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<span class="kw">let </span><font color="Maroon" title="c2">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">i</font> being  <a href="scmfsa6c.html#V1" title="SCMFSA6C:attr.1">parahalting</a>  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b1">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Olive" title="b1">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">i</font> be   <a href="scmfsa6c.html#V1" title="SCMFSA6C:attr.1">parahalting</a>  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c4">Mi</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">sI</font> = <font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Is</font> =  <a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">IC1</font> =  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">Mi9</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font> as   <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a>  <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>  ;<br/>
<a NAME="E2:27"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
 <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#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#T31" title="SCMFSA6B:th.31">SCMFSA6B:31</a></span>;<br/>
<a NAME="E3:27"/>
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a>, <a class="ref" href="scmfsa6b.html#T8" title="SCMFSA6B:th.8">SCMFSA6B:8</a></span>;<br/>
<a NAME="E4:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A2</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">Mi9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#D2" title="SCMFSA6B:def.2">SCMFSA6B:def 2</a></span>;<br/>
<a NAME="E5:27"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#T33" title="SCMFSA6B:th.33">SCMFSA6B:33</a></span>;<br/>
<a NAME="E6:27"/><span class="lab"><font color="Green" title="E13">A4</font></span>: 
 <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E14">A5</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><span class="kw">now </span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c9">Y</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><span class="kw">set </span><font color="Maroon" title="c10">X</font> = <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/><span class="kw">assume </span><a NAME="E1:27_1"/><span class="lab"><font color="Green" title="E15">A6</font></span>: 
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span><br/><a NAME="E2:27_1"/><span class="lab"><font color="Green" title="E16">A7</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T106" title="FUNCT_7:th.106">FUNCT_7:106</a>, <a class="ref" href="funct_7.html#T132" title="FUNCT_7:th.132">FUNCT_7:132</a></span>;<br/><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></span>
;<br/><a NAME="E4:27_1"/><span class="kw">then </span>
 <a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="ref" href="funct_7.html#T106" title="FUNCT_7:th.106">FUNCT_7:106</a></span>;<br/><a NAME="E5:27_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T4" target="_self" title="SCMFSA6C:th.4">Th4</a></span>;<br/><a NAME="E6:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A8</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_3.html#T4" title="SCMFSA_3:th.4">SCMFSA_3:4</a></span>;<br/><a NAME="E7:27_1"/><span class="lab"><font color="Green" title="E18">A9</font></span>: 
<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 ;<br/><a NAME="E8:27_1"/><span class="lab"><font color="Green" title="E19">A10</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/><a NAME="E9:27_1"/><span class="lab"><font color="Green" title="E20">A11</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/><a NAME="E10:27_1"/><span class="lab"><font color="Green" title="E21">A12</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a>, <a class="ref" href="scmfsa_2.html#T8" title="SCMFSA_2:th.8">SCMFSA_2:8</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">thus </span><a NAME="E1:27_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27_1"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="txt" href="#E10:27_1"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a>, <a class="ref" href="scmfsa_2.html#T8" title="SCMFSA_2:th.8">SCMFSA_2:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span><br/><span class="kw">let </span><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c11">x</font> <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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> )</span><br/><span class="kw">assume </span><a NAME="E2:27_1_2"/>
<font color="Maroon" title="c11">x</font> <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"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span><br/><a NAME="E3:27_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A13</font></span>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27_1"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a>, <a class="ref" href="scmfsa_2.html#T8" title="SCMFSA_2:th.8">SCMFSA_2:8</a></span>;<br/><a NAME="E4:27_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T21" title="XBOOLE_1:th.21">XBOOLE_1:21</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">x9</font> = <font color="Maroon" title="c11">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/><a NAME="E6:27_1_2"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1_2"><span class="lab"><font color="Green" title="E22">A13</font></span></a>, <a class="ref" href="xboole_1.html#T21" title="XBOOLE_1:th.21">XBOOLE_1:21</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c12">x9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T3" target="_self" title="SCMFSA6C:th.3">Th3</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E12:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A14</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></span>;<br/><a NAME="E13:27_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/><a NAME="E14:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A15</font></span>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="txt" href="#E10:27_1"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="ref" href="funct_4.html#T93" title="FUNCT_4:th.93">FUNCT_4:93</a>, <a class="ref" href="scmfsa_2.html#T8" title="SCMFSA_2:th.8">SCMFSA_2:8</a></span>;<br/><a NAME="E15:27_1"/>
