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

<b>let </b><font color="Maroon" title="c1">I</font>, <font color="Maroon" title="c2">J</font> be   <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon" title="c3">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c4">i</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>





<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E32">A1</font></i>: 
( ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font> ) &amp; <font color="Maroon" title="c4">i</font> <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>  &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c5">x1</font> =  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c3">k</font>;<br/>
<a NAME="E2:33"/><i><font color="Green" title="E33">A2</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#D6" title="SCMFSA6A:def.6">SCMFSA6A:def 6</a></i>;<br/>
<b>then </b><i><font color="Green" title="E34">A3</font></i>:  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c4">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T61" title="SCMFSA6A:th.61">SCMFSA6A:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6" title="SCMFSA7B:th.6">SCMFSA7B:6</a></i>
;<br/>
<a NAME="E4:33"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E5:33"/><b>then </b><i><font color="Green" title="E35">A4</font></i>: 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c4">i</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E1:33"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="scmbsort.html#E3:33"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="scmfsa6a.html#T15" title="SCMFSA6A:th.15">SCMFSA6A:15</a></i>;<br/>
<a NAME="E6:33"/><i><font color="Green" title="E36">A5</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <font color="Maroon" title="c4">i</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> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T33" title="SCMFSA6B:th.33">SCMFSA6B:33</a></i>;<br/>
<a NAME="E7:33"/><i><font color="Green" title="E37">A6</font></i>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6" title="SCMFSA7B:th.6">SCMFSA7B:6</a></i>;<br/>
<i><font color="Green" title="E38">A7</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c4">i</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> <font color="Maroon" title="c3">k</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <font color="Maroon" title="c4">i</font></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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:33"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="scmfsa6a.html#D6" title="SCMFSA6A:def.6">SCMFSA6A:def 6</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <font color="Maroon" title="c4">i</font>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:33"><i><font color="Green" title="E36">A5</font></i></a>, <a class="txt" href="scmbsort.html#E7:33"><i><font color="Green" title="E37">A6</font></i></a>, <a class="ref" href="scmbsort.html#T48" target="_self" title="SCMBSORT:th.48">Th48</a></i>
<br/>.= 
<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:33"><i><font color="Green" title="E32">A1</font></i></a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c2">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> <font color="Maroon" title="c3">k</font></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"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c4">i</font></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> <font color="Maroon" title="c3">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:33"><i><font color="Green" title="E35">A4</font></i></a>, <a class="ref" href="scmfsa8a.html#T28" title="SCMFSA8A:th.28">SCMFSA8A:28</a></i>
<br/>.= 
<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:33"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="scmbsort.html#E5:33"><i><font color="Green" title="E35">A4</font></i></a>, <a class="txt" href="scmbsort.html#E8:33"><i><font color="Green" title="E38">A7</font></i></a>, <a class="ref" href="scmfsa8a.html#T30" title="SCMFSA8A:th.30">SCMFSA8A:30</a></i>
;<br/>

<b>set </b><font color="Maroon" title="c6">x2</font> =  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<a NAME="E10:33"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E11:33"/><b>then </b><i><font color="Green" title="E39">A8</font></i>: 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c4">i</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E1:33"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="scmbsort.html#E3:33"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="scmfsa6a.html#T15" title="SCMFSA6A:th.15">SCMFSA6A:15</a></i>;<br/>
<a NAME="E12:33"/>
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <font color="Maroon" title="c4">i</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="scmfsa6b.html#T33" title="SCMFSA6B:th.33">SCMFSA6B:33</a></i>;<br/>
<b>then </b><i><font color="Green" title="E40">A9</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c4">i</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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> = 
 <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <span class="p1">(<span class="default"><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> </span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:33"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="scmbsort.html#E2:33"><i><font color="Green" title="E33">A2</font></i></a>, <a class="txt" href="scmbsort.html#E7:33"><i><font color="Green" title="E37">A6</font></i></a>, <a class="ref" href="scmbsort.html#T48" target="_self" title="SCMBSORT:th.48">Th48</a></i>
<br/>.= 
 <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_4.html#T8" title="SCMFSA_4:th.8">SCMFSA_4:8</a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c2">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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></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"><font color="Maroon" title="c1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c4">i</font></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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E11:33"><i><font color="Green" title="E39">A8</font></i></a>, <a class="ref" href="scmfsa8a.html#T28" title="SCMFSA8A:th.28">SCMFSA8A:28</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">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#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E3:33"><i><font color="Green" title="E34">A3</font></i></a>, <a class="txt" href="scmbsort.html#E11:33"><i><font color="Green" title="E39">A8</font></i></a>, <a class="txt" href="scmbsort.html#E13:33"><i><font color="Green" title="E40">A9</font></i></a>, <a class="ref" href="scmfsa8a.html#T30" title="SCMFSA8A:th.30">SCMFSA8A:30</a></i>
;<br/>


</div>
