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<b>let </b><font color="Maroon" title="c1">a</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</font>, <font color="Olive" title="b2">J</font> being  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds <br/> (  <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="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font></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="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font></span>)</span> &amp;  <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="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font></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="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c2">I</font>, <font color="Maroon" title="c3">J</font> be   <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></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="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></span>)</span> &amp;  <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="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></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="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></span>)</span> )</span><br/>



<b>set </b><font color="Maroon" title="c4">i</font> = <font color="Maroon" title="c1">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="c3">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>;<br/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">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#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">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="c2">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#K5" title="SCMFSA6A:func.5">';'</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8b.html#D1" title="SCMFSA8B:def.1">SCMFSA8B:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">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="c3">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#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">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="c2">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#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T67" title="SCMFSA6A:th.67">SCMFSA6A:67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">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="c2">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#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T67" title="SCMFSA6A:th.67">SCMFSA6A:67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">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="c3">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#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">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="c2">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#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T71" title="SCMFSA6A:th.71">SCMFSA6A:71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">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="c2">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#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span>

;<br/>
<a NAME="E2:43"/><b>then </b><i><font color="Green" title="E37">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T56" title="SCMFSA6A:th.56">SCMFSA6A:56</a></i>;<br/>
<a NAME="E3:43"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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="E4:43"/><b>then </b>
(  <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#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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><a NAME="E5:43"/>
(  <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="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></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="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E2:43"><i><font color="Green" title="E37">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></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="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></span>)</span> )</span><br/>

<b>set </b><font color="Maroon" title="c5">i</font> = <font color="Maroon" title="c1">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="c3">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>;<br/>
 <a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">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#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">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="c2">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#K5" title="SCMFSA6A:func.5">';'</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8b.html#D2" title="SCMFSA8B:def.2">SCMFSA8B:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">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="c3">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#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">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="c2">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#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T67" title="SCMFSA6A:th.67">SCMFSA6A:67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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#K6" title="SCMFSA6A:func.6">';'</a> <font color="Maroon" title="c3">J</font></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">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="c2">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#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T67" title="SCMFSA6A:th.67">SCMFSA6A:67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">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="c3">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#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">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="c2">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#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T71" title="SCMFSA6A:th.71">SCMFSA6A:71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">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="c2">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#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span>

;<br/>
<a NAME="E7:43"/><b>then </b><i><font color="Green" title="E38">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T56" title="SCMFSA6A:th.56">SCMFSA6A:56</a></i>;<br/>
<a NAME="E8:43"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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="E9:43"/><b>then </b>
(  <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#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">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="c3">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><a NAME="E10:43"/>
(  <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="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></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="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">J</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E7:43"><i><font color="Green" title="E38">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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