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<b>let </b><font color="Maroon" title="c1">k</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a> <a href="ami_1.html#V14" title="AMI_1:attr.14">standard-ins</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a> <a href="amistd_2.html#V6" title="AMISTD_2:attr.6">regular</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,<font color="Maroon" title="c2">N</font>;<br/><b>let </b><font color="Maroon" title="c4">g</font> be   <a href="ami_1.html#NM7" title="AMI_1:NM.7">FinPartState</a> of <font color="Maroon" title="c3">S</font>;<br/><b>let </b><font color="Maroon" title="c5">il</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Maroon" title="c3">S</font>;<br/>









<b>assume </b><a NAME="E1:56"/><i><font color="Green" title="E46">A1</font></i>: 
<font color="Maroon" title="c3">S</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c6">I</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <font color="Maroon" title="c3">S</font>;<br/>

<b>assume </b><a NAME="E2:56"/><i><font color="Green" title="E47">A2</font></i>: 
( <font color="Maroon" title="c5">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <font color="Maroon" title="c4">g</font></span>)</span> &amp; <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">il</font> )
 ;<br/>

<a NAME="E3:56"/><i><font color="Green" title="E48">A3</font></i>: 
 <a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <font color="Maroon" title="c4">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">g</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">i</font> being  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E5:56"/><i><font color="Green" title="E49">A4</font></i>: 
<font color="Maroon" title="c5">il</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c7">i</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T26" title="AMISTD_1:th.26">AMISTD_1:26</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">ii</font> = <font color="Maroon" title="c5">il</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E7:56"/>
<font color="Maroon" title="c7">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E8:56"/><b>then </b>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<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="c1">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="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  :  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<font color="Olive" title="b1">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <font color="Maroon" title="c4">g</font></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="txt" href="scmring4.html#E2:56"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="scmring4.html#E5:56"><i><font color="Green" title="E49">A4</font></i></a></i>;<br/>
<a NAME="E9:56"/><b>then </b>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:56"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="scmring4.html#T49" target="_self" title="SCMRING4:th.49">Th49</a></i>;<br/>
<a NAME="E10:56"/><b>then </b><i><font color="Green" title="E50">A5</font></i>: 
<font color="Maroon" title="c5">il</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E5:56"><i><font color="Green" title="E49">A4</font></i></a>, <a class="ref" href="scmring4.html#T2" target="_self" title="SCMRING4:th.2">Th2</a></i>;<br/>
<a NAME="E11:56"/><i><font color="Green" title="E51">A6</font></i>: 
<font color="Maroon" title="c5">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2:56"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="amistd_2.html#D15" title="AMISTD_2:def.15">AMISTD_2:def 15</a></i>;<br/>
<a NAME="E12:56"/><i><font color="Green" title="E52">A7</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="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">il</font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2:56"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="scmring4.html#E3:56"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E13:56"/>
 <a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">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/>
<b>hence </b><span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">il</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">il</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E10:56"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p3">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">il</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E1:56"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="scmring4.html#T48" target="_self" title="SCMRING4:th.48">Th48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">il</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring4.html#T54" target="_self" title="SCMRING4:th.54">Th54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">il</font>
<b>by </b><i><a class="txt" href="scmring4.html#E11:56"><i><font color="Green" title="E51">A6</font></i></a>, <a class="ref" href="scmring4.html#T11" target="_self" title="SCMRING4:th.11">Th11</a></i>
<br/>.= 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">pi</a> <span class="p2">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">ProgramPart</a> <font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c8">ii</font></span>)</span>,<font color="Maroon" title="c1">k</font>
<b>by </b><i><a class="txt" href="scmring4.html#E2:56"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="scmring4.html#T53" target="_self" title="SCMRING4:th.53">Th53</a></i>
<br/>.= 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c1">k</font>
<b>by </b><i><a class="txt" href="scmring4.html#E2:56"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="scmring4.html#E12:56"><i><font color="Green" title="E52">A7</font></i></a>, <a class="ref" href="ami_1.html#D47" title="AMI_1:def.47">AMI_1:def 47</a></i>
;<br/><br/>


</div>
