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<b>let </b><font color="Maroon" title="c1">s</font> be  <a href="ami_3.html#V1" title="AMI_3:attr.1">programmed</a>  <a href="ami_1.html#M1" title="AMI_1:mode.1">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">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c3">n</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/>





<a NAME="E1:45"/><i><font color="Green" title="E29">A1</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">*</a> <font color="Maroon" title="c1">s</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="c1">s</font>
 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T2" target="_self" title="SCMFSA_4:th.2">Th2</a></i>;<br/>
<a NAME="E2:45"/><i><font color="Green" title="E30">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">*</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K8" title="SCMFSA_4:func.8">Shift</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c3">n</font></span>)</span></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> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" title="SCMFSA_4:func.8">Shift</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c3">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T2" target="_self" title="SCMFSA_4:th.2">Th2</a></i>;<br/>
<a NAME="E3:45"/><i><font color="Green" title="E31">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#K8" title="SCMFSA_4:func.8">Shift</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c3">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#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span> where <font color="Olive" title="b1">m</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">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"><font color="Maroon" title="c2">f</font> <a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">*</a> <font color="Maroon" title="c1">s</font></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:45"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="scmfsa_4.html#D7" target="_self" title="SCMFSA_4:def.7">Def7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">m</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>assume </b><a NAME="E1:45_1"/><i><font color="Green" title="E32">A4</font></i>: 
 <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"><font color="Maroon" title="c2">f</font> <a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">*</a> <font color="Maroon" title="c1">s</font></span>)</span>
 ;<br/><a NAME="E2:45_1"/><b>then </b>
 <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#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">n</font></span>)</span> <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#K8" title="SCMFSA_4:func.8">Shift</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c3">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E3:45"><i><font color="Green" title="E31">A3</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">*</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K8" title="SCMFSA_4:func.8">Shift</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c3">n</font></span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_4.html#K8" title="SCMFSA_4:func.8">Shift</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <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="Maroon" title="c4">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:45"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="scmfsa_4.html#E1:45_1"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="scmfsa_4.html#D7" target="_self" title="SCMFSA_4:def.7">Def7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">*</a> <font color="Maroon" title="c1">s</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="c4">m</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:45"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="scmfsa_4.html#E1:45_1"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:45"/>
 <a href="scmfsa_4.html#K8" title="SCMFSA_4:func.8">Shift</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">*</a> <font color="Maroon" title="c1">s</font></span>)</span>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="scmfsa_4.html#K6" title="SCMFSA_4:func.6">*</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8" title="SCMFSA_4:func.8">Shift</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c3">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E2:45"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="scmfsa_4.html#E3:45"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="scmfsa_4.html#D7" target="_self" title="SCMFSA_4:def.7">Def7</a></i>;<br/>


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