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<b>let </b><font color="Maroon" title="c3">I</font> be  <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c4">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c5">a</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/>





<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c3">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c5">a</font>
 ;<br/>

<i><font color="Green" title="E20">A2</font></i>:  <a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> = 
 <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">Shift</a> <span class="p2">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <font color="Maroon" title="c3">I</font></span>)</span>,<font color="Maroon" title="c4">n</font></span>)</span>,<font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="ref" href="scmfsa_5.html#T2" title="SCMFSA_5:th.2">SCMFSA_5:2</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">Shift</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>,<font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="ref" href="ami_1.html#T105" title="AMI_1:th.105">AMI_1:105</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">Shift</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>,<font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T35" title="SCMFSA_4:th.35">SCMFSA_4:35</a></i>
;<br/>
<a NAME="E3:21"/><i><font color="Green" title="E21">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">I</font>
 
<b>by </b><i><a class="ref" href="scmfsa_4.html#D6" title="SCMFSA_4:def.6">SCMFSA_4:def 6</a></i>;<br/>
<a NAME="E4:21"/><i><font color="Green" title="E22">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">Shift</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  :  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="scmfsa_4.html#D7" title="SCMFSA_4:def.7">SCMFSA_4:def 7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">i</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>assume </b><a NAME="E1:21_2"/>
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:21_2"/><i><font color="Green" title="E23">A5</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">Shift</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>,<font color="Maroon" title="c4">n</font></span>)</span>
 <b>and </b><br/><a NAME="E4:21_2"/><i><font color="Green" title="E24">A6</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">Shift</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
 <b>by </b><i><a class="txt" href="scmfsa8a.html#E2:21"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><b>consider </b><font color="Maroon" title="c8">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E6:21_2"/><i><font color="Green" title="E25">A7</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c4">n</font></span>)</span>
 <b>and </b><br/><a NAME="E7:21_2"/><i><font color="Green" title="E26">A8</font></i>: 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c8">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8a.html#E4:21"><i><font color="Green" title="E22">A4</font></i></a>, <a class="txt" href="scmfsa8a.html#E3:21_2"><i><font color="Green" title="E23">A5</font></i></a></i>;<br/><a NAME="E8:21_2"/><i><font color="Green" title="E27">A9</font></i>: 
<font color="Maroon" title="c3">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c8">m</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">I</font>
 <b>by </b><i><a class="txt" href="scmfsa8a.html#E3:21"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="scmfsa8a.html#E7:21_2"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E9:21_2"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#T118" title="AMI_1:th.118">AMI_1:118</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c9">ii</font> = <font color="Maroon" title="c3">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c8">m</font></span>)</span> as   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <b>by </b><i><a class="txt" href="scmfsa8a.html#E8:21_2"><i><font color="Green" title="E27">A9</font></i></a></i>;<br/><a NAME="E11:21_2"/><i><font color="Green" title="E28">A10</font></i>: 
<font color="Maroon" title="c9">ii</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">does_not_destroy</a> <font color="Maroon" title="c5">a</font>
 <b>by </b><i><a class="txt" href="scmfsa8a.html#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scmfsa8a.html#E8:21_2"><i><font color="Green" title="E27">A9</font></i></a>, <a class="ref" href="scmfsa7b.html#D4" title="SCMFSA7B:def.4">SCMFSA7B:def 4</a></i>;<br/><font color="Maroon" title="c6">i</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_4.html#K5" title="SCMFSA_4:func.5">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c8">m</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8a.html#E4:21_2"><i><font color="Green" title="E24">A6</font></i></a>, <a class="txt" href="scmfsa8a.html#E6:21_2"><i><font color="Green" title="E25">A7</font></i></a>, <a class="txt" href="scmfsa8a.html#E7:21_2"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="scmfsa_4.html#D7" title="SCMFSA_4:def.7">SCMFSA_4:def 7</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K30" title="AMI_1:func.30">pi</a> <font color="Maroon" title="c3">I</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c8">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="txt" href="scmfsa8a.html#E3:21"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="scmfsa8a.html#E7:21_2"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="scmfsa_4.html#D6" title="SCMFSA_4:def.6">SCMFSA_4:def 6</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K3" title="SCMFSA_4:func.3">IncAddr</a> <font color="Maroon" title="c9">ii</font>,<font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="txt" href="scmfsa8a.html#E3:21"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="scmfsa8a.html#E7:21_2"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
;<br/><b>hence </b><a NAME="E13:21_2"/>
<font color="Maroon" title="c6">i</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">does_not_destroy</a> <font color="Maroon" title="c5">a</font>
 <b>by </b><i><a class="txt" href="scmfsa8a.html#E11:21_2"><i><font color="Green" title="E28">A10</font></i></a>, <a class="ref" href="scmfsa8a.html#T22" target="_self" title="SCMFSA8A:th.22">Th22</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:21"/>
 <a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c5">a</font>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#D4" title="SCMFSA7B:def.4">SCMFSA7B:def 4</a></i>;<br/>


</div>
