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

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>



<b>assume </b><a NAME="E1:59"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:59"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span>;<br/>
<a NAME="E3:59"/>
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a>  <a href="tarski.html#R1">c=</a>  <a href="scmfsa6a.html#K3">Initialized</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T26">SCMFSA6A:26</a></i>;<br/>
<a NAME="E4:59"/><b>then </b><i><font color="Green">E56</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E5:59"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T17" target="_self">Th17</a>, <a class="ref" href="scmfsa6a.html#T61">SCMFSA6A:61</a></i>;<br/>
<a NAME="E6:59"/><b>then </b>
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E7:59"/><b>then </b><i><font color="Green">E57</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/>
<a NAME="E8:59"/><i><font color="Green">E58</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> 
 
<b>by </b><i><a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>;<br/>
<a NAME="E9:59"/><b>then </b>
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E10:59"/><b>then </b><i><font color="Green">E59</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> ,<span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_5.html#T3">SCMFSA_5:3</a></i>;<br/>
<a NAME="E11:59"/><i><font color="Green">E60</font></i>: 
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> ,<span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="scmfsa_5.html#K1">Relocated</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> ,<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T63">AMI_5:63</a></i>;<br/>
<a NAME="E12:59"/>
( <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"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> &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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <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"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="scmfsa8a.html#E1:59"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmfsa8a.html#E2:59"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scmfsa8a.html#T43" target="_self">Th43</a></i>;<br/>
<b>hence </b><a NAME="E13:59"/><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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="scmfsa8a.html#E1:59"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmfsa8a.html#E2:59"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scmfsa8a.html#T45" target="_self">Th45</a></i>;<br/>

<i><font color="Green">E62</font></i>: <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"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8a.html#E4:59"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmfsa8a.html#E7:59"><i><font color="Green">E57</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>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8a.html#E7:59"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmfsa6a.html#T50">SCMFSA6A:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p3">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> ,<span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#D4">SCMFSA6A:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> ,<span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8a.html#E10:59"><i><font color="Green">E59</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> ,<span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8a.html#E10:59"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmfsa8a.html#E11:59"><i><font color="Green">E60</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> ,<span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K4">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8a.html#E8:59"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmfsa8a.html#T16" target="_self">Th16</a>, <a class="ref" href="scmfsa_5.html#T7">SCMFSA_5:7</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T8">SCMFSA_4:8</a></i>
;<br/>
<i><font color="Green">E63</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <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="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8a.html#E13:59"><i><font color="Green">E61</font></i></a>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
<b>by </b><i><a class="txt" href="scmfsa8a.html#E14:59"><i><font color="Green">E62</font></i></a>, <a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
;<br/>
<b>hence </b><a NAME="E16:59"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:59_3"/>
<font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E2:59_3"/><b>then </b><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</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"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E3:59_3"/><b>then </b>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="scmfsa8a.html#E1:59"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmfsa8a.html#E2:59"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scmfsa8a.html#T44" target="_self">Th44</a></i>;<br/><b>hence </b><a NAME="E4:59_3"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="scmfsa8a.html#E1:59"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmfsa8a.html#E2:59"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmfsa8a.html#E2:59_3"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scmfsa8a.html#T43" target="_self">Th43</a></i>;<br/></div><b>end;</b></div>
<a NAME="E18:59"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st  <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"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </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#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  holds <br/><span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font>
 
;<br/>
<b>hence </b><a NAME="E19:59"/>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</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"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmfsa8a.html#E15:59"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scmfsa8a.html#E16:59"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/>


</div>