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_3"/>
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:27_1_3"/><span class="lab"><font color="Green" title="E24">A16</font></span>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">and </span><br/><a NAME="E4:27_1_3"/><span class="lab"><font color="Green" title="E25">A17</font></span>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>;<br/>
<a NAME="E5:27_1_3"/><span class="lab"><font color="Green" title="E26">A18</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  or <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1_3"><span class="lab"><font color="Green" title="E24">A16</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_3_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:27_1_3_1"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  or <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  or <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:27_1_3"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:27_1_3_1_1"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:27_1_3_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27_1_3"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="ref" href="scmfsa_2.html#T13" title="SCMFSA_2:th.13">SCMFSA_2:13</a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:27_1_3_1_2"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:27_1_3_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27_1_3"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="ref" href="scmfsa_2.html#T14" title="SCMFSA_2:th.14">SCMFSA_2:14</a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_3_1_3"><span class="kw">suppose </span></a><a NAME="E1:27_1_3_1_3"/><span class="lab"><font color="Green" title="E27">A19</font></span>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c12">x</font> = <font color="Maroon" title="c11">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27_1_3"><span class="lab"><font color="Green" title="E25">A17</font></span></a></span>;<br/><a NAME="E3:27_1_3_1_3"/>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1_3_1_3"><span class="lab"><font color="Green" title="E27">A19</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E4:27_1_3_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div><a NAME="E16:27_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T87" title="RELAT_1:th.87">RELAT_1:87</a>, <a class="ref" href="xboole_1.html#T63" title="XBOOLE_1:th.63">XBOOLE_1:63</a></span>;<br/><a NAME="E17:27_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="ref" href="funct_4.html#T76" title="FUNCT_4:th.76">FUNCT_4:76</a></span>;<br/><a NAME="E18:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A20</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E14:27_1"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E12:27_1"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></span>;<br/><span class="kw">thus </span> <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27_1"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="ref" href="relat_1.html#T98" title="RELAT_1:th.98">RELAT_1:98</a>, <a class="ref" href="scmfsa_2.html#T8" title="SCMFSA_2:th.8">SCMFSA_2:8</a></span>
<br/>.= 
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:27_1"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="txt" href="#E18:27_1"><span class="lab"><font color="Green" title="E24">A20</font></span></a>, <a class="ref" href="relat_1.html#T98" title="RELAT_1:th.98">RELAT_1:98</a>, <a class="ref" href="scmfsa_2.html#T8" title="SCMFSA_2:th.8">SCMFSA_2:8</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E8:27"/>
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6a.html#T26" title="SCMFSA6A:th.26">SCMFSA6A:26</a></span>;<br/>
<a NAME="E9:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A21</font></span>: 
 <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> <font color="Maroon" title="c3">i</font></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="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a></span>;<br/>
<a NAME="E10:27"/><span class="lab"><font color="Green" title="E16">A22</font></span>: 
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> <font color="Maroon" title="c3">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#T32" title="SCMFSA6B:th.32">SCMFSA6B:32</a></span>;<br/>
<a NAME="E11:27"/><span class="lab"><font color="Green" title="E17">A23</font></span>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#T33" title="SCMFSA6B:th.33">SCMFSA6B:33</a></span>;<br/>
<a NAME="E12:27"/><span class="lab"><font color="Green" title="E18">Y</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/>
<a NAME="E13:27"/><span class="lab"><font color="Green" title="E19">Z</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/>
<span class="lab"><font color="Green" title="E20">A24</font></span>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:27"><span class="lab"><font color="Green" title="E18">Y</font></span></a>, <a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a>, <a class="ref" href="scmfsa6b.html#T34" title="SCMFSA6B:th.34">SCMFSA6B:34</a></span>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E11:27"><span class="lab"><font color="Green" title="E17">A23</font></span></a>, <a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
