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

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <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/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/>





<b>assume </b><a NAME="E1:46"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa7b.html#R2">does_not_refer</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:46"/><i><font color="Green">E42</font></i>: 
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  holds <font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/>

<b>assume </b><a NAME="E3:46"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa7b.html#R5">is_closed_on</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ,  <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ] means ( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">a<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>2</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  holds <font color="Maroon">a<sub>1</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>2</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> ) );<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="ami_1.html#K10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</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>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="ami_1.html#K10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</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>;<br/>
<a NAME="E4:46"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>5</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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="E5:46"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>5</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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/>
<div><i><font color="Green">E46</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:46_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E2:46_1"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; not <font color="Maroon">c<sub>11</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="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> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="scmfsa6b.html#T12">SCMFSA6B:12</a>, <a class="ref" href="scmfsa_2.html#T66">SCMFSA_2:66</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</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="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:46"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:46_1"><i><font color="Green">E47</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</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="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:46_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/><br/></div><b>end;</b></div>
<div><i><font color="Green">E47</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><a NAME="E1:46_2"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; not <font color="Maroon">c<sub>11</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="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> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="scmfsa6b.html#T13">SCMFSA6B:13</a>, <a class="ref" href="scmfsa_2.html#T67">SCMFSA_2:67</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</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="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:46"><i><font color="Green">E42</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</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="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:46_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/><br/></div><b>end;</b></div>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means ( <font color="Maroon">S<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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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">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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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">a<sub>1</sub></font>] &amp;  <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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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">a<sub>1</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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">a<sub>1</sub></font></span>)</span> &amp;  <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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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">a<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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">a<sub>1</sub></font></span>)</span> );<br/>
<a NAME="E8:46"/>
<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</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="scmfsa8a.html#T9">SCMFSA8A:9</a></i>;<br/>
<a NAME="E9:46"/><b>then </b><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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="scmfsa8b.html#E4:46"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmfsa8b.html#E5:46"><i><font color="Green">E45</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E10:46"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_3"><b>proof </b></a><div class="add">

<a NAME="E1:46_3"/><i><font color="Green">E50</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <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="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="sf_mastr.html#T65">SF_MASTR:65</a></i>;<br/>
<a NAME="E2:46_3"/><i><font color="Green">E51</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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="ami_1.html#D19">AMI_1:def 19</a></i>;<br/>
<a NAME="E3:46_3"/><i><font color="Green">E52</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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="ami_1.html#D19">AMI_1:def 19</a></i>;<br/>
<b>hence </b><a NAME="E4:46_3"/>
<font color="Maroon">S<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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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> 0,<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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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> 0]
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E6:46"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:46"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmfsa8b.html#E2:46_3"><i><font color="Green">E51</font></i></a></i>;<br/>

<b>thus </b><i><font color="Green">E53</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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> 0</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</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="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:46_3"><i><font color="Green">E51</font></i></a>, <a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:46_3"><i><font color="Green">E50</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</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="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:46_3"><i><font color="Green">E50</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
 <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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:46_3"><i><font color="Green">E52</font></i></a>, <a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/>

<a NAME="E6:46_3"/><i><font color="Green">E54</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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> 0</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:46"><i><font color="Green">E43</font></i></a>, <a class="ref" href="scmfsa7b.html#D7">SCMFSA7B:def 7</a></i>;<br/>
<b>thus </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> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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> 0</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</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> 0</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:46_3"><i><font color="Green">E51</font></i></a>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</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> 0</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E9:46"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:46_3"><i><font color="Green">E54</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</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> 0</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E9:46"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa8b.html#E5:46_3"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:46_3"><i><font color="Green">E54</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:46_3"><i><font color="Green">E52</font></i></a>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E11:46"/><i><font color="Green">E50</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>2</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>2</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="46_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:46_4"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">c<sub>11</sub></font>]
 ;<br/>

