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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="scmfsa6b.html#V2" target="_self">parahalting</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/>





<b>assume </b><a NAME="E1:28"/><i><font color="Green">E21</font></i>: 
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:28"/>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</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="scmfsa_2.html#T84">SCMFSA_2:84</a></i>;<br/>
<a NAME="E3:28"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T86">RELAT_1:86</a></i>;<br/>
<a NAME="E4:28"/><b>then </b><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3" target="_self">IExec</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<a NAME="E5:28"/><i><font color="Green">E23</font></i>: 
 <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E6:28"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T19" target="_self">Th19</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E8:28"/><i><font color="Green">E24</font></i>: 
(  <a href="ami_1.html#K12">Result</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="ami_1.html#D22">AMI_1:def 22</a></i>;<br/>
<a NAME="E9:28"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa6b.html#E5:28"><i><font color="Green">E23</font></i></a>, <a class="ref" href="scmfsa6b.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E10:28"/><b>then </b><i><font color="Green">E26</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font> holds <br/> <a href="ami_1.html#K6">IC</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"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E11:28"/><i><font color="Green">E27</font></i>: 
( not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T48">SCMFSA6A:48</a>, <a class="ref" href="scmfsa_2.html#T66">SCMFSA_2:66</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3" target="_self">IExec</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="scmfsa6b.html#E1:28"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmfsa6b.html#E4:28"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmfsa6b.html#E8:28"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scmfsa6b.html#E9:28"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmfsa6b.html#E10:28"><i><font color="Green">E26</font></i></a>, <a class="ref" href="sf_mastr.html#T69">SF_MASTR:69</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="scmfsa6b.html#E11:28"><i><font color="Green">E27</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/>


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