;<br/>
<a NAME="E15:27"/><span class="lab"><font color="Green" title="E21">TX</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:27_3"/>
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="scmfsa6b.html#T32" title="SCMFSA6B:th.32">SCMFSA6B:32</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1"><span class="kw">suppose </span></a><a NAME="E1:27_3_1"/><span class="lab"><font color="Green" title="E22">A25</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span><br/><div class="add"><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A26</font></span>:  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E20">A24</font></span></a>, <a class="txt" href="#E13:27"><span class="lab"><font color="Green" title="E19">Z</font></span></a>, <a class="txt" href="#E15:27"><span class="lab"><font color="Green" title="E21">TX</font></span></a>, <a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c3">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E11:27"><span class="lab"><font color="Green" title="E17">A23</font></span></a>, <a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
;<br/> <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a>, <a class="ref" href="scmfsa6b.html#T34" title="SCMFSA6B:th.34">SCMFSA6B:34</a></span>
<br/>.= 
1

;<br/><a NAME="E4:27_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A27</font></span>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,6,7,8</span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E20">A24</font></span></a>, <a class="txt" href="#E1:27_3_1"><span class="lab"><font color="Green" title="E22">A25</font></span></a>, <a class="ref" href="scmfsa6a.html#T23" title="SCMFSA6A:th.23">SCMFSA6A:23</a></span>;<br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:27_3_1_3_1"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27_3_1"><span class="lab"><font color="Green" title="E24">A27</font></span></a>, <a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:27_3_1_3_1_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span><br/><div class="add"><a NAME="E2:27_3_1_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A28</font></span>: 
<font color="Maroon" title="c3">i</font> <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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T122" title="SCMFSA_2:th.122">SCMFSA_2:122</a></span>;<br/><a NAME="E3:27_3_1_3_1_1"/><span class="kw">then </span>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_3_1"><span class="lab"><font color="Green" title="E23">A26</font></span></a>, <a class="ref" href="ami_1.html#T146" title="AMI_1:th.146">AMI_1:146</a></span>;<br/><span class="kw">hence </span><a NAME="E4:27_3_1_3_1_1"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E20">A24</font></span></a>, <a class="txt" href="#E2:27_3_1"><span class="lab"><font color="Green" title="E23">A26</font></span></a>, <a class="txt" href="#E2:27_3_1_3_1_1"><span class="lab"><font color="Green" title="E25">A28</font></span></a>, <a class="ref" href="ami_1.html#D22" title="AMI_1:def.22">AMI_1:def 22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:27_3_1_3_1_2"/><span class="lab"><font color="Green" title="E25">A29</font></span>: 
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span><br/><div class="add"><div><span class="lab"><font color="Green" title="E26">A30</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_3_1_3_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:27_3_1_3_1_2_1_1"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_3_1_3_1_2"><span class="lab"><font color="Green" title="E25">A29</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:27_3_1_3_1_2_1_1_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:27_3_1_3_1_2_1_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">l</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T59" title="SCMFSA_2:th.59">SCMFSA_2:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_3_1_3_1_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:27_3_1_3_1_2_1_1_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:27_3_1_3_1_2_1_1_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">l</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T60" title="SCMFSA_2:th.60">SCMFSA_2:60</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_3_1_3_1_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1_2_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:27_3_1_3_1_2_1_1_3"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:27_3_1_3_1_2_1_1_3"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">l</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T61" title="SCMFSA_2:th.61">SCMFSA_2:61</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_3_1_3_1_2_1_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E3:27_3_1_3_1_2"/><span class="lab"><font color="Green" title="E27">A31</font></span>: 