<a NAME="E2:46_4"/><i><font color="Green">E52</font></i>: 
 <a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>;<br/>
<a NAME="E3:46_4"/><b>then </b><i><font color="Green">E53</font></i>: 
( <font color="Maroon">c<sub>5</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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>11</sub></font> &amp; <font color="Maroon">c<sub>5</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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>11</sub></font> )
 
<b>by </b><i><a class="txt" href="scmfsa8b.html#E9:46"><i><font color="Green">E48</font></i></a>, <a class="ref" href="ami_5.html#T64">AMI_5:64</a></i>;<br/>
<a NAME="E4:46_4"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>5</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <font color="Maroon">c<sub>5</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 
<b>by </b><i><a class="txt" href="scmfsa8b.html#E9:46"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa8b.html#E2:46_4"><i><font color="Green">E52</font></i></a>, <a class="ref" href="ami_5.html#T64">AMI_5:64</a></i>;<br/>
<a NAME="E5:46_4"/><i><font color="Green">E55</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:46"><i><font color="Green">E43</font></i></a>, <a class="ref" href="scmfsa7b.html#D7">SCMFSA7B:def 7</a></i>;<br/>
<i><font color="Green">E56</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"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font></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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</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> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</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>11</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>5</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:46_4"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa8b.html#E5:46_4"><i><font color="Green">E55</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/>
<i><font color="Green">E57</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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="p1">(<span class="default"><font color="Maroon">c<sub>11</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</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>11</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</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">E58</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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="p1">(<span class="default"><font color="Maroon">c<sub>11</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</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>11</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</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="E9:46_4"/>
 <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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa8b.html#E5:46_4"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:46_4"><i><font color="Green">E56</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E10:46_4"/><b>then </b><i><font color="Green">E59</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"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font></span>)</span> <a href="scmfsa7b.html#R1">does_not_refer</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:46"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa7b.html#D2">SCMFSA7B:def 2</a></i>;<br/>
<b>hence </b><a NAME="E11:46_4"/>
<font color="Maroon">S<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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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="p1">(<span class="default"><font color="Maroon">c<sub>11</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<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="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>]
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1:46_4"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:46_4"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmfsa8b.html#E8:46_4"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmfsa8b.html#T37" target="_self">Th37</a></i>;<br/>

<b>thus </b><a NAME="E12:46_4"/><i><font color="Green">E60</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1:46_4"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:46_4"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmfsa8b.html#E8:46_4"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmfsa8b.html#E10:46_4"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmfsa8b.html#T37" target="_self">Th37</a></i>;<br/>

<a NAME="E13:46_4"/><i><font color="Green">E61</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:46"><i><font color="Green">E43</font></i></a>, <a class="ref" href="scmfsa7b.html#D7">SCMFSA7B:def 7</a></i>;<br/>
<b>thus </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> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font> <a href="nat_1.html#K1">+</a> 1</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font> <a href="nat_1.html#K1">+</a> 1</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</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> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></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>5</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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</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> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E4:46_4"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmfsa8b.html#E13:46_4"><i><font color="Green">E61</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font> <a href="nat_1.html#K1">+</a> 1</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>5</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> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E4:46_4"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmfsa8b.html#E12:46_4"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scmfsa8b.html#E13:46_4"><i><font color="Green">E61</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E12:46"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>2</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="scmfsa8b.html#E10:46"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E11:46"><i><font color="Green">E50</font></i></a>);<br/></i>
<b>hence </b><a NAME="E13:46"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <br/>( ( for <font color="Olive">b<sub>2</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> holds <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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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="Olive">b<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>2</sub></font> <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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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="Olive">b<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  holds <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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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="Olive">b<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>2</sub></font> <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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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="Olive">b<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>2</sub></font> ) &amp;  <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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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="Olive">b<sub>1</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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="Olive">b<sub>1</sub></font></span>)</span> &amp;  <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>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</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="Olive">b<sub>1</sub></font></span>)</span> )
 ;<br/>


</div>
