref" href="scmfsa7b.html#T26">SCMFSA7B:26</a></i>
;<br/>


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