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<b>let </b><font color="Maroon" title="c1">p</font> be   <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="c2">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">l</font> be    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>





<b>consider </b><font color="Maroon" title="c4">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E2:5"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c4">m</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a></i>;<br/>
<a NAME="E3:5"/><i><font color="Green" title="E7">A2</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</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="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E2:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="scmfsa_4.html#D1" title="SCMFSA_4:def.1">SCMFSA_4:def 1</a></i>;<br/>
<a NAME="E4:5"/><i><font color="Green" title="E8">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</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="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></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">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span> where <font color="Olive" title="b1">j</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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">j</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="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="scmfsa_5.html#T3" target="_self" title="SCMFSA_5:th.3">Th3</a></i>;<br/>
<a NAME="E5:5"/>
 <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="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></i>;<br/>
<a NAME="E6:5"/><b>then </b><i><font color="Green" title="E9">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</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="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:5_1"/>
<font color="Maroon" title="c3">l</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> <font color="Maroon" title="c1">p</font>
 ;<br/><a NAME="E2:5_1"/><b>then </b>
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c4">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="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E2:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="ami_1.html#T106" title="AMI_1:th.106">AMI_1:106</a></i>;<br/><a NAME="E3:5_1"/><b>then </b>
<font color="Maroon" title="c3">l</font> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</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="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="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E3:5"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="scmfsa_5.html#E4:5"><i><font color="Green" title="E8">A3</font></i></a></i>;<br/><b>hence </b><a NAME="E4:5_1"/>
<font color="Maroon" title="c3">l</font> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</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_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E6:5"><i><font color="Green" title="E9">A4</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E8:5"/>
<font color="Maroon" title="c3">l</font> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</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_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span>
 ;<br/>

<a NAME="E9:5"/><b>then </b>
<font color="Maroon" title="c3">l</font> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</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="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="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T106" title="AMI_1:th.106">AMI_1:106</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">j</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E11:5"/><i><font color="Green" title="E10">A5</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</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="c5">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
 <b>and </b><br/><a NAME="E12:5"/><i><font color="Green" title="E11">A6</font></i>: 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c5">j</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="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E4:5"><i><font color="Green" title="E8">A3</font></i></a></i>;<br/>
<a NAME="E13:5"/>
 <a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></i>;<br/>
<a NAME="E14:5"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<b>hence </b><a NAME="E15:5"/>
<font color="Maroon" title="c3">l</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> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E2:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="scmfsa_5.html#E3:5"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="scmfsa_5.html#E11:5"><i><font color="Green" title="E10">A5</font></i></a>, <a class="txt" href="scmfsa_5.html#E12:5"><i><font color="Green" title="E11">A6</font></i></a></i>;<br/>


</div>