for <font color="Olive" title="b1">l</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Olive" title="b1">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>;<br/><div><span class="lab"><font color="Green" title="E28">A32</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_3_1_3_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1_2_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:27_3_1_3_1_2_2_1"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_3_1_3_1_2"><span class="lab"><font color="Green" title="E25">A29</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1_2_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:27_3_1_3_1_2_2_1_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:27_3_1_3_1_2_2_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">l</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T59" title="SCMFSA_2:th.59">SCMFSA_2:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_3_1_3_1_2_2_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1_2_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:27_3_1_3_1_2_2_1_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:27_3_1_3_1_2_2_1_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">l</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T60" title="SCMFSA_2:th.60">SCMFSA_2:60</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_3_1_3_1_2_2_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_1_3_1_2_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:27_3_1_3_1_2_2_1_3"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:27_3_1_3_1_2_2_1_3"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">l</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T61" title="SCMFSA_2:th.61">SCMFSA_2:61</a></span>;<br/><span class="kw">hence </span><a NAME="E3:27_3_1_3_1_2_2_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E5:27_3_1_3_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E20">A24</font></span></a>, <a class="txt" href="#E1:27_3_1"><span class="lab"><font color="Green" title="E22">A25</font></span></a>, <a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a>, <a class="ref" href="scmfsa6b.html#T34" title="SCMFSA6B:th.34">SCMFSA6B:34</a></span>;<br/><a NAME="E6:27_3_1_3_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A33</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_3_1_3_1_2"><span class="lab"><font color="Green" title="E26">A30</font></span></a>, <a class="txt" href="#E4:27_3_1_3_1_2"><span class="lab"><font color="Green" title="E28">A32</font></span></a>, <a class="txt" href="#E3:27_3_1_3_1_2"><span class="lab"><font color="Green" title="E27">A31</font></span></a>, <a class="ref" href="scmfsa_2.html#T86" title="SCMFSA_2:th.86">SCMFSA_2:86</a></span>;<br/><span class="lab"><font color="Green" title="E30">A34</font></span>:  <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E20">A24</font></span></a>, <a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_3_1_3_1_2_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c9">n</font></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> </span><br/> <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c9">n</font> = 
<font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_3_1_3_1_2"><span class="lab"><font color="Green" title="E29">A33</font></span></a>, <a class="txt" href="#E7:27_3_1_3_1_2"><span class="lab"><font color="Green" title="E30">A34</font></span></a>, <a class="ref" href="ami_1.html#T130" title="AMI_1:th.130">AMI_1:130</a></span>
<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_3_1_3_1_2"><span class="lab"><font color="Green" title="E29">A33</font></span></a>, <a class="txt" href="#E7:27_3_1_3_1_2"><span class="lab"><font color="Green" title="E30">A34</font></span></a>, <a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
<br/>.= 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
;<br/><span class="kw">hence </span><a NAME="E2:27_3_1_3_1_2_4"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c9">n</font></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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_3_1"><span class="lab"><font color="Green" title="E23">A26</font></span></a>, <a class="txt" href="#E1:27_3_1_3_1_2"><span class="lab"><font color="Green" title="E25">A29</font></span></a>, <a class="ref" href="scmfsa_2.html#T124" title="SCMFSA_2:th.124">SCMFSA_2:124</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E9:27_3_1_3_1_2"/><span class="kw">then </span>
not  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T146" title="AMI_1:th.146">AMI_1:146</a></span>;<br/><span class="kw">hence </span><a NAME="E10:27_3_1_3_1_2"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="ami_1.html#D26" title="AMI_1:def.26">AMI_1:def 26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_3_2"><span class="kw">suppose </span></a><a NAME="E1:27_3_2"/><span class="lab"><font color="Green" title="E22">S</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font></span><br/><div class="add"><a NAME="E2:27_3_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A35</font></span>:  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E20">A24</font></span></a>, <a class="txt" href="#E1:27_3_2"><span class="lab"><font color="Green" title="E22">S</font></span></a>, <a class="txt" href="#E15:27"><span class="lab"><font color="Green" title="E21">TX</font></span></a>, <a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E15">A21</font></span></a>, <a class="txt" href="#E10:27"><span class="lab"><font color="Green" title="E16">A22</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
;<br/><a NAME="E4:27_3_2"/><span class="kw">then </span>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T146" title="AMI_1:th.146">AMI_1:146</a></span>;<br/><span class="kw">hence </span><a NAME="E5:27_3_2"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <font color="Maroon" title="c3">i</font></span>)</span>,<font color="Maroon" title="c2">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E20">A24</font></span></a>, <a class="txt" href="#E3:27_3_2"><span class="lab"><font color="Green" title="E23">A35</font></span></a>, <a class="ref" href="ami_1.html#D22" title="AMI_1:def.22">AMI_1:def 22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
