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

<b>set </b><font color="Maroon">SA0</font> =  <a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span>;<br/>
<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="scmfsa6b.html#D4" target="_self">SCMFSA6B:def 4</a><br/>

<b>assume </b><a NAME="E1:54_1_1"/><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font>
 ;<br/>

<a NAME="E2:54_1_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>;<br/>
<a NAME="E3:54_1_1"/>
 <a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E4:54_1_1"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T7" target="_self">Th7</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<i><font color="Green">E52</font></i>: <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T15">FUNCT_4:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#T8" target="_self">Th8</a>, <a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>
;<br/>
<a NAME="E6:54_1_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E7:54_1_1"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 
<b>by </b><i><a class="ref" href="ami_3.html#T34">AMI_3:34</a>, <a class="ref" href="scmfsa_2.html#T81">SCMFSA_2:81</a></i>;<br/>
<a NAME="E8:54_1_1"/><b>then </b>
( not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font> &amp; not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T47">SCMFSA6A:47</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E9:54_1_1"/><b>then </b>
not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E10:54_1_1"/><b>then </b><i><font color="Green">E62</font></i>: 
not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_1_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:54_1_1_2"/>
( <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a> or  not <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_1_1_2_1"><b>suppose </b></a><a NAME="E1:54_1_1_2_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 ;<br/><div class="add"><i><font color="Green">E64</font></i>: <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T15">FUNCT_4:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font>
<b>by </b><i><a class="ref" href="scmfsa6b.html#T8" target="_self">Th8</a>, <a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>
;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_1_1_2_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:54_1_1_2_1_2_1"/>
( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_1_1_2_1_2_1_1"><b>suppose </b></a><a NAME="E1:54_1_1_2_1_2_1_1"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><i><font color="Green">E66</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#T10" target="_self">Th10</a>, </i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/><a NAME="E3:54_1_1_2_1_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa6b.html#T13" target="_self">Th13</a>, , </i>;<br/><b>hence </b><a NAME="E4:54_1_1_2_1_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6b.html#E4:54_1_1"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa6a.html#T30">SCMFSA6A:30</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_1_1_2_1_2_1_2"><b>suppose </b></a><a NAME="E1:54_1_1_2_1_2_1_2"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>set </b><font color="Maroon">LS</font> =  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>;<br/><b>consider </b><font color="Maroon">p</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:54_1_1_2_1_2_1_2"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">p</font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> )
 <b>by </b><i>, <a class="ref" href="fsm_1.html#T1">FSM_1:1</a></i>;<br/><b>consider </b><font color="Maroon">r</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:54_1_1_2_1_2_1_2"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 1 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/><b>reconsider </b><font color="Maroon">r</font> = <font color="Maroon">r</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/><a NAME="E7:54_1_1_2_1_2_1_2"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="ami_3.html#T34">AMI_3:34</a>, <a class="ref" href="scmfsa_2.html#T81">SCMFSA_2:81</a></i>;<br/><a NAME="E8:54_1_1_2_1_2_1_2"/><b>then </b>
( not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">J</font> &amp; not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T47">SCMFSA6A:47</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E9:54_1_1_2_1_2_1_2"/><b>then </b>
not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">J</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E10:54_1_1_2_1_2_1_2"/><b>then </b><i><font color="Green">E76</font></i>: 
not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/><a NAME="E11:54_1_1_2_1_2_1_2"/>
<font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/><b>then </b><i><font color="Green">E77</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">r</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#T13" target="_self">Th13</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#T10" target="_self">Th10</a>, </i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/><b>set </b><font color="Maroon">Rr</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">r</font>;<br/><b>set </b><font color="Maroon">Sr</font> =  <a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span>;<br/><a NAME="E13:54_1_1_2_1_2_1_2"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="ami_3.html#T34">AMI_3:34</a>, <a class="ref" href="scmfsa_2.html#T81">SCMFSA_2:81</a></i>;<br/><a NAME="E14:54_1_1_2_1_2_1_2"/><b>then </b>
not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E15:54_1_1_2_1_2_1_2"/><b>then </b><i><font color="Green">E78</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">r</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">r</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><a NAME="E16:54_1_1_2_1_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">r</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">r</font></span>)</span> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa6b.html#T7" target="_self">Th7</a>, <a class="ref" href="scmfsa6b.html#T9" target="_self">Th9</a>, <a class="ref" href="scmfsa6b.html#T13" target="_self">Th13</a>, <a class="ref" href="scmfsa6b.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa6b.html#T6" target="_self">Th6</a></i>;<br/><b>hence </b><a NAME="E17:54_1_1_2_1_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6b.html#E4:54_1_1"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="scmfsa6b.html#T16" target="_self">Th16</a>, <a class="txt" href="scmfsa6b.html#E5:54_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmfsa6b.html#E6:54_1_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scmfsa6a.html#T30">SCMFSA6A:30</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_1_1_2_2"><b>suppose </b></a><a NAME="E1:54_1_1_2_2"/><i><font color="Green">E79</font></i>: 
not <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 ;<br/><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E2:54_1_1_2_2"/>
<font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/><b>then </b><i><font color="Green">E80</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/><a NAME="E4:54_1_1_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">J</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa6b.html#T13" target="_self">Th13</a>, <a class="ref" href="scmfsa6b.html#T5" target="_self">Th5</a></i>;<br/><b>hence </b><a NAME="E5:54_1_1_2_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6b.html#E4:54_1_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmfsa6b.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa6a.html#T30">SCMFSA6A:30</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
