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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">p</font> be  <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>



<a NAME="E1:48"/><i><font color="Green">E27</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E2:48"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a></i>;<br/>
<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="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span> = 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> </span>}</span> 
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:48"><i><font color="Green">E27</font></i></a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:48"><i><font color="Green">E27</font></i></a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:48_2"/><i><font color="Green">E31</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">j</font></span>)</span> <a href="tarski.html#R1">c=</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="ami_3.html#D13">AMI_3:def 13</a></i>;<br/><b>assume </b><a NAME="E2:48_2"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">j</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <b>by </b><i><a class="txt" href="scmfsa_4.html#E1:48_2"><i><font color="Green">E31</font></i></a></i>;<br/><a NAME="E4:48_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> </span>}</span> 
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E2:48_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa_4.html#E1:48"><i><font color="Green">E27</font></i></a></i>;<br/><b>then consider </b><font color="Maroon">m</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="E6:48_2"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span> &amp;  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> )
 ;<br/><a NAME="E7:48_2"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font></span>)</span> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">j</font>
 <b>by </b><i>, </i>;<br/><a NAME="E8:48_2"/><i><font color="Green">E79</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E9:48_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><font color="Olive">mm</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span> where <font color="Olive">mm</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">mm</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E1:48"><i><font color="Green">E27</font></i></a></i>;<br/><a NAME="E10:48_2"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">x'</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmfsa_4.html#T2" target="_self">Th2</a></i>;<br/><i><font color="Green">E87</font></i>:  <a href="ami_5.html#K5">pi</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font></span>)</span> = 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T2" target="_self">Th2</a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font></span>)</span> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T2" target="_self">Th2</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span>,<font color="Maroon">x'</font>
<b>by </b><i>, , <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">j</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span>,<font color="Maroon">x'</font></span>)</span>,<font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T2" target="_self">Th2</a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:48"/>
 <a href="scmfsa_4.html#K8" target="_self">Shift</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <font color="Maroon">p</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">j</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_4.html#K7" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" target="_self">Shift</a> <font color="Maroon">p</font>,<font color="Maroon">j</font></span>)</span>,<font color="Maroon">i</font>
 <b>by </b><i>, <a class="txt" href="scmfsa_4.html#E3:48"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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