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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="ami_1.html#M1">FinPartState</a> of  <a href="ami_3.html#K1">SCM</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>





<b>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="E2:28"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="ami_5.html#T19">AMI_5:19</a></i>;<br/>
<a NAME="E3:28"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="reloc.html#E2:28"><i><font color="Green">E27</font></i></a>, <a class="ref" href="reloc.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E4:28"/><i><font color="Green">E29</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> :  <a href="ami_3.html#K16">il.</a> <font color="Olive">b<sub>1</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="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="reloc.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E5:28"/>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88">RELAT_1:88</a></i>;<br/>
<a NAME="E6:28"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:28_1"/>
<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>
 ;<br/><a NAME="E2:28_1"/><b>then </b>
 <a href="ami_3.html#K16">il.</a> <font color="Maroon">c<sub>4</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="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="reloc.html#E2:28"><i><font color="Green">E27</font></i></a>, <a class="ref" href="ami_5.html#T73">AMI_5:73</a></i>;<br/><a NAME="E3:28_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">c<sub>2</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="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="reloc.html#E3:28"><i><font color="Green">E28</font></i></a>, <a class="txt" href="reloc.html#E4:28"><i><font color="Green">E29</font></i></a></i>;<br/><b>hence </b><a NAME="E4:28_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">c<sub>2</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="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="reloc.html#E6:28"><i><font color="Green">E30</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E8:28"/>
<font color="Maroon">c<sub>3</sub></font> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">c<sub>2</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="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>

<a NAME="E9:28"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">c<sub>2</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="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T73">AMI_5:73</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E11:28"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E12:28"/><i><font color="Green">E32</font></i>: 
 <a href="ami_3.html#K16">il.</a> <font color="Maroon">c<sub>5</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="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="reloc.html#E4:28"><i><font color="Green">E29</font></i></a></i>;<br/>
<a NAME="E13:28"/>
 <a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88">RELAT_1:88</a></i>;<br/>
<a NAME="E14:28"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</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="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E15:28"/>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="reloc.html#E3:28"><i><font color="Green">E28</font></i></a>, <a class="txt" href="reloc.html#E11:28"><i><font color="Green">E31</font></i></a></i>;<br/>
<a NAME="E16:28"/><b>then </b>
<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="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="reloc.html#E2:28"><i><font color="Green">E27</font></i></a>, <a class="txt" href="reloc.html#E12:28"><i><font color="Green">E32</font></i></a></i>;<br/>
<b>hence </b><a NAME="E17:28"/>
<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="txt" href="reloc.html#E14:28"><i><font color="Green">E33</font></i></a></i>;<br/>


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