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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</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>3</sub></font> be  <a href="scmfsa6b.html#V2" target="_self">parahalting</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:35"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>3</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>
 <b>and </b><br/><a NAME="E2:35"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>3</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>2</sub></font>
 <b>and </b><br/><a NAME="E3:35"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></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> 
 ;<br/>

<a NAME="E4:35"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa6b.html#E1:35"><i><font color="Green">E26</font></i></a>, <a class="ref" href="scmfsa6b.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E5:35"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa6b.html#E2:35"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scmfsa6b.html#T5" target="_self">Th5</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:35_1"/>
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> <font color="Maroon">c<sub>2</sub></font></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>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa6b.html#E2:35"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scmfsa6b.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E2:35_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></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="txt" href="scmfsa6b.html#E3:35"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmfsa6b.html#E4:35"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmfsa6b.html#E5:35"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa6b.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E3:35_1"/><b>then </b><i><font color="Green">E31</font></i>: 
 <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T29">SCMFSA6A:29</a></i>;<br/><a NAME="E4:35_1"/><i><font color="Green">E32</font></i>: 
 <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa6b.html#E1:35"><i><font color="Green">E26</font></i></a>, <a class="ref" href="scmfsa6b.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E5:35_1"/><i><font color="Green">E33</font></i>: 
 <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> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa6b.html#E2:35"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scmfsa6b.html#D2" target="_self">Def2</a></i>;<br/><b>thus </b> <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa6b.html#E5:35"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmfsa6b.html#E5:35_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa6b.html#E4:35"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmfsa6b.html#E3:35_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6b.html#E4:35_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

;<br/></div>
<b>end;</b></div>


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