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

<b>let </b><font color="Maroon" title="c1">l</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c2">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>



<b>set </b><font color="Maroon" title="c3">S</font> = <font color="Maroon" title="c2">s</font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:30"/><i><font color="Green" title="E22">A1</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">l</font>
 <b>and </b><br/><a NAME="E2:30"/><i><font color="Green" title="E23">A2</font></i>: 
<font color="Maroon" title="c2">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Maroon" title="c1">l</font>
 ;<br/>

<a NAME="E3:30"/><i><font color="Green" title="E24">A3</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Maroon" title="c1">l</font>
 
<b>by </b><i><a class="txt" href="scmfsa6b.html#E1:30"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="scmfsa6b.html#E2:30"><i><font color="Green" title="E23">A2</font></i></a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <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> ] <b>means </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s</font></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> <font color="Maroon" title="c2">s</font>;<br/>
<a NAME="E4:30"/><i><font color="Green" title="E25">A4</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<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 NAME="E5:30"/><i><font color="Green" title="E26">A5</font></i>: 
for <font color="Olive" title="b1">m</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 <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">m</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/>

<a NAME="E1:30_1"/><i><font color="Green" title="E27">A6</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Maroon" title="c1">l</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font>
 
<b>by </b><i><a class="txt" href="scmfsa6b.html#E1:30"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></i>;<br/>
<a NAME="E2:30_1"/><i><font color="Green" title="E28">A7</font></i>: 
for <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Maroon" title="c1">l</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Olive" title="b1">a</font>
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></i>;<br/>
<a NAME="E3:30_1"/><i><font color="Green" title="E29">A8</font></i>: 
for <font color="Olive" title="b1">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Maroon" title="c1">l</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Olive" title="b1">f</font>
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></i>;<br/>
<a NAME="E4:30_1"/><i><font color="Green" title="E30">A9</font></i>: 
for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Maroon" title="c1">l</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Olive" title="b1">i</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></i>;<br/>
<b>assume </b><a NAME="E5:30_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font>
 ;<br/>

<b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <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> <font color="Maroon" title="c2">s</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
<font color="Maroon" title="c2">s</font>
<b>by </b><i><a class="txt" href="scmfsa6b.html#E3:30"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="scmfsa6b.html#E1:30_1"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="scmfsa6b.html#E2:30_1"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="scmfsa6b.html#E3:30_1"><i><font color="Green" title="E29">A8</font></i></a>, <a class="txt" href="scmfsa6b.html#E4:30_1"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="scmfsa_2.html#T86" title="SCMFSA_2:th.86">SCMFSA_2:86</a></i>
;<br/><br/>


</div><b>end;</b></div>
<a NAME="E6:30"/><i><font color="Green" title="E27">A10</font></i>: 
for <font color="Olive" title="b1">m</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>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="scmfsa6b.html#E4:30"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="scmfsa6b.html#E5:30"><i><font color="Green" title="E26">A5</font></i></a>);<br/></i>
<b>let </b><font color="Maroon" title="c4">m</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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a><br/>

<a NAME="E7:30"/>
 <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> <font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Maroon" title="c1">l</font>
 
<b>by </b><i><a class="txt" href="scmfsa6b.html#E3:30"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="scmfsa6b.html#E6:30"><i><font color="Green" title="E27">A10</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:30"/>
 <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> <font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c4">m</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T47" title="SCMFSA_2:th.47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T124" title="SCMFSA_2:th.124">SCMFSA_2:124</a></i>;<br/>


</div>
