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

<b>let </b><font color="Maroon" title="c3">a</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><b>let </b><font color="Maroon" title="c4">I</font>, <font color="Maroon" title="c5">J</font> be   <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/>



<b>set </b><font color="Maroon" title="c6">i</font> = <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>;<br/>
<a NAME="E1:18"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T48" title="SCMFSA_2:th.48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T124" title="SCMFSA_2:th.124">SCMFSA_2:124</a></i>;<br/>
<i><font color="Green" title="E17">A2</font></i>:  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T62" title="SCMFSA6A:th.62">SCMFSA6A:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T62" title="SCMFSA6A:th.62">SCMFSA6A:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">J</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T66" title="SCMFSA6A:th.66">SCMFSA6A:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">J</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#D5" title="SCMFSA6A:def.5">SCMFSA6A:def 5</a></i>
;<br/>
<a NAME="E3:18"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T4" title="SCMFSA7B:th.4">SCMFSA7B:4</a></i>;<br/>
<a NAME="E4:18"/><b>then </b><i><font color="Green" title="E18">A3</font></i>: 
(  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:18"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="scmfsa8a.html#T28" title="SCMFSA8A:th.28">SCMFSA8A:28</a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:18"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="scmfsa7b.html#T7" title="SCMFSA7B:th.7">SCMFSA7B:7</a></i>
;<br/><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:18"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:18"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="scmfsa8a.html#T28" title="SCMFSA8A:th.28">SCMFSA8A:28</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa7b.html#T8" title="SCMFSA7B:th.8">SCMFSA7B:8</a></i>
;<br/>

<b>set </b><font color="Maroon" title="c7">i</font> = <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>;<br/>
<a NAME="E7:18"/><i><font color="Green" title="E19">A4</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T49" title="SCMFSA_2:th.49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T124" title="SCMFSA_2:th.124">SCMFSA_2:124</a></i>;<br/>
<i><font color="Green" title="E20">A5</font></i>:  <a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T62" title="SCMFSA6A:th.62">SCMFSA6A:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T62" title="SCMFSA6A:th.62">SCMFSA6A:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">J</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T66" title="SCMFSA6A:th.66">SCMFSA6A:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">J</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#D5" title="SCMFSA6A:def.5">SCMFSA6A:def 5</a></i>
;<br/>
<a NAME="E9:18"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T4" title="SCMFSA7B:th.4">SCMFSA7B:4</a></i>;<br/>
<a NAME="E10:18"/><b>then </b><i><font color="Green" title="E21">A6</font></i>: 
(  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E8:18"><i><font color="Green" title="E20">A5</font></i></a>, <a class="ref" href="scmfsa8a.html#T28" title="SCMFSA8A:th.28">SCMFSA8A:28</a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E7:18"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="scmfsa7b.html#T7" title="SCMFSA7B:th.7">SCMFSA7B:7</a></i>
;<br/><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E8:18"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="scmfsa8b.html#E10:18"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="scmfsa8a.html#T28" title="SCMFSA8A:th.28">SCMFSA8A:28</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa7b.html#T8" title="SCMFSA7B:th.8">SCMFSA7B:8</a></i>
;<br/>


</div>
