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<b>let </b><font color="Maroon">I</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>, <font color="Maroon">J</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>





<b>assume </b><a NAME="E1:42"/><i><font color="Green">E41</font></i>: 
( ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds   <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> ) &amp; <font color="Maroon">i</font> <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>  &amp; <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">I</font> )
 ;<br/>

<b>set </b><font color="Maroon">x1</font> =  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">k</font>;<br/>
<a NAME="E2:42"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#D6">SCMFSA6A:def 6</a></i>;<br/>
<b>then </b><i><font color="Green">E47</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T61">SCMFSA6A:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6">SCMFSA7B:6</a></i>
;<br/>
<a NAME="E4:42"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E5:42"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">k</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">I</font> <a href="scmfsa6a.html#K6">';'</a> <font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:42"><i><font color="Green">E42</font></i></a>, , <a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/>
<a NAME="E6:42"/><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T33">SCMFSA6B:33</a></i>;<br/>
<a NAME="E7:42"/><i><font color="Green">E60</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6">SCMFSA7B:6</a></i>;<br/>
<i><font color="Green">E62</font></i>: <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">k</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <font color="Maroon">i</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"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E2:42"><i><font color="Green">E42</font></i></a>, <a class="ref" href="scmfsa6a.html#D6">SCMFSA6A:def 6</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i>, <a class="txt" href="scmbsort.html#E3:42"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmbsort.html#T3" target="_self">Th3</a></i>
<br/>.= 
<font color="Maroon">i</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E2:42"><i><font color="Green">E42</font></i></a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <font color="Maroon">i</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">k</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <font color="Maroon">i</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> <font color="Maroon">k</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa8a.html#T28">SCMFSA8A:28</a></i>
<br/>.= 
<font color="Maroon">i</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E2:42"><i><font color="Green">E42</font></i></a>, , <a class="txt" href="scmbsort.html#E5:42"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa8a.html#T30">SCMFSA8A:30</a></i>
;<br/>

<b>set </b><font color="Maroon">x2</font> =  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<a NAME="E10:42"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E11:42"/><b>then </b><i><font color="Green">E63</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</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">I</font> <a href="scmfsa6a.html#K6">';'</a> <font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:42"><i><font color="Green">E42</font></i></a>, , <a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/>
<a NAME="E12:42"/>
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 1</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> 
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T33">SCMFSA6B:33</a></i>;<br/>
<b>then </b><i><font color="Green">E64</font></i>: <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <font color="Maroon">i</font></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"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
 <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">I</font></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E2:42"><i><font color="Green">E42</font></i></a>, , <a class="txt" href="scmbsort.html#E3:42"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmbsort.html#T3" target="_self">Th3</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/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <font color="Maroon">i</font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></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"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <font color="Maroon">i</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"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmbsort.html#T4" target="_self">Th4</a>, <a class="ref" href="scmfsa8a.html#T28">SCMFSA8A:28</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K13">goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a>, , <a class="ref" href="scmfsa8a.html#T30">SCMFSA8A:30</a></i>
;<br/>


</div>
